what are graphical representation of data

Graphical Representation of Data

Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables. Graphical representation of data is done through different mediums such as lines, plots, diagrams, etc. Let us learn more about this interesting concept of graphical representation of data, the different types, and solve a few examples.

Definition of Graphical Representation of Data

A graphical representation is a visual representation of data statistics-based results using graphs, plots, and charts. This kind of representation is more effective in understanding and comparing data than seen in a tabular form. Graphical representation helps to qualify, sort, and present data in a method that is simple to understand for a larger audience. Graphs enable in studying the cause and effect relationship between two variables through both time series and frequency distribution. The data that is obtained from different surveying is infused into a graphical representation by the use of some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. This visual representation helps in clarity, comparison, and understanding of numerical data.

Representation of Data

The word data is from the Latin word Datum, which means something given. The numerical figures collected through a survey are called data and can be represented in two forms - tabular form and visual form through graphs. Once the data is collected through constant observations, it is arranged, summarized, and classified to finally represented in the form of a graph. There are two kinds of data - quantitative and qualitative. Quantitative data is more structured, continuous, and discrete with statistical data whereas qualitative is unstructured where the data cannot be analyzed.

Principles of Graphical Representation of Data

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin. On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value. When -axis and y-axis intersect each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV. This form of representation is seen in a frequency distribution that is represented in four methods, namely Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

Advantages and Disadvantages of Graphical Representation of Data

Listed below are some advantages and disadvantages of using a graphical representation of data:

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.
• It is mainly used in statistics to determine the mean, median, and mode for different data

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represent it graphically.

Rules of Graphical Representation of Data

While presenting data graphically, there are certain rules that need to be followed. They are listed below:

• Suitable Title: The title of the graph should be appropriate that indicate the subject of the presentation.
• Measurement Unit: The measurement unit in the graph should be mentioned.
• Proper Scale: A proper scale needs to be chosen to represent the data accurately.
• Index: For better understanding, index the appropriate colors, shades, lines, designs in the graphs.
• Data Sources: Data should be included wherever it is necessary at the bottom of the graph.
• Simple: The construction of a graph should be easily understood.
• Neat: The graph should be visually neat in terms of size and font to read the data accurately.

Uses of Graphical Representation of Data

The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data. It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision. The visual display of data also helps in avoiding confusion and overlapping of any information. Graphs like line graphs and bar graphs, display two or more data clearly for easy comparison. This is important in communicating our findings to others and our understanding and analysis of the data.

Types of Graphical Representation of Data

Data is represented in different types of graphs such as plots, pies, diagrams, etc. They are as follows,

Related Topics

Listed below are a few interesting topics that are related to the graphical representation of data, take a look.

• x and y graph
• Frequency Polygon
• Cumulative Frequency

Examples on Graphical Representation of Data

Example 1 : A pie chart is divided into 3 parts with the angles measuring as 2x, 8x, and 10x respectively. Find the value of x in degrees.

We know, the sum of all angles in a pie chart would give 360º as result. ⇒ 2x + 8x + 10x = 360º ⇒ 20 x = 360º ⇒ x = 360º/20 ⇒ x = 18º Therefore, the value of x is 18º.

Example 2: Ben is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions? i) What is the mode of the plot? ii) What is the mean of the plot? iii) Find the range.

Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.

Hence, mode = 54

ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958

To find the mean, we have to divide the sum by the total number of values.

Mean = Sum of all data values ÷ 19 = 958 ÷ 19 = 50.42

iii) Range = the highest value - the lowest value = 91 - 12 = 79

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Practice Questions on Graphical Representation of Data

Faqs on graphical representation of data, what is graphical representation.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

• Stem and leaf plot
• Scatter diagrams
• Frequency Distribution

Is the Graphical Representation of Numerical Data?

Yes, these graphical representations are numerical data that has been accumulated through various surveys and observations. The method of presenting these numerical data is called a chart. There are different kinds of charts such as a pie chart, bar graph, line graph, etc, that help in clearly showcasing the data.

What is the Use of Graphical Representation of Data?

Graphical representation of data is useful in clarifying, interpreting, and analyzing data plotting points and drawing line segments , surfaces, and other geometric forms or symbols.

What are the Ways to Represent Data?

Tables, charts, and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organization, and analysis of data as part of the process of a scientific study.

What is the Objective of Graphical Representation of Data?

The main objective of representing data graphically is to display information visually that helps in understanding the information efficiently, clearly, and accurately. This is important to communicate the findings as well as analyze the data.

• Math Article

Graphical Representation

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ideas, information and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

• Line Graphs – Line graph or the linear graph is used to display the continuous data and it is useful for predicting future events over time.
• Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.
• Histograms – The graph that uses bars to represent the frequency of numerical data that are organised into intervals. Since all the intervals are equal and continuous, all the bars have the same width.
• Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.
• Frequency Table – The table shows the number of pieces of data that falls within the given interval.
• Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered with 100% and the categories occupied is represented with that specific percentage like 15%, 56%, etc.
• Stem and Leaf Plot – In the stem and leaf plot, the data are organised from least value to the greatest value. The digits of the least place values from the leaves and the next place value digit forms the stems.
• Box and Whisker Plot – The plot diagram summarises the data by dividing into four parts. Box and whisker show the range (spread) and the middle ( median) of the data.

General Rules for Graphical Representation of Data

There are certain rules to effectively present the information in the graphical representation. They are:

• Suitable Title: Make sure that the appropriate title is given to the graph which indicates the subject of the presentation.
• Measurement Unit: Mention the measurement unit in the graph.
• Proper Scale: To represent the data in an accurate manner, choose a proper scale.
• Index: Index the appropriate colours, shades, lines, design in the graphs for better understanding.
• Data Sources: Include the source of information wherever it is necessary at the bottom of the graph.
• Keep it Simple: Construct a graph in an easy way that everyone can understand.
• Neat: Choose the correct size, fonts, colours etc in such a way that the graph should be a visual aid for the presentation of information.

Graphical Representation in Maths

In Mathematics, a graph is defined as a chart with statistical data, which are represented in the form of curves or lines drawn across the coordinate point plotted on its surface. It helps to study the relationship between two variables where it helps to measure the change in the variable amount with respect to another variable within a given interval of time. It helps to study the series distribution and frequency distribution for a given problem.  There are two types of graphs to visually depict the information. They are:

• Time Series Graphs – Example: Line Graph
• Frequency Distribution Graphs – Example: Frequency Polygon Graph

Principles of Graphical Representation

Algebraic principles are applied to all types of graphical representation of data. In graphs, it is represented using two lines called coordinate axes. The horizontal axis is denoted as the x-axis and the vertical axis is denoted as the y-axis. The point at which two lines intersect is called an origin ‘O’. Consider x-axis, the distance from the origin to the right side will take a positive value and the distance from the origin to the left side will take a negative value. Similarly, for the y-axis, the points above the origin will take a positive value, and the points below the origin will a negative value.

Generally, the frequency distribution is represented in four methods, namely

• Smoothed frequency graph
• Pie diagram
• Cumulative or ogive frequency graph
• Frequency Polygon

Merits of Using Graphs

Some of the merits of using graphs are as follows:

• The graph is easily understood by everyone without any prior knowledge.
• It saves time
• It allows us to relate and compare the data for different time periods
• It is used in statistics to determine the mean, median and mode for different data, as well as in the interpolation and the extrapolation of data.

Example for Frequency polygonGraph

Here are the steps to follow to find the frequency distribution of a frequency polygon and it is represented in a graphical way.

• Obtain the frequency distribution and find the midpoints of each class interval.
• Represent the midpoints along x-axis and frequencies along the y-axis.
• Plot the points corresponding to the frequency at each midpoint.
• Join these points, using lines in order.
• To complete the polygon, join the point at each end immediately to the lower or higher class marks on the x-axis.

Draw the frequency polygon for the following data

Mark the class interval along x-axis and frequencies along the y-axis.

Let assume that class interval 0-10 with frequency zero and 90-100 with frequency zero.

Now calculate the midpoint of the class interval.

Using the midpoint and the frequency value from the above table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

To obtain the frequency polygon ABCDEFGHIJ, draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ, and connect all the points.

Frequently Asked Questions

What are the different types of graphical representation.

Some of the various types of graphical representation include:

• Line Graphs
• Frequency Table
• Circle Graph, etc.

Read More:  Types of Graphs

What are the Advantages of Graphical Method?

Some of the advantages of graphical representation are:

• It makes data more easily understandable.
• It saves time.
• It makes the comparison of data more efficient.

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Very useful for understand the basic concepts in simple and easy way. Its very useful to all students whether they are school students or college sudents

Thanks very much for the information

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2.1: Introduction

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Learning Objectives

By the end of this chapter, the student should be able to:

• Display data graphically and interpret graphs: stemplots, bar charts, frequency polygons, histograms, etc.

Once you have collected data, what will you do with it? Data can be described and presented in many different formats. For example, suppose you want to find a change in temperature in a particular city over time. Looking at all the raw data can be confusing and overwhelming. A better way to look at that data would be to create a graph that displays the data in a visual manner. Then patterns can more easily be discerned.

In this chapter, you will study graphical ways to describe and display your data. You will learn to create, and more importantly, interpret a variety of graph types, and you will learn when to use each type of graph.

A statistical graph is a tool that helps you learn about the shape or distribution of a sample or a population. A graph can be a more effective way of presenting data than a mass of numbers because we can see where data clusters and where there are only a few data values. Newspapers and the Internet use graphs to show trends and to enable readers to compare facts and figures quickly. Statisticians often graph data first to get a picture of the data. Then, more formal tools may be applied.

Some of the types of graphs that are used to summarize and organize data are the dot plot, the bar graph, the histogram, the stem-and-leaf plot, the frequency polygon (a type of broken line graph), the pie chart, and the box plot. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs.

This book contains instructions for constructing some graph types using Excel.

Contributors and Attributions

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .

What Is Data Visualization: Brief Theory, Useful Tips and Awesome Examples

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By Al Boicheva

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Updated: June 23, 2022

To create data visualization in order to present your data is no longer just a nice to have skill. Now, the skill to effectively sort and communicate your data through charts is a must-have for any business in any field that deals with data. Data visualization helps businesses quickly make sense of complex data and start making decisions based on that data. This is why today we’ll talk about what is data visualization. We’ll discuss how and why does it work, what type of charts to choose in what cases, how to create effective charts, and, of course, end with beautiful examples.

So let’s jump right in. As usual, don’t hesitate to fast-travel to a particular section of your interest.

Article overview: 1. What Does Data Visualization Mean? 2. How Does it Work? 3. When to Use it? 4. Why Use it? 5. Types of Data Visualization 6. Data Visualization VS Infographics: 5 Main Differences 7. How to Create Effective Data Visualization?: 5 Useful Tips 8. Examples of Data Visualization

1. What is Data Visualization?

Data Visualization is a graphic representation of data that aims to communicate numerous heavy data in an efficient way that is easier to grasp and understand . In a way, data visualization is the mapping between the original data and graphic elements that determine how the attributes of these elements vary. The visualization is usually made by the use of charts, lines, or points, bars, and maps.

• Data Viz is a branch of Descriptive statistics but it requires both design, computer, and statistical skills.
• Aesthetics and functionality go hand in hand to communicate complex statistics in an intuitive way.
• Data Viz tools and technologies are essential for making data-driven decisions.
• It’s a fine balance between form and functionality.
• Every STEM field benefits from understanding data.

2. How Does it Work?

If we can see it, our brains can internalize and reflect on it. This is why it’s much easier and more effective to make sense of a chart and see trends than to read a massive document that would take a lot of time and focus to rationalize. We wouldn’t want to repeat the cliche that humans are visual creatures, but it’s a fact that visualization is much more effective and comprehensive.

In a way, we can say that data Viz is a form of storytelling with the purpose to help us make decisions based on data. Such data might include:

• Tracking sales
• Identifying trends
• Identifying changes
• Monitoring goals
• Monitoring results
• Combining data

3. When to Use it?

Data visualization is useful for companies that deal with lots of data on a daily basis. It’s essential to have your data and trends instantly visible. Better than scrolling through colossal spreadsheets. When the trends stand out instantly this also helps your clients or viewers to understand them instead of getting lost in the clutter of numbers.

With that being said, Data Viz is suitable for:

• Annual reports
• Presentations
• Social media micronarratives
• Informational brochures
• Trend-trafficking
• Candlestick chart for financial analysis
• Determining routes

Common cases when data visualization sees use are in sales, marketing, healthcare, science, finances, politics, and logistics.

4. Why Use it?

Short answer: decision making. Data Visualization comes with the undeniable benefits of quickly recognizing patterns and interpret data. More specifically, it is an invaluable tool to determine the following cases.

• Identifying correlations between the relationship of variables.
• Getting market insights about audience behavior.
• Determining value vs risk metrics.
• Monitoring trends over time.
• Examining rates and potential through frequency.
• Ability to react to changes.

5. Types of Data Visualization

As you probably already guessed, Data Viz is much more than simple pie charts and graphs styled in a visually appealing way. The methods that this branch uses to visualize statistics include a series of effective types.

Map visualization is a great method to analyze and display geographically related information and present it accurately via maps. This intuitive way aims to distribute data by region. Since maps can be 2D or 3D, static or dynamic, there are numerous combinations one can use in order to create a Data Viz map.

COVID-19 Spending Data Visualization POGO by George Railean

The most common ones, however, are:

• Regional Maps: Classic maps that display countries, cities, or districts. They often represent data in different colors for different characteristics in each region.
• Line Maps: They usually contain space and time and are ideal for routing, especially for driving or taxi routes in the area due to their analysis of specific scenes.
• Point Maps: These maps distribute data of geographic information. They are ideal for businesses to pinpoint the exact locations of their buildings in a region.
• Heat Maps: They indicate the weight of a geographical area based on a specific property. For example, a heat map may distribute the saturation of infected people by area.

Charts present data in the form of graphs, diagrams, and tables. They are often confused with graphs since graphs are indeed a subcategory of charts. However, there is a small difference: graphs show the mathematical relationship between groups of data and is only one of the chart methods to represent data.

Infographic Data Visualization by Madeline VanRemmen

With that out of the way, let’s talk about the most basic types of charts in data visualization.

They use a series of bars that illustrate data development.  They are ideal for lighter data and follow trends of no more than three variables or else, the bars become cluttered and hard to comprehend. Ideal for year-on-year comparisons and monthly breakdowns.

These familiar circular graphs divide data into portions. The bigger the slice, the bigger the portion. They are ideal for depicting sections of a whole and their sum must always be 100%. Avoid pie charts when you need to show data development over time or lack a value for any of the portions. Doughnut charts have the same use as pie charts.

They use a line or more than one lines that show development over time. It allows tracking multiple variables at the same time. A great example is tracking product sales by a brand over the years. Area charts have the same use as line charts.

Scatter Plot

These charts allow you to see patterns through data visualization. They have an x-axis and a y-axis for two different values. For example, if your x-axis contains information about car prices while the y-axis is about salaries, the positive or negative relationship will tell you about what a person’s car tells about their salary.

Unlike the charts we just discussed, tables show data in almost a raw format. They are ideal when your data is hard to present visually and aim to show specific numerical data that one is supposed to read rather than visualize.

Data Visualisation | To bee or not to bee by Aishwarya Anand Singh

For example, charts are perfect to display data about a particular illness over a time period in a particular area, but a table comes to better use when you also need to understand specifics such as causes, outcomes, relapses, a period of treatment, and so on.

6. Data Visualization VS Infographics

5 main differences.

They are not that different as both visually represent data. It is often you search for infographics and find images titled Data Visualization and the other way around. In many cases, however, these titles aren’t misleading. Why is that?

• Data visualization is made of just one element. It could be a map, a chart, or a table. Infographics , on the other hand, often include multiple Data Viz elements.
• Unlike data visualizations that can be simple or extremely complex and heavy, infographics are simple and target wider audiences. The latter is usually comprehensible even to people outside of the field of research the infographic represents.
• Interestingly enough, data Viz doesn’t offer narratives and conclusions, it’s a tool and basis for reaching those. While infographics, in most cases offer a story and a narrative. For example, a data visualization map may have the title “Air pollution saturation by region”, while an infographic with the same data would go “Areas A and B are the most polluted in Country C”.
• Data visualizations can be made in Excel or use other tools that automatically generate the design unless they are set for presentation or publishing. The aesthetics of infographics , however, are of great importance and the designs must be appealing to wider audiences.
• In terms of interaction, data visualizations often offer interactive charts, especially in an online form. Infographics, on the other hand, rarely have interaction and are usually static images.

While on topic, you could also be interested to check out these 50 engaging infographic examples that make complex data look great.

7. Tips to Create Effective Data Visualization

The process is naturally similar to creating Infographics and it revolves around understanding your data and audience. To be more precise, these are the main steps and best practices when it comes to preparing an effective visualization of data for your viewers to instantly understand.

1. Do Your Homework

Preparation is half the work already done. Before you even start visualizing data, you have to be sure you understand that data to the last detail.

Knowing your audience is undeniable another important part of the homework, as different audiences process information differently. Who are the people you’re visualizing data for? How do they process visual data? Is it enough to hand them a single pie chart or you’ll need a more in-depth visual report?

The third part of preparing is to determine exactly what you want to communicate to the audience. What kind of information you’re visualizing and does it reflect your goal?

And last, think about how much data you’ll be working with and take it into account.

2. Choose the Right Type of Chart

In a previous section, we listed the basic chart types that find use in data visualization. To determine best which one suits your work, there are a few things to consider.

• How many variables will you have in a chart?
• How many items will you place for each of your variables?
• What will be the relation between the values (time period, comparison, distributions, etc.)

With that being said, a pie chart would be ideal if you need to present what portions of a whole takes each item. For example, you can use it to showcase what percent of the market share takes a particular product. Pie charts, however, are unsuitable for distributions, comparisons, and following trends through time periods. Bar graphs, scatter plots,s and line graphs are much more effective in those cases.

Another example is how to use time in your charts. It’s way more accurate to use a horizontal axis because time should run left to right. It’s way more visually intuitive.

3. Sort your Data

Start with removing every piece of data that does not add value and is basically excess for the chart. Sometimes, you have to work with a huge amount of data which will inevitably make your chart pretty complex and hard to read. Don’t hesitate to split your information into two or more charts. If that won’t work for you, you could use highlights or change the entire type of chart with something that would fit better.

Tip: When you use bar charts and columns for comparison, sort the information in an ascending or a descending way by value instead of alphabetical order.

4. Use Colors to Your Advantage

In every form of visualization, colors are your best friend and the most powerful tool. They create contrasts, accents, and emphasis and lead the eye intuitively. Even here, color theory is important.

When you design your chart, make sure you don’t use more than 5 or 6 colors. Anything more than that will make your graph overwhelming and hard to read for your viewers. However, color intensity is a different thing that you can use to your advantage. For example, when you compare the same concept in different periods of time, you could sort your data from the lightest shade of your chosen color to its darker one. It creates a strong visual progression, proper to your timeline.

Things to consider when you choose colors:

• Different colors for different categories.
• A consistent color palette for all charts in a series that you will later compare.
• It’s appropriate to use color blind-friendly palettes.

5. Get Inspired

Always put your inspiration to work when you want to be at the top of your game. Look through examples, infographics, and other people’s work and see what works best for each type of data you need to implement.

This Twitter account Data Visualization Society is a great way to start. In the meantime, we’ll also handpick some amazing examples that will get you in the mood to start creating the visuals for your data.

8. Examples for Data Visualization

As another art form, Data Viz is a fertile ground for some amazing well-designed graphs that prove that data is beautiful. Now let’s check out some.

Dark Souls III Experience Data

We start with Meng Hsiao Wei’s personal project presenting his experience with playing Dark Souls 3. It’s a perfect example that infographics and data visualization are tools for personal designs as well. The research is pretty massive yet very professionally sorted into different types of charts for the different concepts. All data visualizations are made with the same color palette and look great in infographics.

My dark souls 3 playing data by Meng Hsiao Wei

Greatest Movies of all Time

Katie Silver has compiled a list of the 100 greatest movies of all time based on critics and crowd reviews. The visualization shows key data points for every movie such as year of release, oscar nominations and wins, budget, gross, IMDB score, genre, filming location, setting of the film, and production studio. All movies are ordered by the release date.

100 Greatest Movies Data Visualization by Katie Silver

The Most Violent Cities

Federica Fragapane shows data for the 50 most violent cities in the world in 2017. The items are arranged on a vertical axis based on population and ordered along the horizontal axis according to the homicide rate.

The Most Violent Cities by Federica Fragapane

Family Businesses as Data

These data visualizations and illustrations were made by Valerio Pellegrini for Perspectives Magazine. They show a pie chart with sector breakdown as well as a scatter plot for contribution for employment.

PERSPECTIVES MAGAZINE – Family Businesses by Valerio Pellegrini

Orbit Map of the Solar System

The map shows data on the orbits of more than 18000 asteroids in the solar system. Each asteroid is shown at its position on New Years’ Eve 1999, colored by type of asteroid.

An Orbit Map of the Solar System by Eleanor Lutz

The Semantics Of Headlines

Katja Flükiger has a take on how headlines tell the story. The data visualization aims to communicate how much is the selling influencing the telling. The project was completed at Maryland Institute College of Art to visualize references to immigration and color-coding the value judgments implied by word choice and context.

The Semantics of Headlines by Katja Flükiger

Moon and Earthquakes

This data visualization works on answering whether the moon is responsible for earthquakes. The chart features the time and intensity of earthquakes in response to the phase and orbit location of the moon.

Moon and Earthquakes by Aishwarya Anand Singh

Dawn of the Nanosats

The visualization shows the satellites launched from 2003 to 2015. The graph represents the type of institutions focused on projects as well as the nations that financed them. On the left, it is shown the number of launches per year and satellite applications.

WIRED UK – Dawn of the by Nanosats by Valerio Pellegrini

Final Words

Data visualization is not only a form of science but also a form of art. Its purpose is to help businesses in any field quickly make sense of complex data and start making decisions based on that data. To make your graphs efficient and easy to read, it’s all about knowing your data and audience. This way you’ll be able to choose the right type of chart and use visual techniques to your advantage.

You may also be interested in some of these related articles:

• Infographics for Marketing: How to Grab and Hold the Attention
• 12 Animated Infographics That Will Engage Your Mind from Start to Finish
• 50 Engaging Infographic Examples That Make Complex Ideas Look Great
• Good Color Combinations That Go Beyond Trends: Inspirational Examples and Ideas

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Al Boicheva

Al is an illustrator at GraphicMama with out-of-the-box thinking and a passion for anything creative. In her free time, you will see her drooling over tattoo art, Manga, and horror movies.

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Data visualization is the representation of data through use of common graphics, such as charts, plots, infographics and even animations. These visual displays of information communicate complex data relationships and data-driven insights in a way that is easy to understand.

Data visualization can be utilized for a variety of purposes, and it’s important to note that is not only reserved for use by data teams. Management also leverages it to convey organizational structure and hierarchy while data analysts and data scientists use it to discover and explain patterns and trends.  Harvard Business Review  (link resides outside ibm.com) categorizes data visualization into four key purposes: idea generation, idea illustration, visual discovery, and everyday dataviz. We’ll delve deeper into these below:

Idea generation

Data visualization is commonly used to spur idea generation across teams. They are frequently leveraged during brainstorming or  Design Thinking  sessions at the start of a project by supporting the collection of different perspectives and highlighting the common concerns of the collective. While these visualizations are usually unpolished and unrefined, they help set the foundation within the project to ensure that the team is aligned on the problem that they’re looking to address for key stakeholders.

Idea illustration

Data visualization for idea illustration assists in conveying an idea, such as a tactic or process. It is commonly used in learning settings, such as tutorials, certification courses, centers of excellence, but it can also be used to represent organization structures or processes, facilitating communication between the right individuals for specific tasks. Project managers frequently use Gantt charts and waterfall charts to illustrate  workflows .  Data modeling  also uses abstraction to represent and better understand data flow within an enterprise’s information system, making it easier for developers, business analysts, data architects, and others to understand the relationships in a database or data warehouse.

Visual discovery

Visual discovery and every day data viz are more closely aligned with data teams. While visual discovery helps data analysts, data scientists, and other data professionals identify patterns and trends within a dataset, every day data viz supports the subsequent storytelling after a new insight has been found.

Data visualization

Data visualization is a critical step in the data science process, helping teams and individuals convey data more effectively to colleagues and decision makers. Teams that manage reporting systems typically leverage defined template views to monitor performance. However, data visualization isn’t limited to performance dashboards. For example, while  text mining  an analyst may use a word cloud to to capture key concepts, trends, and hidden relationships within this unstructured data. Alternatively, they may utilize a graph structure to illustrate relationships between entities in a knowledge graph. There are a number of ways to represent different types of data, and it’s important to remember that it is a skillset that should extend beyond your core analytics team.

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The earliest form of data visualization can be traced back the Egyptians in the pre-17th century, largely used to assist in navigation. As time progressed, people leveraged data visualizations for broader applications, such as in economic, social, health disciplines. Perhaps most notably, Edward Tufte published  The Visual Display of Quantitative Information  (link resides outside ibm.com), which illustrated that individuals could utilize data visualization to present data in a more effective manner. His book continues to stand the test of time, especially as companies turn to dashboards to report their performance metrics in real-time. Dashboards are effective data visualization tools for tracking and visualizing data from multiple data sources, providing visibility into the effects of specific behaviors by a team or an adjacent one on performance. Dashboards include common visualization techniques, such as:

• Tables: This consists of rows and columns used to compare variables. Tables can show a great deal of information in a structured way, but they can also overwhelm users that are simply looking for high-level trends.
• Pie charts and stacked bar charts:  These graphs are divided into sections that represent parts of a whole. They provide a simple way to organize data and compare the size of each component to one other.
• Line charts and area charts:  These visuals show change in one or more quantities by plotting a series of data points over time and are frequently used within predictive analytics. Line graphs utilize lines to demonstrate these changes while area charts connect data points with line segments, stacking variables on top of one another and using color to distinguish between variables.
• Histograms: This graph plots a distribution of numbers using a bar chart (with no spaces between the bars), representing the quantity of data that falls within a particular range. This visual makes it easy for an end user to identify outliers within a given dataset.
• Scatter plots: These visuals are beneficial in reveling the relationship between two variables, and they are commonly used within regression data analysis. However, these can sometimes be confused with bubble charts, which are used to visualize three variables via the x-axis, the y-axis, and the size of the bubble.
• Heat maps:  These graphical representation displays are helpful in visualizing behavioral data by location. This can be a location on a map, or even a webpage.
• Tree maps, which display hierarchical data as a set of nested shapes, typically rectangles. Treemaps are great for comparing the proportions between categories via their area size.

Access to data visualization tools has never been easier. Open source libraries, such as D3.js, provide a way for analysts to present data in an interactive way, allowing them to engage a broader audience with new data. Some of the most popular open source visualization libraries include:

• D3.js: It is a front-end JavaScript library for producing dynamic, interactive data visualizations in web browsers.  D3.js  (link resides outside ibm.com) uses HTML, CSS, and SVG to create visual representations of data that can be viewed on any browser. It also provides features for interactions and animations.
• ECharts:  A powerful charting and visualization library that offers an easy way to add intuitive, interactive, and highly customizable charts to products, research papers, presentations, etc.  Echarts  (link resides outside ibm.com) is based in JavaScript and ZRender, a lightweight canvas library.
• Vega:   Vega  (link resides outside ibm.com) defines itself as “visualization grammar,” providing support to customize visualizations across large datasets which are accessible from the web.
• deck.gl: It is part of Uber's open source visualization framework suite.  deck.gl  (link resides outside ibm.com) is a framework, which is used for  exploratory data analysis  on big data. It helps build high-performance GPU-powered visualization on the web.

With so many data visualization tools readily available, there has also been a rise in ineffective information visualization. Visual communication should be simple and deliberate to ensure that your data visualization helps your target audience arrive at your intended insight or conclusion. The following best practices can help ensure your data visualization is useful and clear:

Set the context: It’s important to provide general background information to ground the audience around why this particular data point is important. For example, if e-mail open rates were underperforming, we may want to illustrate how a company’s open rate compares to the overall industry, demonstrating that the company has a problem within this marketing channel. To drive an action, the audience needs to understand how current performance compares to something tangible, like a goal, benchmark, or other key performance indicators (KPIs).

Know your audience(s): Think about who your visualization is designed for and then make sure your data visualization fits their needs. What is that person trying to accomplish? What kind of questions do they care about? Does your visualization address their concerns? You’ll want the data that you provide to motivate people to act within their scope of their role. If you’re unsure if the visualization is clear, present it to one or two people within your target audience to get feedback, allowing you to make additional edits prior to a large presentation.

Choose an effective visual:  Specific visuals are designed for specific types of datasets. For instance, scatter plots display the relationship between two variables well, while line graphs display time series data well. Ensure that the visual actually assists the audience in understanding your main takeaway. Misalignment of charts and data can result in the opposite, confusing your audience further versus providing clarity.

Keep it simple:  Data visualization tools can make it easy to add all sorts of information to your visual. However, just because you can, it doesn’t mean that you should! In data visualization, you want to be very deliberate about the additional information that you add to focus user attention. For example, do you need data labels on every bar in your bar chart? Perhaps you only need one or two to help illustrate your point. Do you need a variety of colors to communicate your idea? Are you using colors that are accessible to a wide range of audiences (e.g. accounting for color blind audiences)? Design your data visualization for maximum impact by eliminating information that may distract your target audience.

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• School Guide
• Class 9 Syllabus
• Maths Notes Class 9
• Science Notes Class 9
• History Notes Class 9
• Geography Notes Class 9
• Political Science Notes Class 9
• NCERT Soln. Class 9 Maths
• RD Sharma Soln. Class 9
• Math Formulas Class 9
• CBSE Class 9 Maths Revision Notes

Chapter 1: Number System

• Number System in Maths
• Natural Numbers | Definition, Examples, Properties
• Whole Numbers - Definition, Properties and Examples
• Rational Number: Definition, Examples, Worksheet
• Irrational Numbers: Definition, Examples, Symbol, Properties
• Real Numbers
• Decimal Expansion of Real Numbers
• Decimal Expansions of Rational Numbers
• Representation of Rational Numbers on the Number Line | Class 8 Maths
• Represent √3 on the number line
• Operations on Real Numbers
• Rationalization of Denominators
• Laws of Exponents for Real Numbers

Chapter 2: Polynomials

• Polynomials in One Variable - Polynomials | Class 9 Maths
• Polynomial Formula
• Types of Polynomials
• Zeros of Polynomial
• Factorization of Polynomial
• Remainder Theorem
• Factor Theorem
• Algebraic Identities

Chapter 3: Coordinate Geometry

• Coordinate Geometry
• Cartesian Coordinate System
• Cartesian Plane

Chapter 4: Linear equations in two variables

• Linear Equations in One Variable
• Linear Equation in Two Variables
• Graph of Linear Equations in Two Variables
• Graphical Methods of Solving Pair of Linear Equations in Two Variables
• Equations of Lines Parallel to the x-axis and y-axis

Chapter 5: Introduction to Euclid's Geometry

• Euclidean Geometry
• Equivalent Version of Euclid’s Fifth Postulate

Chapter 6: Lines and Angles

• Lines and Angles
• Types of Angles
• Pairs of Angles - Lines & Angles
• Transversal Lines
• Angle Sum Property of a Triangle

Chapter 7: Triangles

• Triangles in Geometry
• Congruence of Triangles |SSS, SAS, ASA, and RHS Rules
• Theorem - Angle opposite to equal sides of an isosceles triangle are equal | Class 9 Maths
• Triangle Inequality Theorem, Proof & Applications

Chapter 8: Quadrilateral

• Angle Sum Property of a Quadrilateral
• Quadrilateral - Definition, Properties, Types, Formulas, Examples
• Introduction to Parallelogram: Properties, Types, and Theorem
• Rhombus: Definition, Properties, Formula, Examples
• Kite - Quadrilaterals
• Properties of Parallelograms
• Mid Point Theorem

Chapter 9: Areas of Parallelograms and Triangles

• Area of Triangle | Formula and Examples
• Area of Parallelogram
• Figures on the Same Base and between the Same Parallels

Chapter 10: Circles

• Circles in Maths
• Radius of Circle
• Tangent to a Circle
• What is the longest chord of a Circle?
• Circumference of Circle - Definition, Perimeter Formula, and Examples
• Angle subtended by an arc at the centre of a circle
• What is Cyclic Quadrilateral
• Theorem - The sum of opposite angles of a cyclic quadrilateral is 180° | Class 9 Maths

Chapter 11: Construction

• Basic Constructions - Angle Bisector, Perpendicular Bisector, Angle of 60°
• Construction of Triangles

Chapter 12: Heron's Formula

• Area of Equilateral Triangle
• Area of Isosceles Triangle
• Heron's Formula
• Applications of Heron's Formula
• Area of Quadrilateral
• Area of Polygons

Chapter 13: Surface Areas and Volumes

• Surface Area of Cuboid
• Volume of Cuboid | Formula and Examples
• Surface Area of Cube
• Volume of a Cube
• Surface Area of Cylinder
• Volume of Cylinder
• Surface Area of Cone
• Volume of Cone: Formula, Derivation and Examples
• Surface Area of Sphere | CSA, TSA, Formula and Derivation
• Volume of a Sphere
• Surface Area of a Hemisphere
• Volume of Hemisphere

Chapter 14: Statistics

• Collection and Presentation of Data

Graphical Representation of Data

• Bar Graphs and Histograms
• Central Tendency
• Mean, Median and Mode

Chapter 15: Probability

• Experimental Probability
• Empirical Probability
• CBSE Class 9 Maths Formulas
• NCERT Solutions for Class 9 Maths: Chapter Wise PDF 2024
• RD Sharma Class 9 Solutions

Graphical Representation of Data: In today’s world of the internet and connectivity, there is a lot of data available, and some or other method is needed for looking at large data, the patterns, and trends in it. There is an entire branch in mathematics dedicated to dealing with collecting, analyzing, interpreting, and presenting numerical data in visual form in such a way that it becomes easy to understand and the data becomes easy to compare as well, the branch is known as Statistics .

The branch is widely spread and has a plethora of real-life applications such as Business Analytics, demography, astrostatistics, and so on. In this article, we have provided everything about the graphical representation of data, including its types, rules, advantages, etc.

Table of Content

What is Graphical Representation?

Types of graphical representations, graphical representations used in maths, principles of graphical representations, advantages and disadvantages of using graphical system, general rules for graphical representation of data, solved examples on graphical representation of data.

There are two ways of representing data,

• Pictorial Representation through graphs.

They say, “A picture is worth a thousand words”.  It’s always better to represent data in a graphical format. Even in Practical Evidence and Surveys, scientists have found that the restoration and understanding of any information is better when it is available in the form of visuals as Human beings process data better in visual form than any other form. Does it increase the ability 2 times or 3 times? The answer is it increases the Power of understanding 60,000 times for a normal Human being, the fact is amusing and true at the same time.

Comparison between different items is best shown with graphs, it becomes easier to compare the crux of the data about different items. Let’s look at all the different types of graphical representations briefly: 

Line Graphs

A line graph is used to show how the value of a particular variable changes with time. We plot this graph by connecting the points at different values of the variable. It can be useful for analyzing the trends in the data and predicting further trends. 

A bar graph is a type of graphical representation of the data in which bars of uniform width are drawn with equal spacing between them on one axis (x-axis usually), depicting the variable. The values of the variables are represented by the height of the bars. 

Histograms 

This is similar to bar graphs, but it is based frequency of numerical values rather than their actual values. The data is organized into intervals and the bars represent the frequency of the values in that range. That is, it counts how many values of the data lie in a particular range. 

It is a plot that displays data as points and checkmarks above a number line, showing the frequency of the point. 

Stem and Leaf Plot 

This is a type of plot in which each value is split into a “leaf”(in most cases, it is the last digit) and “stem”(the other remaining digits). For example: the number 42 is split into leaf (2) and stem (4).  

Box and Whisker Plot 

These plots divide the data into four parts to show their summary. They are more concerned about the spread, average, and median of the data. 

It is a type of graph which represents the data in form of a circular graph. The circle is divided such that each portion represents a proportion of the whole. 

Graphs in maths are used to study the relationships between two or more variables that are changing. Statistical data can be summarized in a better way using graphs. There are basically two lines of thoughts of making graphs in maths: 

• Value-Based or Time Series Graphs

Frequency Based

Value-based or time series graphs .

These graphs allow us to study the change of a variable with respect to another variable within a given interval of time. The variables can be anything. Time Series graphs study the change of variable with time. They study the trends, periodic behavior, and patterns in the series. We are more concerned with the values of the variables here rather than the frequency of those values. 

Example: Line Graph

These kinds of graphs are more concerned with the distribution of data. How many values lie between a particular range of the variables, and which range has the maximum frequency of the values. They are used to judge a spread and average and sometimes median of a variable under study. 

Example: Frequency Polygon, Histograms.

All types of graphical representations require some rule/principles which are to be followed. These are some algebraic principles. When we plot a graph, there is an origin, and we have our two axes. These two axes divide the plane into four parts called quadrants. The horizontal one is usually called the x-axis and the other one is called the y-axis. The origin is the point where these two axes intersect. The thing we need to keep in mind about the values of the variable on the x-axis is that positive values need to be on the right side of the origin and negative values should be on the left side of the origin. Similarly, for the variable on the y-axis, we need to make sure that the positive values of this variable should be above the x-axis and negative values of this variable must be below the y-axis. 

• It gives us a summary of the data which is easier to look at and analyze.
• It saves time.
• We can compare and study more than one variable at a time.

Disadvantages

It usually takes only one aspect of the data and ignores the other. For example, A bar graph does not represent the mean, median, and other statistics of the data. 

We should keep in mind some things while plotting and designing these graphs. The goal should be a better and clear picture of the data. Following things should be kept in mind while plotting the above graphs: 

• Whenever possible, the data source must be mentioned for the viewer.
• Always choose the proper colors and font sizes. They should be chosen to keep in mind that the graphs should look neat.
• The measurement Unit should be mentioned in the top right corner of the graph.
• The proper scale should be chosen while making the graph, it should be chosen such that the graph looks accurate.
• Last but not the least, a suitable title should be chosen.

Frequency Polygon

A frequency polygon is a graph that is constructed by joining the midpoint of the intervals. The height of the interval or the bin represents the frequency of the values that lie in that interval. 

People Also View:

Diagrammatic and Graphic Presentation of Data What are the different ways of Data Representation?

Question 1: What are different types of frequency-based plots? 

Types of frequency based plots:  Histogram Frequency Polygon Box Plots

Question 2: A company with an advertising budget of Rs 10,00,00,000 has planned the following expenditure in the different advertising channels such as TV Advertisement, Radio, Facebook, Instagram, and Printed media. The table represents the money spent on different channels. 

Draw a bar graph for the following data. 

Steps:  Put each of the channels on the x-axis The height of the bars is decided by the value of each channel.

Question 3: Draw a line plot for the following data 

Steps:  Put each of the x-axis row value on the x-axis joint the value corresponding to the each value of the x-axis.

Question 4: Make a frequency plot of the following data: 

Steps:  Draw the class intervals on the x-axis and frequencies on the y-axis. Calculate the mid point of each class interval. Class Interval Mid Point Frequency 0-3 1.5 3 3-6 4.5 4 6-9 7.5 2 9-12 10.5 6 Now join the mid points of the intervals and their corresponding frequencies on the graph.  This graph shows both the histogram and frequency polygon for the given distribution.

FAQs on Graphical Representation of Data

What are the advantages of using graphs to represent data.

Graphs offer visualization, clarity, and easy comparison of data, aiding in outlier identification and predictive analysis.

What are the common types of graphs used for data representation?

Common graph types include bar, line, pie, histogram, and scatter plots, each suited for different data representations and analysis purposes.

How do you choose the most appropriate type of graph for your data?

Select a graph type based on data type, analysis objective, and audience familiarity to effectively convey information and insights.

How do you create effective labels and titles for graphs?

Use descriptive titles, clear axis labels with units, and legends to ensure the graph communicates information clearly and concisely.

How do you interpret graphs to extract meaningful insights from data?

Interpret graphs by examining trends, identifying outliers, comparing data across categories, and considering the broader context to draw meaningful insights and conclusions.

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2.1: Types of Data Representation

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Two common types of graphic displays are bar charts and histograms. Both bar charts and histograms use vertical or horizontal bars to represent the number of data points in each category or interval. The main difference graphically is that in a  bar chart  there are spaces between the bars and in a  histogram  there are not spaces between the bars. Why does this subtle difference exist and what does it imply about graphic displays in general?

Displaying Data

It is often easier for people to interpret relative sizes of data when that data is displayed graphically. Note that a  categorical variable  is a variable that can take on one of a limited number of values and a  quantitative variable  is a variable that takes on numerical values that represent a measurable quantity. Examples of categorical variables are tv stations, the state someone lives in, and eye color while examples of quantitative variables are the height of students or the population of a city. There are a few common ways of displaying data graphically that you should be familiar with. 

A  pie chart  shows the relative proportions of data in different categories.  Pie charts  are excellent ways of displaying categorical data with easily separable groups. The following pie chart shows six categories labeled A−F.  The size of each pie slice is determined by the central angle. Since there are 360 o  in a circle, the size of the central angle θ A  of category A can be found by:

CK-12 Foundation -  https://www.flickr.com/photos/slgc/16173880801  - CCSA

A  bar chart  displays frequencies of categories of data. The bar chart below has 5 categories, and shows the TV channel preferences for 53 adults. The horizontal axis could have also been labeled News, Sports, Local News, Comedy, Action Movies. The reason why the bars are separated by spaces is to emphasize the fact that they are categories and not continuous numbers. For example, just because you split your time between channel 8 and channel 44 does not mean on average you watch channel 26. Categories can be numbers so you need to be very careful.

CK-12 Foundation -  https://www.flickr.com/photos/slgc/16173880801  - CCSA

A  histogram  displays frequencies of quantitative data that has been sorted into intervals. The following is a histogram that shows the heights of a class of 53 students. Notice the largest category is 56-60 inches with 18 people.

A  boxplot  (also known as a  box and whiskers plot ) is another way to display quantitative data. It displays the five 5 number summary (minimum, Q1,  median , Q3, maximum). The box can either be vertically or horizontally displayed depending on the labeling of the axis. The box does not need to be perfectly symmetrical because it represents data that might not be perfectly symmetrical.

Earlier, you were asked about the difference between histograms and bar charts. The reason for the space in bar charts but no space in histograms is bar charts graph categorical variables while histograms graph quantitative variables. It would be extremely improper to forget the space with bar charts because you would run the risk of implying a spectrum from one side of the chart to the other. Note that in the bar chart where TV stations where shown, the station numbers were not listed horizontally in order by size. This was to emphasize the fact that the stations were categories.

Create a boxplot of the following numbers in your calculator.

8.5, 10.9, 9.1, 7.5, 7.2, 6, 2.3, 5.5

Enter the data into L1 by going into the Stat menu.

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Then turn the statplot on and choose boxplot.

Use Zoomstat to automatically center the window on the boxplot.

Create a pie chart to represent the preferences of 43 hungry students.

• Other – 5
• Burritos – 7
• Burgers – 9
• Pizza – 22

Create a bar chart representing the preference for sports of a group of 23 people.

• Football – 12
• Baseball – 10
• Basketball – 8
• Hockey – 3

Create a histogram for the income distribution of 200 million people.

• Below $50,000 is 100 million people
• Between $50,000 and $100,000 is 50 million people
• Between $100,000 and $150,000 is 40 million people
• Above $150,000 is 10 million people

1. What types of graphs show categorical data?

2. What types of graphs show quantitative data?

A math class of 30 students had the following grades:

3. Create a bar chart for this data.

4. Create a pie chart for this data.

5. Which graph do you think makes a better visual representation of the data?

A set of 20 exam scores is 67, 94, 88, 76, 85, 93, 55, 87, 80, 81, 80, 61, 90, 84, 75, 93, 75, 68, 100, 98

6. Create a histogram for this data. Use your best judgment to decide what the intervals should be.

7. Find the  five number summary  for this data.

8. Use the  five number summary  to create a boxplot for this data.

9. Describe the data shown in the boxplot below.

10. Describe the data shown in the histogram below.

A math class of 30 students has the following eye colors:

11. Create a bar chart for this data.

12. Create a pie chart for this data.

13. Which graph do you think makes a better visual representation of the data?

14. Suppose you have data that shows the breakdown of registered republicans by state. What types of graphs could you use to display this data?

15. From which types of graphs could you obtain information about the spread of the data? Note that spread is a measure of how spread out all of the data is.

Review (Answers)

To see the Review answers, open this  PDF file  and look for section 15.4. 

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Practice: Types of Data Representation

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Graphical Representation

Graphical representation definition.

Graphical representation refers to the use of charts and graphs to visually display, analyze, clarify, and interpret numerical data, functions, and other qualitative structures. ‍

What is Graphical Representation?

Graphical representation refers to the use of intuitive charts to clearly visualize and simplify data sets. Data is ingested into graphical representation of data software and then represented by a variety of symbols, such as lines on a line chart, bars on a bar chart, or slices on a pie chart, from which users can gain greater insight than by numerical analysis alone. 

Representational graphics can quickly illustrate general behavior and highlight phenomenons, anomalies, and relationships between data points that may otherwise be overlooked, and may contribute to predictions and better, data-driven decisions. The types of representational graphics used will depend on the type of data being explored.

Types of Graphical Representation

Data charts are available in a wide variety of maps, diagrams, and graphs that typically include textual titles and legends to denote the purpose, measurement units, and variables of the chart. Choosing the most appropriate chart depends on a variety of different factors -- the nature of the data, the purpose of the chart, and whether a graphical representation of qualitative data or a graphical representation of quantitative data is being depicted. There are dozens of different formats for graphical representation of data. Some of the most popular charts include:

• Bar Graph -- contains a vertical axis and horizontal axis and displays data as rectangular bars with lengths proportional to the values that they represent; a useful visual aid for marketing purposes
• Choropleth -- thematic map in which an aggregate summary of a geographic characteristic within an area is represented by patterns of shading proportionate to a statistical variable
• Flow Chart -- diagram that depicts a workflow graphical representation with the use of arrows and geometric shapes; a useful visual aid for business and finance purposes
• Heatmap -- a colored, two-dimensional matrix of cells in which each cell represents a grouping of data and each cell’s color indicates its relative value
• Histogram – frequency distribution and graphical representation uses adjacent vertical bars erected over discrete intervals to represent the data frequency within a given interval; a useful visual aid for meteorology and environment purposes
• Line Graph – displays continuous data; ideal for predicting future events over time;  a useful visual aid for marketing purposes
• Pie Chart -- shows percentage values as a slice of pie; a useful visual aid for marketing purposes
• Pointmap -- CAD & GIS contract mapping and drafting solution that visualizes the location of data on a map by plotting geographic latitude and longitude data
• Scatter plot -- a diagram that shows the relationship between two sets of data, where each dot represents individual pieces of data and each axis represents a quantitative measure
• Stacked Bar Graph -- a graph in which each bar is segmented into parts, with the entire bar representing the whole, and each segment representing different categories of that whole; a useful visual aid for political science and sociology purposes
• Timeline Chart -- a long bar labelled with dates paralleling it that display a list of events in chronological order, a useful visual aid for history charting purposes
• Tree Diagram -- a hierarchical genealogical tree that illustrates a family structure; a useful visual aid for history charting purposes
• Venn Diagram -- consists of multiple overlapping usually circles, each representing a set; the default inner join graphical representation

Proprietary and open source software for graphical representation of data is available in a wide variety of programming languages. Software packages often provide spreadsheets equipped with built-in charting functions.

Advantages and Disadvantages of Graphical Representation of Data

Tabular and graphical representation of data are a vital component in analyzing and understanding large quantities of numerical data and the relationship between data points. Data visualization is one of the most fundamental approaches to data analysis, providing an intuitive and universal means to visualize, abstract, and share complex data patterns. The primary advantages of graphical representation of data are:

• Facilitates and improves learning: graphics make data easy to understand and eliminate language and literacy barriers
• Understanding content: visuals are more effective than text in human understanding
• Flexibility of use: graphical representation can be leveraged in nearly every field involving data
• Increases structured thinking: users can make quick, data-driven decisions at a glance with visual aids
• Supports creative, personalized reports for more engaging and stimulating visual  presentations 
• Improves communication: analyzing graphs that highlight relevant themes is significantly faster than reading through a descriptive report line by line
• Shows the whole picture: an instantaneous, full view of all variables, time frames, data behavior and relationships

Disadvantages of graphical representation of data typically concern the cost of human effort and resources, the process of selecting the most appropriate graphical and tabular representation of data, greater design complexity of visualizing data, and the potential for human bias.

Why Graphical Representation of Data is Important

Graphic visual representation of information is a crucial component in understanding and identifying patterns and trends in the ever increasing flow of data. Graphical representation enables the quick analysis of large amounts of data at one time and can aid in making predictions and informed decisions. Data visualizations also make collaboration significantly more efficient by using familiar visual metaphors to illustrate relationships and highlight meaning, eliminating complex, long-winded explanations of an otherwise chaotic-looking array of figures. 

Data only has value once its significance has been revealed and consumed, and its consumption is best facilitated with graphical representation tools that are designed with human cognition and perception in mind. Human visual processing is very efficient at detecting relationships and changes between sizes, shapes, colors, and quantities. Attempting to gain insight from numerical data alone, especially in big data instances in which there may be billions of rows of data, is exceedingly cumbersome and inefficient.

Does HEAVY.AI Offer a Graphical Representation Solution?

HEAVY.AI's visual analytics platform is an interactive data visualization client that works seamlessly with server-side technologies HEAVY.AIDB and Render to enable data science analysts to easily visualize and instantly interact with massive datasets. Analysts can interact with conventional charts and data tables, as well as big data graphical representations such as massive-scale scatterplots and geo charts. Data visualization contributes to a broad range of use cases, including performance analysis in business and guiding research in academia.

Guide On Graphical Representation of Data – Types, Importance, Rules, Principles And Advantages

What are Graphs and Graphical Representation?

Graphs, in the context of data visualization, are visual representations of data using various graphical elements such as charts, graphs, and diagrams. Graphical representation of data , often referred to as graphical presentation or simply graphs which plays a crucial role in conveying information effectively.

Principles of Graphical Representation

Effective graphical representation follows certain fundamental principles that ensure clarity, accuracy, and usability:Clarity : The primary goal of any graph is to convey information clearly and concisely. Graphs should be designed in a way that allows the audience to quickly grasp the key points without confusion.

• Simplicity: Simplicity is key to effective data visualization. Extraneous details and unnecessary complexity should be avoided to prevent confusion and distraction.
• Relevance: Include only relevant information that contributes to the understanding of the data. Irrelevant or redundant elements can clutter the graph.
• Visualization: Select a graph type that is appropriate for the supplied data. Different graph formats, like bar charts, line graphs, and scatter plots, are appropriate for various sorts of data and relationships.

Rules for Graphical Representation of Data

Creating effective graphical representations of data requires adherence to certain rules:

• Select the Right Graph: Choosing the appropriate type of graph is essential. For example, bar charts are suitable for comparing categories, while line charts are better for showing trends over time.
• Label Axes Clearly: Axis labels should be descriptive and include units of measurement where applicable. Clear labeling ensures the audience understands the data’s context.
• Use Appropriate Colors: Colors can enhance understanding but should be used judiciously. Avoid overly complex color schemes and ensure that color choices are accessible to all viewers.
• Avoid Misleading Scaling: Scale axes appropriately to prevent exaggeration or distortion of data. Misleading scaling can lead to incorrect interpretations.
• Include Data Sources: Always provide the source of your data. This enhances transparency and credibility.

Importance of Graphical Representation of Data

Graphical representation of data in statistics is of paramount importance for several reasons:

• Enhances Understanding: Graphs simplify complex data, making it more accessible and understandable to a broad audience, regardless of their statistical expertise.
• Helps Decision-Making: Visual representations of data enable informed decision-making. Decision-makers can easily grasp trends and insights, leading to better choices.
• Engages the Audience: Graphs capture the audience’s attention more effectively than raw data. This engagement is particularly valuable when presenting findings or reports.
• Universal Language: Graphs serve as a universal language that transcends linguistic barriers. They can convey information to a global audience without the need for translation.

Advantages of Graphical Representation

The advantages of graphical representation of data extend to various aspects of communication and analysis:

• Clarity: Data is presented visually, improving clarity and reducing the likelihood of misinterpretation.
• Efficiency: Graphs enable the quick absorption of information. Key insights can be found in seconds, saving time and effort.
• Memorability: Visuals are more memorable than raw data. Audiences are more likely to retain information presented graphically.
• Problem-Solving: Graphs help in identifying and solving problems by revealing trends, correlations, and outliers that may require further investigation.

Use of Graphical Representations

Graphical representations find applications in a multitude of fields:

• Business: In the business world, graphs are used to illustrate financial data, track performance metrics, and present market trends. They are invaluable tools for strategic decision-making.
• Science: Scientists employ graphs to visualize experimental results, depict scientific phenomena, and communicate research findings to both colleagues and the general public.
• Education: Educators utilize graphs to teach students about data analysis, statistics, and scientific concepts. Graphs make learning more engaging and memorable.
• Journalism: Journalists rely on graphs to support their stories with data-driven evidence. Graphs make news articles more informative and impactful.

Types of Graphical Representation

There exists a diverse array of graphical representations, each suited to different data types and purposes. Common types include:

1.Bar Charts:

Used to compare categories or discrete data points, often side by side.

2. Line Charts:

Ideal for showing trends and changes over time, such as stock market performance or temperature fluctuations.

3. Pie Charts:

Display parts of a whole, useful for illustrating proportions or percentages.

4. Scatter Plots:

Reveal relationships between two variables and help identify correlations.

5. Histograms:

Depict the distribution of data, especially in the context of continuous variables.

In conclusion, the graphical representation of data is an indispensable tool for simplifying complex information, aiding in decision-making, and enhancing communication across diverse fields. By following the principles and rules of effective data visualization, individuals and organizations can harness the power of graphs to convey their messages, support their arguments, and drive informed actions.

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FAQs on Graphical Representation of Data

What is the purpose of graphical representation.

Graphical representation serves the purpose of simplifying complex data, making it more accessible and understandable through visual means.

Why are graphs and diagrams important?

Graphs and diagrams are crucial because they provide visual clarity, aiding in the comprehension and retention of information.

How do graphs help learning?

Graphs engage learners by presenting information visually, which enhances understanding and retention, particularly in educational settings.

Who uses graphs?

Professionals in various fields, including scientists, analysts, educators, and business leaders, use graphs to convey data effectively and support decision-making.

Where are graphs used in real life?

Graphs are used in real-life scenarios such as business reports, scientific research, news articles, and educational materials to make data more accessible and meaningful.

Why are graphs important in business?

In business, graphs are vital for analyzing financial data, tracking performance metrics, and making informed decisions, contributing to success.

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6 Data Visualization Examples To Inspire Your Own

• 12 Jan 2017

Data informs virtually every business decision an organization makes. Because of this, it’s become increasingly important for professionals of all backgrounds to be adept at working with data.

While data can provide immense value, it’s important that professionals are able to effectively communicate the significance of the data to stakeholders. This is where data visualization comes into play. By transforming raw data into engaging visuals using various data visualization tools , it’s much easier to communicate insights gleaned from it.

Here are six real-world examples of data visualization that you can use to inspire your own.

What Is Data Visualization?

Data visualization is the process of turning raw data into graphical representations.

Visualizations make it easy to communicate trends in data and draw conclusions. When presented with a graph or chart, stakeholders can easily visualize the story the data is telling, rather than try to glean insights from raw data.

There are countless data visualization techniques , including:

• Scatter plots

The technique you use will vary based on the type of data you’re handling and what you’re trying to communicate.

6 Real-World Data Visualization Examples

1. the most common jobs by state.

Source: NPR

National Public Radio (NPR) produced a color-coded, interactive display of the most common jobs in each state in each year from 1978 to 2014. By dragging the scroll bar at the bottom of the map, you’re able to visualize occupational changes over time.

If you’re trying to represent geographical data, a map is the best way to go.

2. COVID-19 Hospitalization Rates

Source: CDC

Throughout the COVID-19 pandemic, the Centers for Disease Control and Prevention (CDC) has been transforming raw data into easily digestible visuals. This line graph represents COVID-19 hospitalization rates from March through November 2020.

The CDC tactfully incorporated color to place further emphasis on the stark increase in hospitalization rates, using a darker shade for lower values and a lighter shade for higher values.

3. Forecasted Revenue of Amazon.com

Source: Statista

Data visualizations aren’t limited to historical data. This bar chart created by Statista visualizes the forecasted gross revenue of Amazon.com from 2018 to 2025.

This visualization uses a creative title to summarize the main message that the data is conveying, as well as a darker orange color to spike out the most important data point.

4. Web-Related Statistics

Source: Internet Live Stats

Internet Live Stats has tracked web-related statistics and pioneered methods for visualizing data to show how different digital properties have ebbed and flowed over time.

Simple infographics like this one are particularly effective when your goal is to communicate key statistics rather than visualizing trends or forecasts.

5. Most Popular Food Delivery Items

Source: Eater

Eater, Vox’s food and dining brand, has created this fun take on a “pie” chart, which shows the most common foods ordered for delivery in each of the United States.

To visualize this data, Eater used a specific type of pie chart known as a spie chart. Spie charts are essentially pie charts in which you can vary the height of each segment to further visualize differences in data.

6. Netflix Viewing Patterns

Source: Vox

Vox created this interesting visualization depicting the viewing patterns of Netflix users over time by device type. This Sankey diagram visualizes the tendency of users to switch to streaming via larger device types.

Visualizing Data to Make Business Decisions

The insights and conclusions drawn from data visualizations can guide the decision-making and strategic planning processes for your organization.

To ensure your visualizations are relevant, accurate, and ethical, familiarize yourself with basic data science concepts . With a foundational knowledge in data science, you can maintain confidence in your data and better understand its significance. An online analytics course can help you get started.

Are you interested in improving your data science and analytical skills? Download our Beginner’s Guide to Data & Analytics to learn how you can leverage the power of data for professional and organizational success.

This post was updated on February 26, 2021. It was originally published on January 12, 2017.

16 Best Types of Charts and Graphs for Data Visualization [+ Guide]

Published: June 08, 2023

There are more type of charts and graphs than ever before because there's more data. In fact, the volume of data in 2025 will be almost double the data we create, capture, copy, and consume today.

This makes data visualization essential for businesses. Different types of graphs and charts can help you:

• Motivate your team to take action.
• Impress stakeholders with goal progress.
• Show your audience what you value as a business.

Data visualization builds trust and can organize diverse teams around new initiatives. Let's talk about the types of graphs and charts that you can use to grow your business.

Free Excel Graph Templates

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Click this link to access this resource at any time.

Different Types of Graphs for Data Visualization

1. bar graph.

A bar graph should be used to avoid clutter when one data label is long or if you have more than 10 items to compare.

Best Use Cases for These Types of Graphs

Bar graphs can help you compare data between different groups or to track changes over time. Bar graphs are most useful when there are big changes or to show how one group compares against other groups.

The example above compares the number of customers by business role. It makes it easy to see that there is more than twice the number of customers per role for individual contributors than any other group.

A bar graph also makes it easy to see which group of data is highest or most common.

For example, at the start of the pandemic, online businesses saw a big jump in traffic. So, if you want to look at monthly traffic for an online business, a bar graph would make it easy to see that jump.

Other use cases for bar graphs include:

• Product comparisons.
• Product usage.
• Category comparisons.
• Marketing traffic by month or year.
• Marketing conversions.

Design Best Practices for Bar Graphs

• Use consistent colors throughout the chart, selecting accent colors to highlight meaningful data points or changes over time.
• Use horizontal labels to improve readability.
• Start the y-axis at 0 to appropriately reflect the values in your graph.

2. Line Graph

A line graph reveals trends or progress over time, and you can use it to show many different categories of data. You should use it when you chart a continuous data set.

Line graphs help users track changes over short and long periods. Because of this, these types of graphs are good for seeing small changes.

Line graphs can help you compare changes for more than one group over the same period. They're also helpful for measuring how different groups relate to each other.

A business might use this graph to compare sales rates for different products or services over time.

These charts are also helpful for measuring service channel performance. For example, a line graph that tracks how many chats or emails your team responds to per month.

Design Best Practices for Line Graphs

• Use solid lines only.
• Don't plot more than four lines to avoid visual distractions.
• Use the right height so the lines take up roughly 2/3 of the y-axis' height.

3. Bullet Graph

A bullet graph reveals progress towards a goal, compares this to another measure, and provides context in the form of a rating or performance.

In the example above, the bullet graph shows the number of new customers against a set customer goal. Bullet graphs are great for comparing performance against goals like this.

These types of graphs can also help teams assess possible roadblocks because you can analyze data in a tight visual display.

For example, you could create a series of bullet graphs measuring performance against benchmarks or use a single bullet graph to visualize these KPIs against their goals:

• Customer satisfaction.
• Average order size.
• New customers.

Seeing this data at a glance and alongside each other can help teams make quick decisions.

Bullet graphs are one of the best ways to display year-over-year data analysis. You can also use bullet graphs to visualize:

• Customer satisfaction scores.
• Customer shopping habits.
• Social media usage by platform.

Design Best Practices for Bullet Graphs

• Use contrasting colors to highlight how the data is progressing.
• Use one color in different shades to gauge progress.

Different Types of Charts for Data Visualization

To better understand these chart types and how you can use them, here's an overview of each:

1. Column Chart

Use a column chart to show a comparison among different items or to show a comparison of items over time. You could use this format to see the revenue per landing page or customers by close date.

Best Use Cases for This Type of Chart

You can use both column charts and bar graphs to display changes in data, but column charts are best for negative data. The main difference, of course, is that column charts show information vertically while bar graphs show data horizontally.

For example, warehouses often track the number of accidents on the shop floor. When the number of incidents falls below the monthly average, a column chart can make that change easier to see in a presentation.

In the example above, this column chart measures the number of customers by close date. Column charts make it easy to see data changes over a period of time. This means that they have many use cases, including:

• Customer survey data, like showing how many customers prefer a specific product or how much a customer uses a product each day.
• Sales volume, like showing which services are the top sellers each month or the number of sales per week.
• Profit and loss, showing where business investments are growing or falling.

Design Best Practices for Column Charts

2. dual-axis chart.

A dual-axis chart allows you to plot data using two y-axes and a shared x-axis. It has three data sets. One is a continuous data set, and the other is better suited to grouping by category. Use this chart to visualize a correlation or the lack thereof between these three data sets.

A dual-axis chart makes it easy to see relationships between different data sets. They can also help with comparing trends.

For example, the chart above shows how many new customers this company brings in each month. It also shows how much revenue those customers are bringing the company.

This makes it simple to see the connection between the number of customers and increased revenue.

You can use dual-axis charts to compare:

• Price and volume of your products.
• Revenue and units sold.
• Sales and profit margin.
• Individual sales performance.

Design Best Practices for Dual-Axis Charts

• Use the y-axis on the left side for the primary variable because brains naturally look left first.
• Use different graphing styles to illustrate the two data sets, as illustrated above.
• Choose contrasting colors for the two data sets.

3. Area Chart

An area chart is basically a line chart, but the space between the x-axis and the line is filled with a color or pattern. It is useful for showing part-to-whole relations, like showing individual sales reps’ contributions to total sales for a year. It helps you analyze both overall and individual trend information.

Best Use Cases for These Types of Charts

Area charts help show changes over time. They work best for big differences between data sets and help visualize big trends.

For example, the chart above shows users by creation date and life cycle stage.

A line chart could show more subscribers than marketing qualified leads. But this area chart emphasizes how much bigger the number of subscribers is than any other group.

These charts make the size of a group and how groups relate to each other more visually important than data changes over time.

Area graphs can help your business to:

• Visualize which product categories or products within a category are most popular.
• Show key performance indicator (KPI) goals vs. outcomes.
• Spot and analyze industry trends.

Design Best Practices for Area Charts

• Use transparent colors so information isn't obscured in the background.
• Don't display more than four categories to avoid clutter.
• Organize highly variable data at the top of the chart to make it easy to read.

4. Stacked Bar Chart

Use this chart to compare many different items and show the composition of each item you’re comparing.

These graphs are helpful when a group starts in one column and moves to another over time.

For example, the difference between a marketing qualified lead (MQL) and a sales qualified lead (SQL) is sometimes hard to see. The chart above helps stakeholders see these two lead types from a single point of view — when a lead changes from MQL to SQL.

Stacked bar charts are excellent for marketing. They make it simple to add a lot of data on a single chart or to make a point with limited space.

These graphs can show multiple takeaways, so they're also super for quarterly meetings when you have a lot to say but not a lot of time to say it.

Stacked bar charts are also a smart option for planning or strategy meetings. This is because these charts can show a lot of information at once, but they also make it easy to focus on one stack at a time or move data as needed.

You can also use these charts to:

• Show the frequency of survey responses.
• Identify outliers in historical data.
• Compare a part of a strategy to its performance as a whole.

Design Best Practices for Stacked Bar Graphs

• Best used to illustrate part-to-whole relationships.
• Use contrasting colors for greater clarity.
• Make the chart scale large enough to view group sizes in relation to one another.

5. Mekko Chart

Also known as a Marimekko chart, this type of graph can compare values, measure each one's composition, and show data distribution across each one.

It's similar to a stacked bar, except the Mekko's x-axis can capture another dimension of your values — instead of time progression, like column charts often do. In the graphic below, the x-axis compares the cities to one another.

Image Source

You can use a Mekko chart to show growth, market share, or competitor analysis.

For example, the Mekko chart above shows the market share of asset managers grouped by location and the value of their assets. This chart clarifies which firms manage the most assets in different areas.

It's also easy to see which asset managers are the largest and how they relate to each other.

Mekko charts can seem more complex than other types of charts and graphs, so it's best to use these in situations where you want to emphasize scale or differences between groups of data.

Other use cases for Mekko charts include:

• Detailed profit and loss statements.
• Revenue by brand and region.
• Product profitability.
• Share of voice by industry or niche.

Design Best Practices for Mekko Charts

• Vary your bar heights if the portion size is an important point of comparison.
• Don't include too many composite values within each bar. Consider reevaluating your presentation if you have a lot of data.
• Order your bars from left to right in such a way that exposes a relevant trend or message.

6. Pie Chart

A pie chart shows a static number and how categories represent part of a whole — the composition of something. A pie chart represents numbers in percentages, and the total sum of all segments needs to equal 100%.

The image above shows another example of customers by role in the company.

The bar graph example shows you that there are more individual contributors than any other role. But this pie chart makes it clear that they make up over 50% of customer roles.

Pie charts make it easy to see a section in relation to the whole, so they are good for showing:

• Customer personas in relation to all customers.
• Revenue from your most popular products or product types in relation to all product sales.
• Percent of total profit from different store locations.

Design Best Practices for Pie Charts

• Don't illustrate too many categories to ensure differentiation between slices.
• Ensure that the slice values add up to 100%.
• Order slices according to their size.

7. Scatter Plot Chart

A scatter plot or scattergram chart will show the relationship between two different variables or reveal distribution trends.

Use this chart when there are many different data points, and you want to highlight similarities in the data set. This is useful when looking for outliers or understanding your data's distribution.

Scatter plots are helpful in situations where you have too much data to see a pattern quickly. They are best when you use them to show relationships between two large data sets.

In the example above, this chart shows how customer happiness relates to the time it takes for them to get a response.

This type of graph makes it easy to compare two data sets. Use cases might include:

• Employment and manufacturing output.
• Retail sales and inflation.
• Visitor numbers and outdoor temperature.
• Sales growth and tax laws.

Try to choose two data sets that already have a positive or negative relationship. That said, this type of graph can also make it easier to see data that falls outside of normal patterns.

Design Best Practices for Scatter Plots

• Include more variables, like different sizes, to incorporate more data.
• Start the y-axis at 0 to represent data accurately.
• If you use trend lines, only use a maximum of two to make your plot easy to understand.

8. Bubble Chart

A bubble chart is similar to a scatter plot in that it can show distribution or relationship. There is a third data set shown by the size of the bubble or circle.

In the example above, the number of hours spent online isn't just compared to the user's age, as it would be on a scatter plot chart.

Instead, you can also see how the gender of the user impacts time spent online.

This makes bubble charts useful for seeing the rise or fall of trends over time. It also lets you add another option when you're trying to understand relationships between different segments or categories.

For example, if you want to launch a new product, this chart could help you quickly see your new product's cost, risk, and value. This can help you focus your energies on a low-risk new product with a high potential return.

You can also use bubble charts for:

• Top sales by month and location.
• Customer satisfaction surveys.
• Store performance tracking.
• Marketing campaign reviews.

Design Best Practices for Bubble Charts

• Scale bubbles according to area, not diameter.
• Make sure labels are clear and visible.
• Use circular shapes only.

9. Waterfall Chart

Use a waterfall chart to show how an initial value changes with intermediate values — either positive or negative — and results in a final value.

Use this chart to reveal the composition of a number. An example of this would be to showcase how different departments influence overall company revenue and lead to a specific profit number.

The most common use case for a funnel chart is the marketing or sales funnel. But there are many other ways to use this versatile chart.

If you have at least four stages of sequential data, this chart can help you easily see what inputs or outputs impact the final results.

For example, a funnel chart can help you see how to improve your buyer journey or shopping cart workflow. This is because it can help pinpoint major drop-off points.

Other stellar options for these types of charts include:

• Deal pipelines.
• Conversion and retention analysis.
• Bottlenecks in manufacturing and other multi-step processes.
• Marketing campaign performance.
• Website conversion tracking.

Design Best Practices for Funnel Charts

• Scale the size of each section to accurately reflect the size of the data set.
• Use contrasting colors or one color in graduated hues, from darkest to lightest, as the size of the funnel decreases.

11. Heat Map

A heat map shows the relationship between two items and provides rating information, such as high to low or poor to excellent. This chart displays the rating information using varying colors or saturation.

Best Use Cases for Heat Maps

In the example above, the darker the shade of green shows where the majority of people agree.

With enough data, heat maps can make a viewpoint that might seem subjective more concrete. This makes it easier for a business to act on customer sentiment.

There are many uses for these types of charts. In fact, many tech companies use heat map tools to gauge user experience for apps, online tools, and website design .

Another common use for heat map graphs is location assessment. If you're trying to find the right location for your new store, these maps can give you an idea of what the area is like in ways that a visit can't communicate.

Heat maps can also help with spotting patterns, so they're good for analyzing trends that change quickly, like ad conversions. They can also help with:

• Competitor research.
• Customer sentiment.
• Sales outreach.
• Campaign impact.
• Customer demographics.

Design Best Practices for Heat Map

• Use a basic and clear map outline to avoid distracting from the data.
• Use a single color in varying shades to show changes in data.
• Avoid using multiple patterns.

12. Gantt Chart

The Gantt chart is a horizontal chart that dates back to 1917. This chart maps the different tasks completed over a period of time.

Gantt charting is one of the most essential tools for project managers. It brings all the completed and uncompleted tasks into one place and tracks the progress of each.

While the left side of the chart displays all the tasks, the right side shows the progress and schedule for each of these tasks.

This chart type allows you to:

• Break projects into tasks.
• Track the start and end of the tasks.
• Set important events, meetings, and announcements.
• Assign tasks to the team and individuals.

Download the Excel templates mentioned in the video here.

5 Questions to Ask When Deciding Which Type of Chart to Use

1. do you want to compare values.

Charts and graphs are perfect for comparing one or many value sets, and they can easily show the low and high values in the data sets. To create a comparison chart, use these types of graphs:

• Scatter plot

2. Do you want to show the composition of something?

Use this type of chart to show how individual parts make up the whole of something, like the device type used for mobile visitors to your website or total sales broken down by sales rep.

To show composition, use these charts:

• Stacked bar

3. Do you want to understand the distribution of your data?

Distribution charts help you to understand outliers, the normal tendency, and the range of information in your values.

Use these charts to show distribution:

4. Are you interested in analyzing trends in your data set?

If you want more information about how a data set performed during a specific time, there are specific chart types that do extremely well.

You should choose one of the following:

• Dual-axis line

5. Do you want to better understand the relationship between value sets?

Relationship charts can show how one variable relates to one or many different variables. You could use this to show how something positively affects, has no effect, or negatively affects another variable.

When trying to establish the relationship between things, use these charts:

Featured Resource: The Marketer's Guide to Data Visualization

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Title: haar graphical representations of finite groups and an application to poset representations.

Abstract: Let $R$ be a group and let $S$ be a subset of $R$. The Haar graph $\mathrm{Haar}(R,S)$ of $R$ with connection set $S$ is the graph having vertex set $R\times\{-1,1\}$, where two distinct vertices $(x,-1)$ and $(y,1)$ are declared to be adjacent if and only if $yx^{-1}\in S$. The name Haar graph was coined by Tomaž Pisanski in one of the first investigations on this class of graphs. For every $g\in R$, the mapping $\rho_g:(x,\varepsilon)\mapsto (xg,\varepsilon)$, $\forall (x,\varepsilon)\in R\times\{-1,1\}$, is an automorphism of $\mathrm{Haar}(R,S)$. In particular, the set $\hat{R}:=\{\rho_g\mid g\in R\}$ is a subgroup of the automorphism group of $\mathrm{Haar}(R,S)$ isomorphic to $R$. In the case that the automorphism group of $\mathrm{Haar}(R,S)$ equals $\hat{R}$, the Haar graph $\mathrm{Haar}(R,S)$ is said to be a Haar graphical representation of the group $R$. Answering a question of Feng, Kovács, Wang, and Yang, we classify the finite groups admitting a Haar graphical representation. Specifically, we show that every finite group admits a Haar graphical representation, with abelian groups and ten other small groups as the only exceptions. Our work on Haar graphs allows us to improve a 1980 result of Babai concerning representations of groups on posets, achieving the best possible result in this direction. An improvement to Babai's related result on representations of groups on distributive lattices follows.

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• Published: 22 April 2024

TO-UGDA: target-oriented unsupervised graph domain adaptation

• Zhuo Zeng 1 , 2 ,
• Jianyu Xie 1 , 2 ,
• Zhijie Yang 1 , 2 ,
• Tengfei Ma 3 &
• Duanbing Chen 1 , 2 , 4  

Scientific Reports volume  14 , Article number:  9165 ( 2024 ) Cite this article

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• Computational science
• Computer science
• Information technology

Graph domain adaptation (GDA) aims to address the challenge of limited label data in the target graph domain. Existing methods such as UDAGCN, GRADE, DEAL, and COCO for different-level (node-level, graph-level) adaptation tasks exhibit variations in domain feature extraction, and most of them solely rely on representation alignment to transfer label information from a labeled source domain to an unlabeled target domain. However, this approach can be influenced by irrelevant information and usually ignores the conditional shift of the downstream predictor. To effectively address this issue, we introduce a target-oriented unsupervised graph domain adaptive framework for graph adaptation called TO-UGDA. Particularly, domain-invariant feature representations are extracted using graph information bottleneck. The discrepancy between two domains is minimized using an adversarial alignment strategy to obtain a unified feature distribution. Additionally, the meta pseudo-label is introduced to enhance downstream adaptation and improve the model’s generalizability. Through extensive experimentation on real-world graph datasets, it is proved that the proposed framework achieves excellent performance across various node-level and graph-level adaptation tasks.

Introduction

Graph neural networks (GNNs) typically rely on end-to-end supervision for training, which often demands a large amount of labeled data 1 , 2 . Manual labeling of graph data 3 , 4 , especially in the case of protein-protein interaction (PPI) networks 5 , is a time-consuming task. Furthermore, the absence of labels poses a significant challenge in newly-formed graph domains such as subway and aviation networks 6 , 7 . It is urgent to alleviate the challenge of sparse labels in the target domain by utilizing relevant or similar labeled domain graph data to train the models. However, recent research demonstrates that graph neural networks’ performance degrades when training models rely solely on labeled source data. The reason for this performance discrepancy is that the data used for training (labeled source data) and inference (unlabeled target data) originate from distinct distributions 8 , 9 . Consequently, training a well-generalized graph neural network model, especially for only source domain labeled data, presents a significant challenge.

In order to deal with this challenge, many scholars 10 , 11 , 12 , 13 adopt the framework of joint learning to reduce the difference between the representation distributions of two domains. The framework of joint learning can effectively improve the accuracy of target domain unlabeled data, but there are still several critical problems:

(1) The adaptive performance of representation alignment is limited by irrelevant feature interference 14 , 15 , 16 . For instance, in social networks, social networks where the distributions of users’ friendships (the input) and their activity patterns (the label) are significantly influenced by the time and location of data collection 17 . In financial networks 18 , the flows of payments between transactions (the input) and the emergence of illicit transactions (the label) exhibit a strong correlation with external contextual factors such as the time of day or market conditions. These external factors can act as confounding variables, hindering the effectiveness of representation alignment methods. (2) Alignment strategies of domain feature design exhibit variations in different-level graph tasks 19 , 20 , 21 . For example, in the field of graph-level biomolecular, enhancing the feature representation of the subgraph functional groups in a molecule that yield its certain properties may provide insights to guide further experiments 22 . In protein-protein interaction (PPI) networks 5 , node pairs of protein are often used for domain feature extraction to explore the interaction principles between two protein nodes. (3) Ignoring the semantic distribution shift of the target domain 23 , 24 , such as feature scarcity, varying noise, and temporal evolution, can lead to suboptimal performance in graph adaptation tasks. For instance, in citation networks, the distribution of citations and subject areas changes over time 25 , reflecting the evolving nature of academic research. To address this, it’s crucial to incorporate techniques that adapt to such shifts, enabling models to capture the current state of the network more accurately.

In this report, TO-UGDA addresses the challenge of irrelevant feature interference by leveraging the Graph Information Bottleneck (GIB) 26 , 27 . This innovative approach effectively filters out superfluous information, focusing solely on the most pertinent features for domain adaptation. This is achieved by learning a compressed representation of the graph structure, which captures the crucial patterns for task performance while excluding noise and irrelevant features. Furthermore, TO-UGDA offers a flexible framework that can seamlessly adapt to varying levels of graph tasks. By establishing a specific sub-graph i.i.d. assumption 28 and incorporating GIB-based adversarial adaptation training, our framework ensures robust alignment of domain features across diverse graph structures and tasks. This ranges from micro-level information in cross-network node classification to macro-level topology in cross-domain graph classification. Additionally, TO-UGDA incorporates meta pseudo-labels 29 , enabling the model to adapt to semantic distribution shifts in the target domain. By extracting self-semantic information from the target domain data, the model becomes more resilient to feature noise and time evolution, leading to enhanced adaptation and generalization capabilities. Experimental results demonstrate the effectiveness of our proposed method, achieving exceptional performance in two different-level graph tasks while exhibiting remarkable stability.

In summary, this report makes the following contributions:

From the perspective of the joint probability distribution, we define and explain the adaptation error bounds of the encoder and predictor.

We introduce a novel Target-Oriented Unsupervised Graph Domain Adaptation framework (TO-UGDA) that adopts a GIB-based adversarial strategy to align invariant graph feature representations and incorporates meta pseudo-labeling to bridge the gap in downstream semantic conditional adaptation, resulting in a more generalizable model.

TO-UGDA outperforms the baseline in adaptation of micro information in cross-network node classification tasks and macro topology information in cross-domain graph classification tasks.

Related works

Unsupervised domain adaptation.

Unsupervised domain adaptation (UDA), a crucial branch of transfer learning 30 , aims to address the problem of different distributions by minimizing the distribution discrepancy and transferring label knowledge of source domain 31 , 32 .

In recent years, many researchers have constantly advocated and paid attention to UDA, such as MMD 33 , DANN 34 , CDAN 35 and TLDA 36 . In this report, we mainly discuss the adversarial-based domain adaptation method 35 , 37 used in our framework. The main idea is minimizing the distance between the source and target domain representation to maximize the confusion of the domain discriminator, which forces the graph encoder can share relevant label knowledge and align feature distribution. The pioneering work DANN 34 uses the generative-adversarial method of GAN 38 to align two domains. MADA 39 and CDAN 35 take the downstream classification probability as the additional condition information to relieve the problem of downstream conditional shift.

However, it is noted that the assumption of independent and identically distributed (i.i.d.) of representation samples, which holds in classic research fields like computer vision 40 , 41 , natural language processing 42 , and signal processing technology 43 , does not directly apply to graph domain adaptation. In the graph domain, the graph representation depends on neighboring nodes and edges 44 , making it challenging to satisfy the i.i.d. assumption.

• Graph domain adaptation

In recent years, many researchers in the graph field have proposed graph adaptive learning methods to resolve the alignment challenge under the non-i.i.d. assumptions, which can be divided into two different level types, node-level adaptation, and graph-level adaptation.

Node-level adaptation, which can also be considered as a cross-network task involving the alignment of source and target entire connected networks, has been explored in recent years. UDAGCN 10 introduces the gradient reversal layer to align cross-network node embedding and develops a dual GCN component to ensure the local and global representation consistency of each node and reduce the irrelevant domain feature dependence. GRADE 45 proposes a novel graph subtree discrepancy to measure the graph distribution shift between source and target networks, reduces irrelevant domain feature messages passing through graph subtrees and establishes constrained generalized error boundaries.

Graph-level adaptation gives rise to an interesting phenomenon where the graph macro topology representation satisfies the assumption of i.i.d. within the intra-domain (between graphs), but not within the node embedding of the graph itself (between nodes in the same graph) 46 , 47 . Therefore, it is crucial to strike a balance in the multi-player game of graph node representation, intra-domain topology information, and reducing outer-domain discrepancy. To tackle this challenge, DEAL 24 employs a clever strategy that combines data augmentation with contrastive learning to address the challenging balance issue that arises in multi-party games. Furthermore, it leverages the encoding features of shallow graph neural networks as clustering information, enabling a clear and distinct differentiation between labels in the target domain. This approach not only enhances the extraction of domain topology feature information but also ensures a more robust and effective performance in handling the complexities of multi-party gaming scenarios. COCO 48 proposes a coupled graph representation learning approach to extract invariant domain topology information and reduce the domain discrepancy by two different feature encoding modules, which incorporates graph representations learned from complementary views for enhanced domain topology information understanding.

These methods effectively relieve the problem of unsupervised graph domain adaptation. Below we briefly introduce the two main methods used in this report: Graph Information Bottleneck (GIB) 26 , 27 is a principle used in graph neural networks to balance the complexity and robustness of learned representations. It ensures that the representation captures enough information to perform the task while avoiding irrelevant information that could lead to overfitting and alignment interference. Meta Pseudo-Labels 29 is a knowledge distillation technique where the model generating pseudo labels for unlabeled data adjusts its predictions based on the performance of another model trained with these labels. This feedback loop refines the pseudo labels, leading to better model performance over time.

Problem definition and analysis

This section defines two graph adaptation tasks and analyzes the adaptive error bound of the encoder and predictor from the perspective of the joint probability distribution.

Problem statement

Inspired by previous works on graph domain adaptation 10 , 45 , 48 , 49 , we formally define two different problems of graph domain adaptation in detail.

Problem Formulation 1

(Cross-Network Node Adaptation) Given an unlabeled target single network \(G^{t}\) and a labeled source network \((G^{s},Y)\) , cross-network node adaptation aims to improve the prediction performance of Node-Level task in the target network by using knowledge from the source network.

Problem Formulation 2

(Cross-Domain Graph Adaptation) Given an unlabeled target domain dataset \(D^{t}\) and a labeled source domain dataset \((D^{s},Y)\) , the purpose of cross-domain graph adaptation is to improve the accuracy of Graph-Level property prediction in the target domain dataset by using knowledge from the source domain.

Adaptation error bound of encoder and predictor

In graph tasks, it is common to utilize classic architecture such as GNN encoder P ( X ) and classifier P ( Y | X ) to model the joint distribution P ( X ,  Y ) between data and labels 50 :

Aligning the joint distribution requires two steps, as shown in Fig. 1 . The first step is to align the representations of the source domain and target domain data as closely as possible, and the second step is to fine-tune the source domain classifier by extracting the conditional information from the target domain itself.

Two main steps of domain adaptation.

According to two main steps in Fig. 1 , we provide adaptation objective definitions from the perspectives of marginal distribution alignment and conditional distribution alignment.

Adaptation Objective 1

(Marginal Distribution Adaptation) Given the source and target graph representations \({H^{s}, H^{t}}\) obtained using the same GNN module with parameter \(\theta _f\) , margin distribution adaptation refers to minimize the distribution discrepancy of \(d\big (P_{s}(x), P_{t}(x)\big )\) of \(\{H^{s}, H^{t}\}\) , which can be defined as \(\underset{\theta _f}{{\text {argmin}}} \Delta _{d}=\underset{\theta _f}{{\text {argmin}}} \int _{-{\infty }}^{+{\infty }} d\big (P_s({x}), P_t({x})\big )dx\) .

Adaptation Objective 2

(Conditional Distribution Adaptation) Given source and target graph classifiers with parameter \(\{\theta _c^{s},\theta _c^{t}\}\) , assume conditional distribution \(\{P_{s}(y|x),P_{t}(y|x)\}\) of two classifiers can be applied on share representation P ( x ), therefore semantic distribution adaptation can be defined as \(\underset{\theta _c^{s},\theta _c^{t}}{{\text {argmin}}} \Delta _{d}=\underset{\theta _c^{s},\theta _c^{t}}{{\text {argmin}}} \int _{-{\infty }}^{+{\infty }} d\big (P_{s}(y|x),P_{t}(y|x)\big )P(x)dxdy\) .

Methodology

To optimize these two objectives, there are three key steps in the TO-UGDA training process: (1) Joint pre-training of source and target domain data; (2) GIB-based domain adaptation; (3) Unsupervised meta pseudo-label learning. The model architecture is depicted in Fig. 2 .

Joint pre-training initialization based on contrastive learning

Contrastive pre-training initialization has been proven to be beneficial for various graph tasks 51 , 52 . By combining data from two domains and applying self-supervised contrastive learning, the GNN encoder \(Z=F(x)\) is capable of learning generalized feature embedding and unifying the representation space.

For a given original sample \(x_i\) , multiple similar disturbance samples \({ x_j }\) constitute a part of the positive pairs, and other samples that are far from the given original sample are constructed as negative pairs. The initialization GNN encoder is trained using a contrastive learning loss function:

where \(sim(\cdot , \cdot )\) denotes cosine similarity between two vectors and \(\tau\) is a temperature parameter. This loss function encourages the embeddings of the positive pair \((x_i, x_j^+)\) to be close to each other while pushing the embeddings of the negative pair \((x_i, x_j^-)\) further apart.

TO-UGDA model architecture includes three main modules: 1) Joint pre-training module for initialization; 2) GIB-based domain adaptation module for aligning invariant features; 3) Meta pseudo-label learning for conditional distribution adaptation.

GIB-based invariant representation domain adaptation

Graph embedding violates the i.i.d. assumption, posing an alignment challenge for acquiring invariant information due to the node representation dependence on their neighboring nodes. Therefore, TO-UGDA needs to design a special encoder to extract invariant information, and then build GIB-based domain adaptation.

Invariant graph representation

As assumed by information theory 26 , 28 , node representations can be locally dependent on their important neighboring structures. Therefore, we establish a specific i.i.d. assumption that local neighborhood structure can represent each node in the graph, which enables it to adopt representation learning based on mutual information to extract invariant features.

In this report, we extract crucial neighborhood structural information from the original graph structure, denoted as \(A_v^{(l)}\) and described by a Bernoulli distribution with parameter \(\alpha _{v}^{(l)} \in [0, 1]\) . This information is obtained to update the node representation \(Z_v^{(l)}\in R^{n}\) using the l -th layer GNN with parameter \(W^{(l)}\) , as detailed below:

where, \(N_v\) represents the node number about neighborhood structure \(G_v\) of node v . Furthermore, the graph-level representation utilizes a \({\text {Readout}}(\cdot )\) function to represent each graph in the dataset, which is defined as:

where \(Z_G\in R^{n}\) is the n -dimensional invariant feature representation of input samples.

GIB-based domain adaptation

Inspired by information bottleneck theory 26 , 53 , the adaptation module of TO-UGDA is encouraged to maximize the mutual information between the source domain representation \(Z_s\) and the label \(Y_s\) to enhance prediction accuracy on source labeled data \((X_s,Y_s)\) , and maximize the mutual information between two domains representation \((Z_s,Z_t)\) to align domain distribution. Finally, the graph information bottleneck avoids the interference of excessive irrelevant information. Therefore, the multi-objective optimization can be defined as:

where, \(\Omega\) is the search space of the optimal representation model \(\mathbb {P} (Z|X)\) , \(I(\cdot ;\cdot )\) denotes the mutual information, \(I^{S}(X_s; Z_s) \le \gamma\) and \(I^{T}(X_t; Z_t) \le \gamma\) act as double GIBs constraints enable to limit the propagation of both domains information between the original input samples X and their invariant feature representation Z .

Due to the high computational complexity of mutual information measurement in the calculation process of constraint term, the variational upper bound \(I^{up}(X; Z)\) is used to effectively implement double GIBs information constraints about \(I^{S}(X_s; Z_s)\) and \(I^{T}(X_t; Z_t)\) , and the proof is detailed in Supplementary Appendix A .

The first objective term \(\max I\left( Z_s; Y_s\right)\) in Eq. ( 5 ) can be equivalently achieved by minimizing the classification loss \(\mathcalligra {L}_{c l a}\left( F, C ; \theta _{f, c}\right)\) for the representation Z about the graph data G via invariant sub-information \(G_{sub}\) , as follows:

where, \(\mathbb {P}_{\theta }\left( Y \mid G_{sub}\right)\) is a variational approximation of \(\mathbb {P}\left( Y \mid G_{sub}\right)\) to solve the intractable challenge of \(\mathbb {P}\left( Y \mid G_{sub}\right)\) , the proof is detailed in Supplementary Appendix B1 and B2 .

Meanwhile, the second objective term \(\max I\left( Z_s; Z_t\right)\) in Eq. ( 5 ) can be equivalently achieved by the adversarial loss \(\mathcalligra {L}_{a d v}\left( F, D ; \theta _{f, d}\right)\) of the discriminator D to maximize the lower-bound Donsker-Varadhan Representation 54 , 55 , as follows:

where, \(\mathcalligra {L}_{adv}\left( F, D ; \theta _{f, d}\right)\) is an instance \(D_{\theta }\) of any class \(\mathcalligra {F}\) of function \(T:\Omega \rightarrow \mathbb {R}\) , which satisfying the integrability constraints of the Donsker-Varadhan Representation by a deep neural network with parameter \(\theta \in \Theta\) to obtain the lower-bound Donsker-Varadhan Representation \(I_{\theta }^{DV} \left( Z_s; Z_t\right)\) , the proof is detailed in Supplementary Appendix B3 .

Each mutual information term in Eq. ( 5 ) can be efficiently calculated, therefore, the final adaptation optimization loss function is:

where \(\beta\) is the weight factor about invariant representation, and the Eq. ( 8 ) is derived from Eq. ( 5 ) by GIB paradigm 26 and Lagrange multiplier approach, the proof is detailed in Supplementary Appendix B4 .

The GIB-based domain adaptation ensures that only the invariant features of two domains can be aligned to the same representation distribution and transfer the label information Y .

Unsupervised meta pseudo-label distillation

Inspired by meta pseudo-label knowledge distillation 29 , the teacher model actively participates in Boundary Bargaining Game (a term referring to the process of refining decision boundaries) and knowledge propagation on unlabeled data. Meanwhile, the student’s performance, which feeds back on labeled data testing after pseudo-label distillation from the teacher model, influences the direction and weight of the boundary games in the teacher model’s next step. This balance ensures both the generalization of unlabeled data and the fitting of labeled data.

In our work, we also consider target domain as the most crucial aspect, that the approach effectively reduces the discrepancy of conditional distribution adaptation \(\int _{-{\infty }}^{+{\infty }} d\big (P_{s}(y|x),P_{t}(y|x)\big )P(x)dxdy\) about the self-semantic information of target domain and the transfer knowledge of the source domain by the student testing performance. Furthermore, it alleviates the limitation of current graph adaptation methods, which often overemphasize source-labeled data and neglect target domain semantic conditional information. However, the most crucial step here is how the teacher model updates based on the performance of the student model.

Let T and S denote the teacher model and the student model, respectively, parameterized by \(\theta _T\) and \(\theta _S\) . The ultimate training objective of TO-UGDA lies in achieving Bargaining Game’s Nash equilibrium between the self-semantic information of the target domain and the transfer knowledge of the source domain, by quantifying the classification loss of the student \(\theta _S\) on unseen true labeled source domain data:

where \(\theta _S(\theta _T)\) represents the relationship that student \(\theta _S\) rely on the pseudo-label generated by teacher \(\theta _T\) .

During the bargaining distillation process, the student model is trained using pseudo labels generated by the teacher model in the target domain, and the teacher model is updated based on the student’s test performance on unseen true labeled source domain data. However, it is a challenge to directly update the teacher model’s parameters and achieve the Nash equilibrium of the bargaining distillation process by the performance of the student model. This process involves three key steps, as follows:

(1) Training the teacher model using labeled source domain dataset and unlabeled target domain dataset, with the optimization objective for \(\theta _T\) can be defined as:

where \(\mathcalligra {L}_{\text{ adapt }}\) is the adaptation loss function presented in Eq. ( 8 ).

(2) Training the student model \(\theta _S\) using the pseudo labels \((x_t, {\hat{y}}_t)\) generated by the teacher model \(\theta _T\) , the optimization objective is:

where student model \(\theta _S\) is initialized based on unsupervised semantic clustering.

(3) Obtaining the bargaining distillation loss \(\mathcalligra {L}_{\text{ distill }}(T,S;[x_s, x_t, y_s])\) , which is used to correct the updating direction of the teacher model based on the performance of the student model’s parameters, as follows:

where \(\mathcalligra {L}_{\text{ distill }}\) is expressed as the product of two derivatives (the student testing performance of pseudo-label and the teacher adaptation of soft pseudo-label), the details of the proof are described in Supplementary Appendix C1 . Therefore, the updated adaptation loss function of teacher model is:

In the learning process, the student model can improve the adaptive ability of the overall model in the target domain, by leveraging target domain self-semantic information to limit the parameter search space of the teacher model. This method is helpful to improve the accuracy and efficiency of target domain prediction. Specifically, we describe the training algorithm of TO-UGDA in the Supplementary Appendix C2 .

Experiments and analysis

The effectiveness of the method is evaluated on multiple adaptation datasets with varying cause types, demonstrating its generalized adaptability. Detailed statistics are presented in Tables 1 and 2 . In addition, we present the results of experiments on cross-network (node-level) and cross-domain (graph-level) adaptation tasks.

Cross-network

Air-Traffic Network 56 : The dataset comprises air traffic networks in the United States, Europe, and Brazil, where each node represents an airport and an edge indicates the presence of commercial flights. The categories of airports are determined based on building size and aircraft activity.

Citation Networks 57 : The citation networks DBLPv8 and ACMv9 are two paper citation networks. Each edge in these networks represents the citation relationship between two papers, where each node represents a paper and the class label indicates the research topic.

Cross-domain

In our experiment, we utilized various real-world datasets from different research areas and backgrounds in TUDataset 58 to compare the performance of different baselines.

Mutagenicity : The mutagenicity dataset comprises molecular structures and Ames test data. We divide the molecular structures into four different distribution sub-datasets (namely M0, M1, M2, and M3) based on the edge density of these structures.

Letter-Drawings : This dataset consists of distorted letter drawings, as well as their variations at different intensity levels (low, medium, and high). For each class, multiple prototype drawings are manually constructed by using undirected edges and nodes to represent the handwritten alphabet.

NCI : A biological dataset for the classification of anticancer activities. In this dataset, each graph represents a chemical compound, where nodes and edges represent atoms and chemical bonds, respectively. NCI1 is an activity screening for non-small cell lung cancer cells, and NCI109 is an activity screening for ovarian cancer cells.

Three type baseline models are used for cross-network node classification adaptation: (1) Source-Only: GCN 59 , SGC 60 , GCNII 61 ; (2) Node Feature-Only adaptation: CDAN 35 , DANN 62 , MDD 63 ; (3) cross-network adaptation: AdaGCN 64 , UDAGCN 10 , EGI 49 , and GRADE 45 . For cross-domain graph classification adaptation, the following three type baselines are used to compare: (1) Source-Only: GCN 59 , SGC 60 , GIN 44 , (2) Traditional domain adaptation methods: CDAN 35 , ToAlign 65 and MetaAlign 66 , whose feature encoder is replaced with GCN. (3) Graph cross-domain adaptation: DEAL 24 and COCO 48 , a customized framework for adaptation tasks of graph classification.

Implementation details

We adopt a two-hidden-layer graph convolutional network as the feature extractor and a single layer of fully connected neural networks. In addition, the teacher model and the student model are optimized using SGD and Adam optimizers, with learning rates of 0.02 and 0.001. Each experimental result is the mean value through three repetitions and 200 epochs. We use Accuracy(ACC) as the classification metric.

Performance comparison

We conducted extensive experiments on the Air-Traffic Networks and Citation Networks. The experiment results of all methods in node classification are shown in Tables 3 and 4 . From Tables 3 and 4 , it can be seen that (1) Node Feature-Only adaptation performs worse than the Source-Only method in Citation Network. This can be attributed to the presence of an obvious community structure and topic citation style in Citation Network. (2) Cross-network adaptation achieves the best performance in node adaptation classification compared to other baselines. The reason is that the cross-network adaptation method can simultaneously align node features and topological structure information, effectively enhancing the model’s adaptability to graph-structured data. (3) TO-UGDA outperforms all other methods in node adaptation classification. Specifically, TO-UGDA achieves improvements of 3.8% to 14.5%, and 6.5% to 25.3% on the Air-Traffic and Citation networks, respectively.

Cross-domain adaptation is a multi-graph alignment problem, resulting in diverse application scenarios for adaptation. We conducted experiments on three representative datasets: Mutagenesis (for edge density adaptation), Letter-drawing (for noise interference adaptation), and NCI (for label application adaptation).

The experimental results of all methods in graph classification are shown in Tables 5 , 6 , and 7 . Several observations need to be highlighted: (1) Traditional domain adaptation methods did not show performance improvement, compared to the Source-Only method in three graph domain datasets. This is because cross-domain adaptation is susceptible to noise affecting the graph structure and irrelevant feature information from neighboring nodes. (2) Graph cross-domain adaptation outperforms other baselines by incorporating shallow representation semantic information and topological structure alignment. (3) TO-UGDA outperforms all compared methods in graph adaptation classification. Specifically, TO-UGDA achieves improvements of 0.2% to 18.9%, 3.8% to 18.92%, and 3.26% to 11.06% on the Mutagenicity, Letter-Drawing and NCI datasets, respectively. These significant breakthroughs can be attributed to the incorporation of GIB-based domain adversarial learning and pseudo-label knowledge distillation, making our model more generalized and adaptable to diverse adaptation scenarios.

Ablation study

We conduct an ablation study and analysis using citation networks as an example. In this study, we selectively remove components of TO-UGDA: pre-training with joint contrastive learning (Pre-Training), GIB-based domain adversarial adaptation (GIBDA), and pseudo-label knowledge distillation (Distill). This process results in six different variant models (A-F).

The results of ablation studies on Citation Dataset, ‘/’ represents the removal of the module.

The ablation results are shown in Fig. 3 , and we can obtain several observations. (1) The complete TO-UGDA outperforms all other variant models, which validates the importance of each module in unsupervised graph adaptation. (2) The score of variant C rapidly drops by 10.9% and 9.2% when the GIBDA component is removed, empirically validating the significance of invariant feature alignment. (3) Compared to variant D, the removal of the Distill component caused a decrease of 4.5% and 5.1%. This demonstrates that pseudo-label knowledge distillation effectively mines latent target-oriented information. (4) Comparing variants C and E, after removing GIBDA, the existence of the Distill module still reduces the accuracy by 2.5% and 1.2%, indicating that the latent information mining of Distill relies on the invariant feature filter and alignment.

Training stability evaluation and adaptation weight analysis

Models with weak adaptive ability are prone to exhibiting significant fluctuations in target domain accuracy, both before and after each round of parameter updates. Furthermore, our method exhibits superior convergence performance compared to other methods, even in early training iterations, as depicted in Fig. 4 . This demonstrates the effectiveness of our approach, which benefits from the initialization of joint pre-training, enabling faster convergence and reduced training costs.

Additionally, in Fig. 5 , we observed that the performance of TO-UGDA initially increases and then decreases as the adaptation weight parameter \(\beta\) varies from 0 to 0.05. This phenomenon occurs because a small weight for GIBDA fails to provide sufficient graph adaptation and invariant feature representation ability, while a large weight misleads the objective function, neglecting the learning of source domain features and labels.

Training stability (Left:L \(\rightarrow\) M; Right:M \(\rightarrow\) L).

Adaptation weight analysis.

Visualization of T-SNE

The visualization of the graph representations learned from our method and other baselines has been presented in Fig. 6 . We observed that (1) Traditional adversarial domain adaptive method CDAN overly focus on complete feature distribution alignment, causing significant alignment interference by irrelevant features, as shown in Figs. 6 b and f. (2) The representation distribution of TO-UGDA exhibits better local clustering and global separation in classification than GIN and DEAL in Fig. 6 d. The source domain and target domain data distributions exhibit good alignment performance in Fig. 6 h.

Source(Letter-Low) \(\rightarrow\) Target(Letter-Med): Visualize the extracted features through T-SNE. The colors in the first row represent different categories, while the colors in the second row represent different domains.

Conclusions and future work

In conclusion, we have defined the adaptive error bounds of the encoder and predictor, explaining them from the perspective of joint distribution probability. Drawing inspiration from this analysis, we propose TO-UGDA, a novel graph domain adaptation framework that leverages invariant feature alignment to extract essential information while discarding irrelevant details. TO-UGDA effectively addresses the challenges of Target-Oriented Unsupervised Graph Domain Adaptation. Extensive experimentation has demonstrated the superior performance of TO-UGDA over all baselines. The experimental outcomes demonstrate that by aligning invariant features, our model can effectively capture shared invariant features between the source and target domains. These invariant features remain consistent across different domains, enabling the model to seamlessly adapt to novel and unprecedented data, thereby enhancing its generalization capabilities. Furthermore, by emphasizing these invariant features, our approach minimizes the negative transfer effects that often arise due to domain discrepancies. Additionally, incorporating semantic information into the target domain further aids the model in grasping the intricate relationships between transferred knowledge and the inherent structure and meaning of the target domain data. Consequently, the model becomes more adept at precisely capturing semantic information within the target domain and learning label knowledge from the source domain, ultimately leading to improved performance in the target domain.

In the future, we will further research and explore how graph information bottleneck theory can select efficient compression strategies in graph adaptation tasks and avoid overfitting in the source domain. And how to avoid the potential amplification of the impact of adversarial attacks on meta pseudo labels during multiple distillation processes. At the same time, we plan to conduct experiments on the domain adaptation task of node-link prediction. We also aim to explore interpretable research to identify the invariant features in the source and target domains and uncover the captured semantic information in the target domain. This deeper understanding and analysis of graph adaptation tasks will facilitate further advancements in the field.

Data availability

The data supporting the findings of this study are available within the manuscript or supplementary information files.

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Acknowledgements

This work was supported by the Major Program of the National Natural Science Foundation of China with Grant No T2293771, by the Innovation Research Group Project of the Natural Science Foundation of Sichuan with Grant No 24NSFTD0129 and by the Key Research and Development Project of Sichuan with Grant No 24ZDYF0004.

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Zhuo Zeng, Jianyu Xie, Zhijie Yang & Duanbing Chen

Chengdu Union Big Data Tech. Inc., Chengdu, 610041, China

College of Information Science and Engineering, Hunan University, Changsha, 410082, China

Suining Institute of Digital Economy, Suining, 629018, China

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Z. Z. developed the theoretical framework, conducted the majority of the experiments, and wrote the initial draft of the manuscript. J. X. and Z. Y. contributed to the initial brainstorming sessions, offering ideas and assisting with some experiments. T. M. provided analysis and advice on the research problems. D. C. provided valuable guidance, funding support, and essential computational resources for the research, and revised the manuscript. All authors have read and approved the final version of the manuscript.

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Zeng, Z., Xie, J., Yang, Z. et al. TO-UGDA: target-oriented unsupervised graph domain adaptation. Sci Rep 14 , 9165 (2024). https://doi.org/10.1038/s41598-024-59890-y

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DOI : https://doi.org/10.1038/s41598-024-59890-y

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