Multidimensional Data Visualizations

Applied Big Data and Visualization

P. Healy

CS1-08Computer Science Bldg.

tel: 202727patrick.healy@ul.ie

Spring 2019–2020

P. Healy (University of Limerick) CS6502 Spring 2019–2020 1 / 12

Multidimensional Data Visualizations

Outline

1 Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

P. Healy (University of Limerick) CS6502 Spring 2019–2020 2 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Outline

1 Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

P. Healy (University of Limerick) CS6502 Spring 2019–2020 3 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Perception

We are good at perceiving data values for two variablesrepresented on spatial (xy ) axes, but we have difficulty athigher dimensionsWhen we need to encode more than 3 attributes... whathappens?For example, if we wish to present visually data brokendown by all of the following categories

sales personoffice locationsales in dollarsmonth

Bertin’s “Image Theory” (1983) considers this

P. Healy (University of Limerick) CS6502 Spring 2019–2020 4 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Bertin’s “Image Theory”

We can only perceive 3 variables (2 planar and 1 retinal)“efficiently”Efficient = preattentive, without additional eye motion orattention required

PlanarSpatial dimension xSpatial dimension y

Retinal

According to this theory we cannot effectively visualize 4dimensions using a graphical representation on a2-dimensional surface e.g. screen, paper.

P. Healy (University of Limerick) CS6502 Spring 2019–2020 5 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Bertin’s “Image Theory” (contd.)

Bertin’s retinal variables:PositionSizeShapeValue (lightness)Color hueOrientationTexture

Visual variables are “the differences in map elements asperceived by the human eye” wiki.gis.com

P. Healy (University of Limerick) CS6502 Spring 2019–2020 6 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Bertin’s “Image Theory” (contd.)

Four “levels” of perception of visual variablesSelective: allows us to immediately isolate a group ofentities based on a change in the variableAssociative: allows grouping across changes in the variableOrdered: these variables have an immediately recognizablesequenceQuantative: variables allow an estimation of the actualnumerical difference between symbols

©axismaps

P. Healy (University of Limerick) CS6502 Spring 2019–2020 7 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Bertin’s “Image Theory” (contd.)

Example: Shape is neither ordered nor quantitativebecause it can’t be scaled for magnitude. Does a trianglerepresent a larger value than a square?Bertin: “failure to match the [graphical] component and thevisual ’level’ (type of scale) is the single major source oferror in design of visualizations”

P. Healy (University of Limerick) CS6502 Spring 2019–2020 8 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Mitigation Strategies

How to overcome limitations of Bertin’s “2+1” theoryDivide-and-conquer: provide a number of different views ofthe same data. For example, data could be decomposedinto an array of relatively simple 2 or 3-D graphs (e. g.,Cleveland, 1984) with different axes.

Or, present different views in different formats orgranularities including in-text visualizations such as Tufte’ssparklineIn either case, the observer must integrate informationwhich has been distributed over space and/or time.

P. Healy (University of Limerick) CS6502 Spring 2019–2020 9 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Mitigation Strategies

How to overcome limitations of Bertin’s “2+1” theoryDivide-and-conquer: provide a number of different views ofthe same data. For example, data could be decomposedinto an array of relatively simple 2 or 3-D graphs (e. g.,Cleveland, 1984) with different axes.

Or, present different views in different formats orgranularities including in-text visualizations such as Tufte’ssparklineIn either case, the observer must integrate informationwhich has been distributed over space and/or time.

P. Healy (University of Limerick) CS6502 Spring 2019–2020 9 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Mitigation Strategies

How to overcome limitations of Bertin’s “2+1” theoryDivide-and-conquer: provide a number of different views ofthe same data. For example, data could be decomposedinto an array of relatively simple 2 or 3-D graphs (e. g.,Cleveland, 1984) with different axes.

Or, present different views in different formats orgranularities including in-text visualizations such as Tufte’ssparklineIn either case, the observer must integrate informationwhich has been distributed over space and/or time.

P. Healy (University of Limerick) CS6502 Spring 2019–2020 9 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Mitigation Strategies

How to overcome limitations of Bertin’s “2+1” theoryDivide-and-conquer: provide a number of different views ofthe same data. For example, data could be decomposedinto an array of relatively simple 2 or 3-D graphs (e. g.,Cleveland, 1984) with different axes.

Or, present different views in different formats orgranularities including in-text visualizations such as Tufte’ssparklineIn either case, the observer must integrate informationwhich has been distributed over space and/or time.

P. Healy (University of Limerick) CS6502 Spring 2019–2020 9 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Outline

1 Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

P. Healy (University of Limerick) CS6502 Spring 2019–2020 10 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Parallel Co-ordinates and Others

Previous slide presented a decomposition ofmulti-dimensional data into a matrix of 2-D plotsAlternative approach: linearize parameter space parallelcoordinates (PC)

Though positioning of axes may falsely suggest arelationship amongst variables

P. Healy (University of Limerick) CS6502 Spring 2019–2020 11 / 12

Multidimensional Data VisualizationsCognitive LimitationsMultivariate Data

Parallel Co-ordinates and Others (contd.)

Augmenting PC with heatmaps; but is it understandable?Information overload?Radar chart: a visualization with coordinate axes arrangedradially so that they appear like a “rolled-up in a circle”parallel co-ordinate plot; though similar criticism applies toarrangement / ordering of axesAndrews plot: a “smoothed” parallel co-ordinate plot

P. Healy (University of Limerick) CS6502 Spring 2019–2020 12 / 12