Fundamental Graphs and Data Transformation

CS-GY 6313 - Information Visualization - Fall 2025

Claudio Silva

NYU Tandon School of Engineering

2025-09-12

Today’s Agenda

Learning Objectives: - Understand the two-step visualization process - Master the five fundamental graph types - Apply expressiveness and effectiveness principles - Learn essential data transformation techniques - Recognize the impact of scales and axes choices

Today we’re building the foundation for effective visualization design. We’ll move from abstract principles to concrete techniques you can apply immediately.

The Visualization Process

The fundamental question: How do I visualize this data?

• Step 1: What to visualize? (Data selection & transformation)
• Step 2: How to visualize? (Visual encoding & design)

Start with the fundamental question every data analyst faces. The process breaks down into two critical steps that we’ll explore in detail today. This isn’t just theory - it’s the practical workflow you’ll use in every visualization project.

Step 1: What to Visualize?

Data Selection & Transformation:

• Which attributes matter for your question?
• What level of detail is appropriate?
• How should data be aggregated or filtered?
• What derived attributes might be useful?

Example: Domain questions to data transformation

This step is often underestimated but crucial. The wrong data selection can make even the best visual design ineffective. We’ll see concrete examples of transformations that unlock insights.

Step 2: How to Visualize?

Visual Encoding & Design:

• Which visual channels best represent your data?
• How do you map data attributes to visual properties?
• What design choices enhance clarity?
• How do you avoid misleading representations?

Example: Same data, different visual encodings

This is where art meets science. We’ll learn principled approaches to make these choices, backed by research on human perception and cognition.

The Five Fundamental Graphs

Scatter Plot

These five chart types are your visualization toolkit’s power tools. Master these, and you’ll be able to tackle the vast majority of visualization challenges. They’re also building blocks for more complex designs.

Bar Chart: Categorical Comparisons

Distribution across categories

Purpose: Compare quantities across categories

Data Types: - Categorical/Ordinal + Quantitative - Example: Sales by product category

Best For: - Rankings and comparisons - Part-to-whole relationships

Bar charts are the workhorses of categorical data visualization. The key insight: our visual system excels at comparing lengths along a common baseline. Always start the y-axis at zero for accurate magnitude comparison.

Line Chart: Trends Over Time

Change over continuous dimension

Purpose: Show trends and changes over time

Data Types: - Temporal + Quantitative - Example: Stock prices over months

Best For: - Trends and patterns - Multiple series comparison

Line charts excel at showing continuity and change. The connecting lines imply a continuous relationship - use them only when this makes sense (typically with time or other ordered dimensions).

Scatter Plot: Relationships

Correlation between two quantitative variables

Purpose: Explore relationships between variables

Data Types: - Quantitative + Quantitative - Example: Height vs. weight

Best For: - Correlation analysis - Outlier detection - Pattern recognition

Scatter plots reveal relationships that summary statistics might miss. They’re essential for exploratory data analysis and can reveal clusters, outliers, and non-linear relationships.

Matrix (Heatmap): Two-Way Comparisons

Quantity across two categorical dimensions

Purpose: Compare across two categorical dimensions

Data Types: - Categorical + Categorical + Quantitative - Example: Sales by month and region

Best For: - Cross-tabulations - Correlation matrices - Dense data display

Matrices efficiently display large amounts of data in compact form. Color encoding allows us to process many values quickly, though precise comparison is harder than with position-based encodings.

Symbol Map: Spatial Distribution

Geographic distribution of quantities

Purpose: Show spatial distribution of data

Data Types: - Spatial coordinates + Quantitative - Example: Population by city

Best For: - Geographic patterns - Location-based analysis - Spatial clustering

Symbol maps leverage our spatial reasoning abilities. They’re powerful for revealing geographic patterns but require careful design to avoid overlapping symbols and ensure accurate size perception.

Principles: Expressiveness & Effectiveness

Expressiveness: Show all and only the facts in the data

Effectiveness: Information should be readily perceived

Marks and channels determine effectiveness

These are the foundational principles from Jacques Bertin and Jock Mackinlay. They provide objective criteria for evaluating visualization designs and guide our decision-making process.

Expressiveness Violations

Line chart with categorical data implies false ordering

Problem: Ordered visual channel (line) with unordered data

Bar chart ordering suggests ranking where none exists

Problem: Arbitrary ordering implies non-existent relationship

These examples show how visual choices can mislead. The line chart suggests temporal trends where none exist, while the bar chart ordering implies a ranking of categories that may be meaningless.

Effectiveness: A Quick Experiment

Compare these different encodings

Which value is larger?

Results show position is more effective

Which value is larger?

Result: Length comparison is faster and more accurate than color comparison

This demonstrates why we need systematic understanding of visual channel effectiveness. Our perceptual system has different capabilities for different visual properties.

Channel Effectiveness Rankings

Ranking of visual channels by data type

This ranking from Cleveland and McGill is based on empirical studies of human perception. Position along a common scale is most effective for quantitative data, while color hue works well for categorical distinctions but poorly for quantitative comparison.

Applying Channel Rankings

More Effective:

Bar chart using position enables accurate comparison

Position encoding enables accurate comparison

Less Effective:

Pie chart using area/angle makes comparison harder

Area and angle are harder to compare accurately

This principle explains why bar charts often outperform pie charts for precise comparison. When accuracy matters most, prioritize position-based encodings.

Data Transformation: The First Step

Data transformation pipeline

• Raw data rarely answers your questions directly
• Transformation creates the information you need
• Different transformations reveal different insights
• This step is often more important than visual design choices

Many visualization failures stem from poor data preparation, not poor design. The most beautiful chart is useless if it doesn’t contain the right information to answer your question.

Aggregation: Summarizing for Insight

Raw Data:

Sales transactions: 50,000 records
Date, Product, Amount, Customer...

Questions: - Which products sell best? - How do sales vary by month? - What’s the geographic distribution?

Aggregated Data:

By Product: Sum(Amount)
By Month: Avg(Amount) 
By Region: Count(Transactions)

Example: Flight data transformation

Aggregation is essential for moving from individual records to patterns and trends. The key is choosing the right aggregation function (sum, average, count, etc.) and grouping variables for your specific question.

Common Transformation Types

Temporal Aggregation: - Year → Month → Week → Day → Hour

Spatial Aggregation: - Country → State → City → Neighborhood

Binning: - Age: 18-25, 26-35, 36-45, etc. - Income: Low, Medium, High

Derived Attributes: - Growth rate from sequential values - Ratios and percentages

Each transformation type serves different analytical purposes. Temporal aggregation reveals trends, spatial aggregation shows geographic patterns, binning simplifies continuous variables, and derived attributes can reveal relationships invisible in raw data.

Interactive Exercise: Transformation Choices

Dataset: E-commerce transactions - Product, Date, Amount, Customer

Questions to explore: 1. How do you identify seasonal trends? 2. Which customer segments are most valuable? 3. How has product popularity changed over time?

Your turn: What transformations would you apply for each question?

• Temporal aggregation?
• Customer segmentation?
• Product ranking over time?

Pause here for student discussion. This exercise helps them think through the connection between analytical questions and data transformation choices. Different questions require different ways of preparing the data.

Scales and Axes: The Foundation

Scale: A function mapping data domain to visual range

Data Domain → Scale Function → Visual Range

• Linear scales: Equal data differences = equal visual differences
• Logarithmic scales: Equal ratios = equal visual differences
  
• Ordinal scales: Preserve order, not magnitude

Scales are fundamental but often invisible. The choice of scale dramatically affects what patterns are visible and how data relationships are perceived.

Linear vs. Logarithmic Scales

Linear Scale Example

Linear Scale: - Absolute differences - Additive changes - Most common choice

Log Scale Example

Logarithmic Scale: - Relative differences - Multiplicative changes - Wide data ranges

Stock prices are a classic example: linear scales show absolute price changes, while log scales show percentage changes. Choose based on whether absolute or relative change matters more for your analysis.

The Zero Baseline Rule

Truncated Axis Example

Truncated Axis: Exaggerates small differences

Zero Baseline Example

Zero Baseline: Accurate magnitude representation

Bar charts encode data as length from a baseline. Without zero, these lengths misrepresent the data. This is one of the most common ways visualizations mislead, often unintentionally.

When to Break the Rules

Log scales instead of zero baseline: - Data spans multiple orders of magnitude - Ratios matter more than absolute values

Truncated axes for line charts: - Small changes in large values - When trend matters more than magnitude

Appropriate Truncation Example

Context determines when breaking rules is acceptable

Rules exist for good reasons, but context matters. The key is understanding why the rules exist so you can make informed decisions about when to break them. Always consider what story your scale choices tell.

Design Exercise: Scale Choices

Scenario: Visualizing country populations

Data range: 1,000 (Vatican) to 1.4 billion (China)

Questions: 1. What scale would you choose? 2. How would you handle the extreme range? 3. What alternatives might you consider?

Consider: Log scale vs. filtering vs. grouping

This exercise highlights the challenge of extreme data ranges. Students should consider log scales, filtering small countries, or using different visualization types like maps where geographic size provides context.

Putting It All Together

The Visualization Design Process:

1. Understand your question
2. Transform data appropriately
3. Choose effective visual encodings
4. Select appropriate scales
5. Test and iterate

Workflow: Question → Transform → Encode → Scale → Iterate

Design Process Workflow

This systematic approach helps avoid common pitfalls. Each step builds on the previous ones, and iteration often reveals better approaches. Don’t expect to get it right on the first try.

Common Pitfalls to Avoid

• Skipping data exploration: Visualize without understanding the data
• Chart junk: Adding visual elements that don’t encode information
• Color overuse: Using color when position would be more effective
• Ignoring scale effects: Not considering how scale choices affect perception
• 3D when 2D suffices: Adding dimensions that don’t encode information

These mistakes are common even among experienced practitioners. Developing an awareness of these pitfalls is the first step toward avoiding them.

Best Practices Summary

Expressiveness: Match visual properties to data properties

Effectiveness: Use the most effective encoding for your most important data

Transformation: Prepare data to answer your specific questions

Scales: Choose scales that honestly represent relationships

Iteration: Test your designs with real users when possible

These principles provide a framework for making systematic visualization decisions. They’re not rigid rules but guidelines that help you think through design choices systematically.

Interactive Quiz

Question 1: For comparing sales across product categories, which encoding is most effective?

1. Color saturation
2. Bar length
3. Symbol size
4. Line style

Answer: B) Bar length (position along common scale)

Why? Position is the most effective visual channel for quantitative comparison.

Use this quiz to reinforce key concepts. Encourage students to explain their reasoning, not just give answers.

Interactive Quiz

Question 2: You have website traffic data spanning 5 years. For showing long-term growth trends, you should:

1. Use a zero baseline always
2. Use a log scale if growth is exponential
3. Show only the most recent year
4. Use a pie chart for each year

Answer: B) Use a log scale if growth is exponential

Why? Log scales reveal multiplicative relationships and growth rates.

This question tests understanding of when to break the zero baseline rule and when log scales are appropriate.

Next Steps

For next class: - Read Munzner Chapter 7 (Arrange Tables) - Practice with the fundamental charts using your own data - Complete Lab Exercise: Build all five chart types with sample dataset

Looking ahead: - Interactive visualization techniques - Multi-dimensional data representation - Advanced transformation methods

Give students concrete actions to reinforce today’s learning. The lab exercise helps them practice the concepts immediately while the reading prepares them for more advanced topics.

Key Takeaways

• Two-step process: What to show, then how to show it
• Five fundamental charts solve most visualization problems
• Expressiveness and effectiveness guide design decisions
• Data transformation is often more important than visual design
• Scale choices dramatically affect perception and interpretation

End with the core messages students should remember. These principles will guide them in every visualization project they undertake.

Questions & Discussion

Think about: - What visualization challenges do you face in your work/research? - How might these principles apply to your domain? - What questions do you have about applying these techniques?

Next class: Interactive visualization techniques and advanced encodings

Thank you

End with open discussion to connect the general principles to students’ specific interests and challenges. This helps them see the practical relevance of what they’ve learned.