Agenda

• What's Vis, and Why Do It?
• Analysis: Nested Model
• Data Abstraction
• Task Abstraction
• Marks & Channels
• Review & Discussion
• Palmer-Penguins
• Arrange Tables
• Review & Discussion
• Gapminder

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Visualization Analysis & Design

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Arrange Tables (Ch 7) I

@tamaramunzner

Focus on Tables

4

Keys and values

• key
• independent attribute
• used as unique index to look up items
• simple tables: 1 key
• multidimensional tables: multiple keys
• value
• dependent attribute, value of cell

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Keys and values

• key
• independent attribute
• used as unique index to look up items
• simple tables: 1 key
• multidimensional tables: multiple keys
• value
• dependent attribute, value of cell
• classify arrangements by keys used
• 0, 1, 2, ...

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Idiom: scatterplot

• express values (magnitudes)
• quantitative attributes
• no keys, only values

7

[A layered grammar of graphics. Wickham. Journ. Computational and Graphical Statistics 19:1 (2010), 3–28.]

Idiom: scatterplot

• express values (magnitudes)
• quantitative attributes
• no keys, only values
• data
• 2 quant attribs
• mark: points
• channels
• horiz + vert position

8

[A layered grammar of graphics. Wickham. Journ. Computational and Graphical Statistics 19:1 (2010), 3–28.]

Idiom: scatterplot

• express values (magnitudes)
• quantitative attributes
• no keys, only values
• data
• 2 quant attribs
• mark: points
• channels
• horiz + vert position
• tasks
• find trends, outliers, distribution, correlation, clusters
• scalability
• hundreds of items

9

[A layered grammar of graphics. Wickham. Journ. Computational and Graphical Statistics 19:1 (2010), 3–28.]

Scatterplots: Encoding more channels

• additional channels viable since using point marks
• color
• size (1 quant attribute, used to control 2D area)
• note radius would mislead, take square root since area grows quadratically
• shape

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https://observablehq.com/@d3/scatterplot-with-shapes

https://www.d3-graph-gallery.com/graph/bubble_basic.html

Scatterplot tasks

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Scatterplot tasks

• correlation

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https://www.mathsisfun.com/data/scatter-xy-plots.html

Scatterplot tasks

• correlation

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• clusters/groups, and clusters vs classes

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https://www.mathsisfun.com/data/scatter-xy-plots.html

https://www.cs.ubc.ca/labs/imager/tr/2014/DRVisTasks/

Some keys

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Some keys: Categorical regions

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Regions: Separate, order, align

• regions: contiguous bounded areas distinct from each other
• separate into spatial regions: one mark per region (for now)
• use categorical or ordered attribute to separate into regions
• no conflict with expressiveness principle for categorical attributes
• use ordered attribute to order and align regions

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Separated and aligned and ordered

• best case

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Separated and aligned but not ordered

• limitation: hard to know rank. what's 4th? what's 7th?

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Separated but not aligned or ordered

• limitation: hard to make comparisons with size (vs aligned position)

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Idiom: bar chart

• one key, one value
• data
• 1 categ attrib, 1 quant attrib
• mark: lines
• channels
• length to express quant value
• spatial regions: one per mark
• separated horizontally, aligned vertically
• ordered by quant attrib
• by label (alphabetical), by length attrib (data-driven)
• task
• compare, lookup values
• scalability
• dozens to hundreds of levels for key attrib [bars], hundreds for values

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Idiom: stacked bar chart

• one more key
• data
• 2 categ attrib, 1 quant attrib
• 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: asymmetric
• for stacked key attrib, 10-12 levels [segments]
• for main key attrib, dozens to hundreds of levels [bars]

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https://www.d3-graph-gallery.com/graph/barplot_stacked_basicWide.html

Idiom: streamgraph

• generalized stacked graph
• emphasizing horizontal continuity
• vs vertical items
• data
• 1 categ key attrib (movies)
• 1 ordered key attrib (time)
• 1 quant value attrib (counts)
• derived data
• geometry: layers, where height encodes counts
• 1 quant attrib (layer ordering)

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[Stacked Graphs Geometry & Aesthetics. Byron and Wattenberg. IEEE Trans. Visualization and Computer Graphics (Proc. InfoVis 2008) 14(6): 1245–1252, (2008).]

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Idiom: streamgraph

• generalized stacked graph
• emphasizing horizontal continuity
• vs vertical items
• data
• 1 categ key attrib (movies)
• 1 ordered key attrib (time)
• 1 quant value attrib (counts)
• derived data
• geometry: layers, where height encodes counts
• 1 quant attrib (layer ordering)
• scalability
• hundreds of time keys
• dozens to hundreds of movies keys
• more than stacked bars: most layers don’t extend across whole chart

23

[Stacked Graphs Geometry & Aesthetics. Byron and Wattenberg. IEEE Trans. Visualization and Computer Graphics (Proc. InfoVis 2008) 14(6): 1245–1252, (2008).]

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https://flowingdata.com/2008/02/25/ebb-and-flow-of-box-office-receipts-over-past-20-years/

Idiom: dot / line chart

• one key, one value
• data
• 2 quant attribs
• mark: points �AND line connection marks between them
• channels
• aligned lengths to express quant value
• separated and ordered by key attrib into horizontal regions
• task
• find trend
• connection marks emphasize ordering of items along key axis by explicitly showing relationship between one item and the next
• scalability
• hundreds of key levels, hundreds of value levels

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Idiom: dot / line chart

• one key, one value
• data
• 2 quant attribs
• mark: points �AND line connection marks between them
• channels
• aligned lengths to express quant value
• separated and ordered by key attrib into horizontal regions
• task
• find trend
• connection marks emphasize ordering of items along key axis by explicitly showing relationship between one item and the next
• scalability
• hundreds of key levels, hundreds of value levels

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Choosing bar vs line charts

• depends on type of key attrib
• bar charts if categorical
• line charts if ordered
• do not use line charts for categorical key attribs
• violates expressiveness principle
• implication of trend so strong that it overrides semantics!
• “The more male a person is, the taller he/she is”

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after [Bars and Lines: A Study of Graphic Communication. Zacks and Tversky. Memory and Cognition 27:6 (1999), 1073–1079.]

Chart axes: label them!

• best practice to label
• few exceptions: individual small multiple views could share axis label

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https://xkcd.com/833/

Chart axes: avoid cropping y axis

• include 0 at bottom left or slope misleads

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[Truncating the Y-Axis: Threat or Menace?�Correll, Bertini, & Franconeri, CHI 2020.]

Chart axes: avoid cropping y axis

• include 0 at bottom left or slope misleads
• some exceptions (arbitrary 0, small change matters)

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[Truncating the Y-Axis: Threat or Menace?�Correll, Bertini, & Franconeri, CHI 2020.]

Idiom: Indexed line charts

• data: 2 quant attribs
• 1 key + 1 value
• derived data: new quant value attrib
• index
• plot instead of original value
• task: show change over time
• principle: normalized, not absolute
• scalability
• same as standard line chart

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https://public.tableau.com/profile/ben.jones#!/vizhome/CAStateRevenues/Revenues

Idiom: Gantt charts

• one key, two (related) values
• data
• 1 categ attrib, 2 quant attribs
• mark: line
• length: duration
• channels
• horiz position: start time �(+end from duration)
• task
• emphasize temporal overlaps & start/end dependencies between items
• scalability
• dozens of key levels [bars]
• hundreds of value levels [durations]

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https://www.r-bloggers.com/gantt-charts-in-r-using-plotly/

Idiom: Slopegraphs

• two values
• data
• 2 quant value attribs
• (1 derived attrib: change magnitude)
• mark: point + line
• line connecting mark between pts
• channels
• 2 vertical pos: express attrib value
• (linewidth/size, color)
• task
• emphasize changes in rank/value
• scalability
• hundreds of value levels
• dozens of items

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https://public.tableau.com/profile/ben.jones#!/vizhome/Slopegraphs/Slopegraphs

2 Keys

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Idiom: heatmap

• two keys, one value
• data
• 2 categ attribs (gene, experimental condition)
• 1 quant attrib (expression levels)
• marks: point
• separate and align in 2D matrix
• indexed by 2 categorical attributes
• channels
• color by quant attrib
• (ordered diverging colormap)
• task
• find clusters, outliers
• scalability
• 1M items, 100s of categ levels, ~10 quant attrib levels

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Heatmap reordering

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https://blogs.sas.com/content/iml/2018/05/02/reorder-variables-correlation-heat-map.html

Idiom: cluster heatmap

• in addition
• derived data
• 2 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

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Visualization Analysis & Design

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Tables (Ch 7) II

@tamaramunzner

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Idioms: radial bar chart, star plot

• star plot
• line mark, radial axes meet at central point
• radial bar chart
• line mark, radial axes meet at central ring
• channels: length, angle/orientation
• bar chart
• rectilinear axes, aligned vertically

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• accuracy
• length not aligned with radial layouts
• less accurately perceived than rectilinear aligned

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[Vismon: Facilitating Risk Assessment and Decision Making In Fisheries Management. Booshehrian, Möller, Peterman, and Munzner. Technical Report TR 2011-04, Simon Fraser University, School of Computing Science, 2011.]

Idiom: radar plot

• radial line chart
• point marks, radial layout
• connecting line marks

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• avoid unless data is cyclic

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

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http://www.thefunctionalart.com/2012/11/radar-graphs-avoid-them-999-of-time.html

original�difficult to interpret

redesign for�rectilinear

Idioms: pie chart, coxcomb chart

• pie chart
• interlocking area marks with angle channel: 2D area varies
• separated & ordered radially, uniform height
• accuracy: area less accurate than rectilinear aligned line length
• task: part-to-whole judgements
• coxcomb chart
• line marks with length channel: 1D length varies
• separated & ordered radially, uniform width
• direct analog to radial bar charts
• data
• 1 categ key attrib, 1 quant value attrib

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[A layered grammar of graphics. Wickham. Journ. Computational and Graphical Statistics 19:1 (2010), 3–28.]

Coxcomb / nightingale rose / polar area chart

• invented by Florence Nightingale: �Diagram of the Causes of Mortality in the Army in the East

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Coxcomb: perception

• encode: 1D length
• decode/perceive: 2D area

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• nonuniform line/sector width as length increases
• so area variation is nonlinear wrt line mark length!

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• bar chart safer: uniform width, so area is linear with line mark length
• both radial & rectilinear cases

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nonuniform width as length increases

uniform width as length increases

radial & rectilinear bars: uniform width as length increases

Pie charts: perception

• some empirical evidence that people respond to arc length
• decode/perceive: not angles
• maybe also areas?…
• donut charts no worse than pie charts

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https://eagereyes.org/blog/2016/an-illustrated-tour-of-the-pie-chart-study-results

[Arcs, Angles, or Areas: Individual Data Encodings in Pie and Donut Charts. �Skau and Kosara. Proc. EuroVis 2016.]

Pie charts: best practices

• not so bad for two (or few) levels, for part-to-whole task

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https://eagereyes.org/pie-charts

Pie charts: best practices

• not so bad for two (or few) levels, for part-to-whole task
• dubious for several levels if details matter

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https://eagereyes.org/pie-charts

Pie charts: best practices

• not so bad for two (or few) levels, for part-to-whole task
• dubious for several levels if details matter
• terrible for many levels

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https://eagereyes.org/pie-charts

Idioms: normalized stacked bar chart

• task
• part-to-whole judgements
• normalized stacked bar chart
• stacked bar chart, normalized to full vert height
• single stacked bar equivalent to full pie
• high information density: requires narrow rectangle
• pie chart
• information density: requires large circle

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http://bl.ocks.org/mbostock/3886208,

http://bl.ocks.org/mbostock/3887235,

http://bl.ocks.org/mbostock/3886394.

Idiom: glyphmaps

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• rectilinear good for �linear vs nonlinear trends

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• radial good for cyclic patterns
• evaluating periodicity

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

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Idiom: SPLOM

• scatterplot matrix (SPLOM)
• rectilinear axes, �point mark
• all possible pairs of axes
• scalability
• one dozen attribs
• dozens to hundreds of items

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Idioms: parallel coordinates

• scatterplot limitation
• visual representation with orthogonal axes
• can show only two attributes with spatial position channel

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after [Visualization Course Figures. McGuffin, 2014. http://www.michaelmcguffin.com/courses/vis/]

Idioms: parallel coordinates

• scatterplot limitation
• visual representation with orthogonal axes
• can show only two attributes with spatial position channel
• alternative: line up axes in parallel to show many attributes with position
• item encoded with a line with n segments
• n is the number of attributes shown
• parallel coordinates
• parallel axes, jagged line for item
• rectilinear axes, item as point
• axis ordering is major challenge
• scalability
• dozens of attribs
• hundreds of items

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after [Visualization Course Figures. McGuffin, 2014. http://www.michaelmcguffin.com/courses/vis/]

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

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[Hyperdimensional Data Analysis Using Parallel Coordinates. Wegman. Journ. American Statistical Association 85:411 (1990), 664–675.]

https://www.mathsisfun.com/data/scatter-xy-plots.html

Parallel coordinates, limitations

• visible patterns only between neighboring axis pairs
• how to pick axis order?
• usual solution: reorderable axes, interactive exploration
• same weakness as many other techniques
• downside of interaction: human-powered search
• some algorithms proposed, none fully solve

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Orientation limitations

• rectilinear: scalability wrt #axes
• 2 axes best, 3 problematic, 4+ impossible

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Orientation limitations

• rectilinear: scalability wrt #axes
• 2 axes best, 3 problematic, 4+ impossible
• parallel: unfamiliarity, training time

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Orientation limitations

• rectilinear: scalability wrt #axes
• 2 axes best, 3 problematic, 4+ impossible
• parallel: unfamiliarity, training time
• radial: perceptual limits
• polar coordinate asymmetry
• angles lower precision than length
• nonuniform sector width/size depending on radial distance
• frequently problematic
• but sometimes can be deliberately exploited!
• for 2 attribs of very unequal importance

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[Uncovering Strengths and Weaknesses of Radial Visualizations - an Empirical Approach. Diehl, Beck and Burch. IEEE TVCG (Proc. InfoVis) 16(6):935--942, 2010.]

Layout density

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Idiom: Dense software overviews

• data: text
• text + 1 quant attrib per line
• derived data:
• one pixel high line
• length according to original
• color line by attrib
• scalability
• 10K+ lines

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[Visualization of test information to assist fault localization. Jones, Harrold, Stasko. Proc. ICSE 2002, p 467-477.]

Arrange tables

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