This lecture forms part of an Information Visualisation course given at the Vrije Universiteit Brussel.

1. 2 December 2005
Information Visualisation
Visualisation Techniques
Prof. Beat Signer
Department of Computer Science
Vrije Universiteit Brussel
beatsigner.com

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April 1, 2021
Visual Encoding of Datasets
▪ So far we have seen the presentation (visual encoding)
of data types (see lecture 5)
▪ Visualisation techniques and visual encoding of datasets
▪ tables
▪ spatial data
- geometry
- fields
▪ network and trees

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Arrange Tables

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Arrange Tables …

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Arrange Tables …
▪ Why the arrange design choice?
▪ most crucial visual encoding since the use of space
dominates a user's mental model of a dataset
▪ spatial position covers three most effective channels
for ordered attributes → primacy of spatial position channels
- planar position against a common scale
- planar position along an unaligned scale
- length
▪ best channel for categorical attributes (grouping items
in the same region) is also about spatial position

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Arrange by Keys and Values
▪ Distinction between key and value attributes introduced
earlier is highly relevant for visually encoding table data
▪ Core design choices (idioms) for visually encoding
tables depend on the semantics of the table attributes
(key or value)
▪ scatterplot: visually encoding two value attributes
▪ bar chart: visually encoding one key and one value attribute
▪ heatmap: visually encoding two keys and one value attribute
▪ …
▪ Keys typically used to define a spatial region for each
item in which one or multiple value attributes are shown

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Express Values
▪ Spatial position channel can be used to
visually encode quantitative attributes
▪ each item is encoded with a mark at some position along an axis
▪ additional attributes encoded on the same mark via other non-
spatial channels (e.g. colour or size)
▪ glyphs can be used for more complex cases (multiple marks) as
shown later in this course

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Scatterplot Example (Bubble Plot)
▪ Each point mark
represents a country
▪ horizontal and vertical
positions encoding life
expectancy and infant
mortality
- colour channel for categorical
country attribute
- size channel for quantitative
population attribute (bubble plot)
▪ Highly negatively
correlated dataset
▪ downward sloping diagonal

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Scatterplot Example
▪ Relation between diamond price and weight
▪ Derived attributes (logarithmically scaled) in right figure
▪ strongly positively correlated attributes
- calculated regression line often superimposed to support the task

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Scatterplots
Scatterplots
What(Data) Table: two quantitative value attributes.
Why(Task) Find trends, outliers, distribution, correlation; locate clusters.
How(Encode) Express values with horizontal and vertical spatial position and point
marks.
Scale Hundreds of items.

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Separate, Order & Align Regions
▪ Categorical attributes have unordered identity semantics
▪ encoding them with spatial position would violate the principle of
expressiveness
▪ Use spatial regions to group similar categorical attributes
▪ distribution of regions via three operations
- separation into regions (based on categorical attribute)
- ordering of regions (based on ordered attribute)
- aligning of regions (optional, based on ordered attribute)
▪ One-dimensional list alignment often used for
a single key (separation with one region per item)
▪ view itself covers a two-dimensional area
- aligned list of items on one spatial dimension
- region in which the values are shown on a second dimension (e.g. bar charts)

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Bar Chart Example
▪ Categorical species key attribute separates the marks
along the horizontal spatial axis
▪ alphabetical ordering (left picture) → easy lookup by name
▪ data-driven ordering by weight (right picture) → easier to
see data trends
▪ Separate line marks for weight attribute in each region

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Bar Charts
Bar Charts
What(Data) Table: one quantitative value attribute, one categorical key attribute.
Why(Task) Lookup and compare values.
How(Encode) Line marks, express value attribute with aligned vertical position,
separate key attribute with horizontal position.
Scale Key attribute: dozens to hundreds of levels.

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Stacked Bar Chart Example
▪ Bars distributed along the
x-axis based on combina-
tion of processor and pro-
cedure
▪ More complex glyph for
each bar
▪ multiple sub-bars stacked
vertically
- uses colour (type of cache miss)
as well as length (number of
misses) coding
- common scale only for lowest
bar component → order of
stacking is relevant

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Stacked Bar Charts
Stacked Bar Charts
What(Data) Multidimensional table: one quantitative value attribute, two categorical
key attributes.
Why(Task) Part-to-whole relationship, lookup values, find trends.
How(Encode) Bar glyph with length-coded subcomponents of value attribute for each
category of secondary key attribute. Separate bars by category of
primary key attribute.
Scale Key attribute (main axis): dozens to hundreds of levels.
Key attribute (stacked glyph axis): several to one dozen.

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Streamgraph Example
▪ Music listening history example
▪ one time series per artist counting the number of times their music
was listened to each week
▪ Continuity of the horizontal layers
▪ emphasises legibility of individual streams
▪ deliberate organic silhouette (instead of x-axis as baseline

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Streamgraphs
Streamgraphs
What(Data) Multidimensional table: one quantitative value attribute (e.g. counts),
one ordered key attribute (time), one categorical key attribute.
What(Derived) One quantitative attribute (for computation of layer ordering).
Why(Task) Find trends.
How(Encode) Use derived geometry showing artist layers across time, layer height
encodes counts.
Scale Key attribute (time, main axis) hundreds of time points. Key attributes
(artists, not always over entire time axis): dozens to hundreds.

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Dot Chart vs. Line Chart Example
▪ Dot chart (dot plot) and line chart for the same dataset
showing a cat's weight over time
▪ trends are emphasised by line charts
▪ dot chart is like a bar chart where the quantitative attribute
is encoded with point marks rather than line marks

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Dot Charts
Dot Charts
What(Data) Table: one quantitative value attribute, one ordered key attribute.
Why(Task) Lookup and compare values.
How(Encode) Express value attribute with aligned vertical position and point marks.
Separate/order into horizontal regions by key attribute.
Scale Key attribute: dozens to hundreds of levels.

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Line Charts
▪ Line charts should only be used for ordered key attri-
butes but not for categorical key attributes!
▪ would imply trends that do not exist (violation of expressiveness
principle)
▪ Aspect ratio (width/height)
▪ we are better in judging angles close to 45°
▪ banking to 45° idiom computes the best aspect ratio with as many
lines as possible close to 45°
Line Charts
What(Data) Table: one quantitative value attribute, one ordered key attribute.
Why(Task) Show trends.
How(Encode) Dot chart with connection marks between dots.
Scale Key attribute: hundreds of levels.

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Matrix Alignment
▪ Datasets with two keys often arranged in a
two-dimensional matrix alignment
▪ one key distributed along the rows and one key along the columns
▪ rectangular cell in the matrix shows item values
▪ Examples of matrix alignments are heatmaps or the
scatterplot matrix (SPLOM)

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Heatmap Example

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Heatmaps
Heatmaps
What(Data) Table: two categorical key attributes, one quantitative value attribute.
Why(Task) Find clusters, outliers; summarise.
How(Encode) 2D matrix alignment of area marks, diverging colourmap.
Scale Items: one million. Categorical attribute levels: hundreds. Quantitative
attribute levels: 3 to11.

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Scatterplot Matrix (SPLOM) Example

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Scatterplot Matrix (SPLOM)
▪ Usually only the lower or upper triangle of the matrix is
shown (avoid redundancy)
Scatterplot Matrix (SPLOM)
What(Data) Table.
What(Derived) Ordered key attribute: list of original attributes.
Why(Task) Find correlation, trends, outliers.
How(Encode) Scatterplots in 2D matrix alignment.
Scale Attributes: one dozen. Items: dozens to hundreds.

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Volumetric Grids and Recursive Subdivison
▪ Volumetric grid aligns data in three dimensions
based on three key attributes
▪ typically not recommended for non-spatial (abstract)
data due to perceptual problems (e.g. occlusion or
perspective distortion)
▪ Recursive Subdivision
▪ recursively subdivides a cell via a list or matrix
and thereby supports multiple keys
▪ discussed later in the course

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Spatial Axis Orientation
▪ Rectilinear layouts
▪ regions or items are distributed along
an orthogonal horizontal and vertical axis
▪ Parallel layouts
▪ parallel coordinates can be used to visualise many quantitative
attributes at once
▪ provides overview over all attributes
- also shows the range of values for individual attributes
▪ Radial layouts
▪ items distributed around a circle using the angle channel in
addition to one or multiple linear spatial channels
- more efficient in showing periodic patterns

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Parallel Coordinates Example

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Parallel Coordinates
Parallel Coordinates
What(Data) Table: many value attributes.
Why(Task) Find trends, outliers, extremes, correlation.
How(Encode) Parallel layout: horizontal spatial position used to separate axes,
vertical spatial position used to express value along each aligned axis
with connection line marks as segments between them.
Scale Attributes: dozens along secondary axis. Items: hundreds.

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Radial Bar Chart Example
Radial Bar Charts
What(Data) Table: one quantitative attribute, one categorical attribute.
Why(Task) Find periodic patterns.
How(Encode) Length coding of line marks; radial layout.

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Pie Chart Examples
Pie chart Bar chart Polar area chart
Pie chart Normalised stacked bar chart
Relative contributions of parts to a whole
Pie chart versus bar chart accuracy
Stacked bar chart

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Pie Charts and Polar Area Charts
Pie Charts
What(Data) Table: one quantitative attribute, one categorical attribute.
Why(Task) Part-whole relationship.
How(Encode) Area marks (wedges) with angle channel; radial layout.
Scale One dozen categories.
Polar Area Charts
What(Data) Table: one quantitative attribute, one categorical attribute.
Why(Task) Part-whole relationship.
How(Encode) Area marks (wedges) with length channel; radial layout.
Scale One dozen categories.

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Normalised Stacked Bar Charts
Normalised Stacked Bar Charts
What(Data) Multidimensional table: one quantitative value attribute, two
categorical key attributes.
What (Derived) One quantitative value attribute (normalised version of original
attribute).
Why(Task) Part-whole relationship.
How(Encode) Line marks with length channel; rectilinear layout.
Scale One dozen categories for stacked attribute. Several dozen categories
for axis attribute.

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Spatial Layout Density
▪ Layout can be dense or sparse
▪ Dense layout uses small and densely packed marks to
provide an overview of as many items as possible
▪ maximally dense layout uses a single pixel for each point mark
- only planar position and colour channels can be used
▪ Space-filling layout fills all available space in the view
▪ typically uses area marks for items and containment marks for
relationships (e.g. treemaps discussed later)
▪ maximises the available room for colour coding and might offer
space for labels
▪ disadvantage: cannot make use of white space in the layout

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Dense Software Overview Example

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Dense Software Overviews
Dense Software Overviews
What(Data) Text with numbered lines (source code, test results log).
What (Derived) Two quantitative attributes (test execution results).
Why(Task) Locate faults, summarise results and coverage.
How(Encode) Dense layout. Spatial position and line length from text ordering,
Colour channels of hue and brightness.
Scale Lines of text: ten thousand.

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Arrange Spatial Data

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Arrange Spatial Data …
▪ Two main spatial data types
▪ Geometry
▪ Spatial Fields
- scalar fields with single value associated with each cell in the field
- vector fields with multiple values associated with each cell
(e.g. computational fluid dynamics)
- tensor fields with matrix associated with each cell capturing more complex
structure (e.g. for stress, conductivity etc.)
▪ Given spatial position is the attribute of primary
importance
▪ use provided position as the substrate for the visual layout

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Geometry
▪ Geometric data does not necessarily have
attributes associated with it
▪ can be derived from raw source data
(e.g. geographic data about the earth)
▪ Geographic Data
▪ derive a geometry dataset based on abstractions (e.g. filtering,
aggregation or level of detail) on the underlying raw data
▪ cartographic data (non-spatial information) can be used
to size code the marks
- e.g. size of point marks representing cities by their population
▪ Other derived geometry data
▪ e.g. based on computations on spatial fields

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Choropleth Map Example

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Choropleth Map
Choropleth Map
What(Data) Geographic geometry data. Table with one quantitative attribute per
region.
Why(Task) Find clusters.
How(Encode) Space: use given geometry for area mark boundaries.
Colour: sequential segmented colourmap.

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Scalar Fields
▪ Scalar spatial field has a single value
associated with each spatially defined cell
▪ e.g. data from medical scans with radio-opacity (CT scan) or
proton density (MRI scan)
▪ Isocontours use isolines to represent the contours of a
particular level of the scalar value.
▪ isolines close together for regions with fast change

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Topographic Terrain Map Example

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Topographic Terrain Maps
Topographic Terrain Maps
What(Data) 2D spatial field; geographic data.
What (Derived) Geometry: set of isolines computed from the field.
Why(Task) Query shape.
How(Encode) Use given geographic data geometry of points, lines, and region
marks. Used derived geometry as line marks (blue in example).
Scale Dozens of contour levels.

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Arrange Networks and Trees

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Arrange Networks and Trees …
▪ Connections (links) can be represented
in different ways
▪ node-link diagrams with explicit connection marks
- well-suited for tasks that involve the understanding of the network topology
(e.g. shortest path between two nodes or finding all adjacent nodes)
▪ adjacency matrix
▪ enclosure with containment marks
- only works for trees but not for networks

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Node-Link Diagram Examples (Trees)
Triangular vertical node-link layout
Spline radial layout

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Node-Link Diagram Examples (Trees) …
Rectangular horizontal node-link layout Bubble tree node-link layout

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Force-Directed Placement Example
Force-directed placement with size coding of edges Force-directed placement of larger network with size coding of nodes

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Force-directed Placement
▪ Increased scalability via multilevel network idioms
▪ e.g. multilevel scalable force-directed placement (SFDP)
algorithm
Force-directed Placement
What(Data) Network.
Why(Task) Explore topology, locate paths.
How(Encode) Point marks for node, connection marks for links.
Scale Nodes: dozens to hundreds. Links: hundreds. Node/link density: L<4N.

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SFDP Example

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Multilevel Force-Directed Placement (SFDP)
Multilevel Force-directed Placement (SFDP)
What(Data) Network.
What (Derived) Cluster hierarchy on top of original network.
Why(Task) Explore topology, locate paths and clusters.
How(Encode) Point marks for nodes, connection marks for links.
Scale Nodes: 1000-10'000. Links: 1000-10'000. Node/link density: L<4N.

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Adjacency Matrix View Example
▪ Network nodes laid out along the horizontal and vertical
edges of a square region
▪ links between nodes indicated by colouring an area mark in the
cell forming the intersection of the two nodes' row and column
▪ additional attribute can be visualised by colouring the matrix cells

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Adjacency Matrix View
▪ Better scalability than node-link diagrams
▪ Predictability and stability and support for reordering
▪ Drawback: impossible to investigate topological structure
Adjacency Matrix View
What(Data) Network.
What (Derived) Table: network nodes as keys, link status between two nodes as
values.
Why(Task) "Explore" strongly connected networks.
How(Encode) Area marks in 2D matrix alignment.
Scale Nodes: 1000. Links: one million.

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Enclosure
▪ Containment marks are effective for showing
complete information about hierarchical structure
(instead of pairwise relationships only)
▪ Treemaps as an alternative to node-link diagrams
▪ hierarchical relationships shown via containment rather than
connection marks

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Treemap Example

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Treemaps
Treemaps
What(Data) Tree.
Why(Task) Query attributes at leaf nodes.
How(Encode) Area marks and containment, with rectilinear layout.
Scale Leaf nodes: one million. Links: one million.

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GrouseFlocks Example
▪ Visualisation for compound networks (tree on top
of a network)
▪ network nodes form the leaves of the tree
▪ tree encoded via containment on top of the original graph
(picture on the right)

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GrouseFlocks
Grouse Flocks
What(Data) Network.
What (Derived) Cluster hierarchy on top of the original network.
How(Encode) Connection marks for original network, containment marks for cluster
hierarchy

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Exercise 7
▪ Lab Session (online)

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Further Reading
▪ This lecture is mainly based on the
book Visualization Analysis & Design
▪ chapter 7
- Arrange Tables
▪ chapter 8
- Arrange Spatial Data
▪ chapter 9
- Arrange Networks and Trees

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References
▪ Visualization Analysis & Design, Tamara
Munzner, Taylor & Francis Inc, (Har/Psc edition),
May, November 2014,
ISBN-13: 978-1466508910

63. 2 December 2005
Next Lecture
View Manipulation and Reduction