Visualizing Tabular Data
Information Visualization

What We Are Going to Learn

  • Arranging tables
  • Zero keys
    • Scatterplots
  • Some keys
    • Barcharts
    • Heatmaps
  • Other axis orientations
    • Sploms
    • Parallel coordinates
    • Navio
  • Radial representations
    • Pie charts
    • Radar plots

Recap What/Why/How

Arranging Tables

Why Arrange?

Space is the most important channel.

How to arrange

  • Quantitative data
    👉 Express
  • Categorical data
    👉 Separate, order, align
How, encode, Arrange

Arrange Tables

Express Separate Order and AlignAxis OrientationKeys


  • Independent attribute
  • Used as unique index to look up items
  • Simple tables: one key
  • Multidimensional tables: multiple keys


What Tables
  • Dependent attribute, value of cell
  • Classify arrangements by key count
  • Zero, one, two, many...

Zero Keys

0 Keys

Idiom: Scatterplot

  • Express values
    • Quantitative attributes
  • No keys, only values
    • Data: two quantitative attributes
    • Mark: points
    • Channels: horizontal and vertical position
    • Tasks: identify trends, outliers, distribution, correlation, clusters
    • Scalability: hundreds of items
Scatterplot example
[A layered grammar of graphics. Wickham. Journ. Computational and Graphical Statistics 19:1 (2010), 3–28.]

Scatterplot Overplotting

Some Keys

Some Keys

Some Keys: Categorical Regions

Separate Order and Align
  • Regions: contiguous bounded areas distinct from each other
    • Using space to separate (proximity)
    • Following expressiveness principle for categorical attributes
  • Use ordered attribute to order and align regions

Idiom: Barchart

  • One key, one value
  • Data:
    • One categorical attribute, one quantitative attribute
  • Mark: lines
  • Channels:
    • Length to express quantitative value
    • Spatial regions: one per mark
      • Separated horizontally, aligned vertically
      • Ordered by quantitative attribute
      • By label (alphabetical), by length attribute (data-driven)
  • Task:
    • Compare, lookup values
  • Scalability
    • Dozens to hundreds of levels for key attribute
Barchart example

Separate, Order, and Align

  • Separate: helps differentiating
  • Order: helps locating/lookup
  • Align: helps comparing

Idiom: Stacked Bar Chart

  • Two keys, one value
  • Data:
    • Two categorical attributes
    • One quantitative attribute
  • Mark: vertical stack of line marks
  • Glyph: composite object, internal structure from multiple marks
  • Channels: length and color hue
    • Spatial regions: one per glyph
    • Aligned: full glyph, lowest bar component
    • Unaligned: other bar components
  • Task: part-to-whole relationship
  • Scalability: few bars, few stacked

Grouped Bar Chart

Stacked to Grouped

Idiom: Dot Plot

"Stacked Bar Charts Are the Worst."

Interesting discussion from Robert Kosara's blog.

Make sure to read the comments.

Idiom: Marimekko Chart

Chart Axes

  • Labeled axis is critical
  • Avoid cropping y-axis
  • Include 0 at bottom left
  • Or slope misleads

Two Keys

    Idiom: Heatmap

    • Two keys, one value
      • Data
        • Two categorical attributes (gene, experimental condition)
        • One quantitative attribute (expression levels)
      • Marks: area
        • Separate and align in 2D matrix
        • Indexed by two categorical attributes
      • Channels
        • Color by quantitative attrib
          • (Ordered diverging colormap)
      • Task: find clusters, outliers
      • Scalability
        • One million items, hundreds of categorical levels, about ten quantitative attribute levels

    Idiom: Cluster Heatmap

    • In addition
      • Derived data
        • Two cluster hierarchies
      • Dendrogram
        • Parent-child relationships in tree with connection line marks
        • Leaves aligned so interior branch heights easy to compare
      • Heatmap
        • Marks (re-)ordered by cluster hierarchy traversal
        • Task: assess quality of clusters found by automatic methods
    Cluster Heatmap
    Two Keys

    Axis Orientation

    Axis orientation

    Idiom: Scatterplot Matrix

    • Rectilinear axes, point mark
    • All possible pairs of axes
    • Scalability
      • One dozen attributes
      • Dozens to hundreds of items
    • Task:
      • Summarize/explore

    Idiom: Parallel Coordinates

    • Parallel axes, jagged line representing item
    • Rectilinear axes, item as point
    • Axis ordering is major challenge
    • Scalability
      • Dozens of attributes
      • Hundreds of items
    • Task:
      • Summarize/explore

    Parallel Coordinates example

    Nutrients Explorer by Kai

    Task Correlation

    • Scatterplot matrix
      • Positive correlation
        • Diagonal low-to-high
      • Negative correlation
        • Diagonal high-to-low
      • Uncorrelated: spread out
    • Parallel coordinates
      • Positive correlation
        • Parallel line segments
      • Negative correlation
        • All segments cross at halfway point
      • Uncorrelated
        • Scattered crossings
    [Hyperdimensional Data Analysis Using Parallel Coordinates. Wegman. Journ. American Statistical Association 85:411 (1990), 664–675.]
    [A layered grammar of graphics. Wickham. Journ. Computational and Graphical Statistics 19:1 (2010), 3–28.]

    Orientation Limitations

    • Rectilinear: scalability with regard to #axes
      • Two axes best
      • Three problematic
      • Four or more impossible
    • Parallel: unfamiliarity, training time


    Bonus: InMens

    What about millions of points?

    Radial Orientations

    Idioms: Radial Bar Chart, Star Plot

    • Radial bar chart
      • Radial axes, meet at central ring, line mark
    • Star plot
      • Radial axes, meet at central point, line mark
    • Bar chart
      • Rectilinear axes, aligned vertically

    • Accuracy
      • Length unaligned with radial
      • Less accurate than aligned with rectilinear

    Idiom: Radar Plots

    • Task: comparison
    • Scalability: similar to parallel coordinates
    • Order of attributes matter
    [Slide courtesy of Ben Jones]

    “Radar Graphs: Avoid them (99.9% of the time).”

    Avoid Radar ChartsRadar graph fixed
    [Slide courtesy of Ben Jones]

    Idioms: Pie Chart, Polar Area Chart

    • Pie chart:
      • Area marks with angle channel
      • Accuracy: angle/area much less accurate than line length

    • Polar area chart:
      • Area marks with length channel
      • More direct analog to bar charts

    • Data:
      • One categorical key attribute, 1 quantitative value attribute
    • Task:
      • Part-to-whole judgements
    Pie Polar
    [A layered grammar of graphics. Wickham. Journ. Computational and Graphical Statistics 19:1 (2010), 3–28.]

    Pie Chart Perception

    • Some empirical evidence that people respond to arc length
      • Not angles
      • Maybe also areas...?
    • Donut charts no worse than pie charts
    Pie chart perception
    [Arcs, Angles, or Areas: Individual Data Encodings in Pie and Donut Charts.
Skau and Kosara. Proc. EuroVis 2016.]

    Pie chart Perception (cont.)

    • Meta-points
      • Redesign of paper figures in later blog post
        • Violin plots good for analysis but too detailed for presentation
      • Tamara's advice: still dubious for pie/donut charts
        • Sometimes okay if just two attributes

    Idioms: Normalized Stacked Bar Chart

    • Task:
      • Part-to-whole judgments

    • Normalized stacked bar chart
      • Stacked bar chart, normalized to full vertical height
      • Single stacked bar equivalent to full pie
        • High information density: requires narrow rectangle

    • Pie chart
      • Information density: requires large circle

    Idiom: Glyphmaps

    • Rectilinear good for linear vs. nonlinear trends
    • Radial good for cyclic patterns

    Axis rectilinear and radial
    [Glyph-maps for Visually Exploring Temporal Patterns in Climate Data and Models. Wickham, Hofmann, Wickham, and Cook. Environmetrics 23:5 (2012), 382–393.]

    Film Flowers

    Film Flowers by Shirley Wu

    Radial Orientation

    • Perceptual limits
      • Polar coordinate asymmetry
        • Angles lower precision than lengths
        • Frequently problematic
        • Sometimes can be deliberately exploited!
          • For two attributes of very unequal importance
    Radial Weaknesses
    [Uncovering Strengths and Weaknesses of Radial Visualizations - an Empirical Approach. Diehl, Beck and Burch. IEEE TVCG (Proc. InfoVis) 16(6):935--942, 2010.]
    Axis Orientation

    Idiom: Dense Software Overviews

    • Data: text
      • Text and one quantitative attribute per line
    • Derived data:
      • One pixel high line
      • Length according to original
    • Color line by attribute
    • Scalability
    • Over 10,000 lines
    Dense Software Overviews
    [Visualization of test information to assist fault localization. Jones, Harrold, Stasko. Proc. ICSE 2002, p 467-477.]

    Tables with D3

    Idiom: Scatterplot


    Stacked Barchart

    d3.Stack and d3.Nest

    d3 Stack stack


    Scatterplot Matrix

    Parallel Coordinates

    Polar Area Chart

    Pie chart

    Donut chart

    Stacked bar chart normalized

    What We Learned

    • Arranging tables
    • Zero keys
      • Scatterplots
    • Some keys
      • Barcharts
      • Heatmaps
    • Other axis orientations
      • Sploms
      • Parallel coordinates
      • Navio
    • Radial representations
      • Pie charts
      • Radar plots