Data Visualization¶

Display of data in a graphical/tabular format

Helps us understand the data; humans are better at recognizing visual patterns than numeric patterns

Limitation: Pareidolia; seeing patterns that do not exist

Why is visualization important?¶

Widely different distributions can have the same statistical properties

Example Case	Visualization
Anscombe’s Quartet
Datasaurus Dozen		All have the same mean, std, and correlation

Characteristics of Great Visualization¶

• Story
• Truthful: not aimed to mislead viewers, accurate representation
• Perception: Easy to understand
• Functional: useful and enlightening
• Insightful: reveals something that wouldn't have been possible otherwise
• Aesthetics: Grammar of Graphics
• Beautiful

Grammar of Graphics¶

• Theme
  • Grid
  • Background
  • Typography
• Labels
  • Title
  • Subtitle
  • Caption: Extra text, source of data, etc
  • Axis Labels
  • Legend
    • Title
    • Items: try your best to align with the actual elements
• Coordinates
  • System
    • Cartesian
    • Polar
  • Range
    • Do not skew the axis: Use the correct minimum & max range
    • Exceptions
      • only possible values are included
        • For eg: for human body temperature, you should show 98-105 F; you shouldn’t start at 0
      • small movements matter
        • GDP across time
      • important time range
    • Tip: When presenting, show the full view, then zoom in clarifying the reason
• Facets: Subplots
• Scales: Axis
  • Discrete
  • Continuous
  • Continuous, breaks
  • Continuous, Log
  • Almost never use dual y-axes
    • Will lead to appearance of spurious correlations
    • Exception: When the 2 axes measure the same thing. For eg
      • Axis 1: Percentages; Axis 2: Absolute value
      • Axis 1: Celsius; Axis 2: Fahrenheit
• Geometries: Type of Plot (check below)
• Aesthetics
  • Position-X
  • Position-Y
  • Color
    • Discrete
    • Continuous
  • Size
  • Shape
  • Opacity
  • Animation (for Time)
• Data

Plots¶

Type	Chart	Purpose	Visual	Limitations
Uni-Variate	Pie Chart	Part of a whole		Not easy to compare between parts as it uses angles and areas
	Bar Chart	Comparing values of groups
	Lollipop Chart	Comparing values of groups where only the end of the bar matters
	Column Chart	Comparing value across time
	Waffle Chart	Show values as squares
	Box/Box-Whiskers Plot	Helps understand the distribution of a variable
	1D Histogram	Visualizes the frequency distribution of attribute Relative uncertainty of each bin frequency \(\propto \dfrac{1}{\sqrt{\text{count}}}\) The convention of analyzing these bins: Values are left-inclusive and right-exclusive; Last bin is right-inclusive Continuous Data: binning		- Shape may change dramatically depending on bin settings - Bins with few counts have high statistical uncertainty - Interpretation can be difficult without huge amounts of data
	Density Plot	Smooth version of histogram - Bandwidth - Kernel
	Pyramid Histogram
	Violin Plot	Smooth version of pyramid histogram
	Strip	Jitter
	Q-Q Plot	Quantile-Quantile plot comparing a distribution’s quantiles with quantiles of a known distribution (such as Normal distribution)
	Beeswarm
	Ridge Plot	Multi-variate density plot offsetting the densities
	Raincloud Plot	Jitter plot + Box Plot + Violin Plot
	Treemap			Hard to interpret
	Conditional Quantitative	- Bin quantitative data - Make different plots This will be useful for error distribution inspection
Bi-Variate	Scatter Plot
	Line Plot	Comparing trend of value across time
	2D Histogram	Helps understand frequency of co-occurance of 2 attributes
	Heatmap	Looking at overall patterns
	Mosaic Plot			Hard to interpret
	Stem & Leaf Plots	Understand the distribution of values of an attribute Useful when there aren’t many values Steps - Split values into groups, where each group contains those values that are the same except for the last digit - Each group becomes a stem, while the last digit of a group are the leaves - Stems will be the higher-order digits - Leaves will be the lower-order digits - Plot stems vertically and leaves horizontally
Tri-Variate	Contour Plots	Used for spacial data
Multi-Variate	Parallel Coordinates
	Pair Plot/ Scatter plot matrix	Basically a matrix of scatter plots		May get overwhelming for large number of variables
	Correlogram Heatmap
	Correlogram Bar
Regression	Coefficients plot
	Marginal effects plot
Comparison	Sparklines
	Slopegraphs
Geospatial/ Map	Choropleth			May hide details, such as population
	IDK
	IDK
	2D Map	Requires 'projection' Best: Robinson Most-common: Mercator, but worst		Distortion of area
Text	Word cloud			Looks cool, but not very useful Kinda like Pie Charts Just use bar chart instead

Cheat Sheet¶

Uncertainty Visualization¶

Helps avoid misunderstanding of uncertainty

• Histogram
• Box plot

Data Visualization Guidelines¶

IDK¶

• Human visual system
  • detects differences, not absolute values
  • attracted to edges
    • designer should maximize contrast with background if outlines of shapes are important
  • perceives surface color base on edge contrast informations
  • higher contrast sensitivity in luminance than in chrominance
  • color recognition is not an automatic process
    • stoop effect

Cleveland's Visual Operations of Pattern Perception¶

1. Detection
2. Assembly
3. Estimation

Gestalt Laws of Perpetual Organization¶

1. Emergence: mind sees the whole and then the parts. It often sees more than what is specifically states by its individual parts
2. Invariance: mind recognizes simple objects independent of rotation, translation, scale deformations, and lighting
3. Proximity: Elements closer together are perceived to be more related than elements farther apart
4. Similarity: Similar elements that are perceived to be more related than dissimilar elements
5. Enclosure: Elements enclosed together are perceived as belonging together
6. Continuity: Mind tries to continue visual, auditory, and kinetic patterns
7. Closure: Mind perceives set of individual elements as a single, recognizable pattern
8. Symmetry: Mind perceives objects as symmetrical shapes that form around their center
9. Figure-ground: elements are perceived as either figures (objects of focus) or ground (rest of the perceptual field)
10. Connection: Elements connected together (for eg: by a line) are perceived as belonging together
11. Common-fate: Elements that share a common fate (eg: moving in the same direction) are perceived as belonging together

Tufte’s design principles for graphical excellence¶

1. Maximize the data-ink ratio, within reason
2. Mobilize every graphical element, perhaps several times over, to show the data
3. Maximize data density and the size of the data matrix, within reason
4. Establish context
5. Show cause and effect, where possible
6. Compare and contrast, utilize layering & separation
7. Escape flatland, use small multiples, parallel sequencing (reality is multivariate)
8. Show multiple dimensions
9. Utilize narratives of space and time
10. Integrate image, number and text

Encoding Methods¶

From most effective to least effective

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