multi-dimensional visualization (1) · stick figures [pic 70, pg88] shape coding [bed 90] color...

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Information Visualization

Jing YangSpring 2008

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Multi-dimensional Visualization (1)

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Multi-dimensional (Multivariate) Dataset

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Data Item (Object, Record, Case)

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Dimension (Variable, Attribute)

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1-Dimensional Dataset

Discussion:I have price information of 200 or more houses.

Please find ways to visualization this dataset.

$210k $270k $400k $160k $600k $300k $...

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2-Dimensional Dataset

Discussion:I also know the distances from the houses to

UNCC. Please find ways to visualization both the distances and prices of the houses.

$210k

15 miles

$270k

40 miles

$400k

10 miles

$160k

13 miles

$600k

30 miles

$300k

50 miles

$...

.. miles

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3-Dimensional Dataset

Discussion:I also know the builders of the houses. Please

find ways to visualization the distances, prices, and builders of the houses.

$210k

15 miles

Sheahome

$270k

40 miles

Weirland

$400k

10 miles

Ryan

$160k

13 miles

Ryan

$600k

30 miles

Sheahome

$...

.. Miles

..

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Multi-Dimensional Dataset

Discussion:I collected more information about the houses,

including home school ranking, distances to shopping centers etc. Please find ways to visualize the dataset!

$210k

15 miles

Sheahome

1st school

$270k

40 miles

Weirland

50st school

$400k

10 miles

Ryan

20st school

$160k

13 miles

Ryan

1st

school

$600k

30 miles

Sheahome

50st school

$...

.. Miles

..

...

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Novel Examples

1. InfoCanvas2. Dust & Manget3. Dynamic queries

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ClassificationGeometric techniques

Scatterplot matrices, parallel coordinates, landscapes, Dust&Magnet …

Icon-based techniquesglyphs, shape-coding, color icons, …

Hierarchical techniquesDimensional stacking, worlds-within-worlds, …

Pixel-oriented techniquesRecursive pattern, circle segments, spiral, axes techniques,…

Table-based techniquesHeatMap, tableLens

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Example Dataset: Iris

Scientists measured the sepal length, sepal width, petal length, petal width of many kinds of iris...

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Multidimensional DataExample: Iris Data

sepallength

sepalwidth

petallength

petalwidth

5.1 3.5 1.4 0.2

4.9 3 1.4 0.2

... ... ... ...

5.9 3 5.1 1.8

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Geometric TechniquesBasic idea: Visualization of geometric transformations and projections of data

Scatterplot-matrices [And 72, Cle 93]Parallel coordinates [Ins 85, ID 90]Parallel Glyphs [Fanea:05] Parallel Sets [Bendix:05]Star coordinates [Kan 2000]Landscapes [Wis 95]Dust & Magnet [Yi 2005]Projection Pursuit Techniques [Hub 85]Prosection Views [FB 94, STDS 95]Hyperslice [WL 93]

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Recall 1-Dimensional Visualization

1 2

(1.6)

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Parallel Coordinates

sepallength

sepalw idth

peta llength

peta lw id th

5.1 3.5 1.4 0.2

4.9 3 1.4 0.2

... ... ... ...

5 .9 3 5.1 1.8

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5.1

3.5

sepa lleng th

sepa lw id th

peta lleng th

peta lw id th

5 .1 3 .5 1 .4 0 .2

1.4 0.2

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Geometry of Data ItemsThe straight lines

Pak Wong, 1997

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Geometry of Data ItemsThe aircraft collision example

Pak Wong, 1997

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Cluster and Outlier

ClusterA group of data items that are similar in all dimensions.

Outlier A data item that is similar to FEW or No other data items.

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Scatterplot Matrix

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Scatterplot Matrix

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Star Coordinates

E. Kandogan, “Star Coordinates: A Multi-dimensional VisualizationTechnique with Uniform Treatment of Dimensions”, InfoVis 2000Late-Breaking Hot Topics, Oct. 2000

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Landscapes

Hot topics of a news collectionL. Nowell, E. Hetzler, and T. Tanasse. “Change Blindness in Information Visualization: A Case Study”. Infovis 2001

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Landscapes

How was the figure generated?Documents (data items)

Keywords (dimensions)

N-d vector for each documents

Projection from N-d space to 2-d space

Landscape view

Wise, J., Thomas, J., et al. “Visualizing theNon-Visual: Spatial Analysis and Interaction withInformation from Text Documents”, Infovis 95

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Projection Pursuit Techniques

Idea: For High-Dimensional Dataset1. locate projections to low-dimensional space that reveal most details about dataset structure 2. extract and analyze projections structures from projections

Two general approaches: manual and automatic.

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Automatic Projection PursuitFriedman and Tukey

Friedman and Tukey’s method

1. characterize a given projection by a numerical index that indicates the amount of structure that is present. 2. heuristically search to locate the ``interesting'' projections using the index. 3. remove detected structures from the data. 4. Iterate until there is no remaining structure detectable within the data.

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Dust & Magnet Dust & Magnet: Multivariate Information Visualization using a Magnet Metaphor, Yi et al. Information Visualization (2005) (video)

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Hierarchical Techniques

Basic ideas: Visualization of the data using a hierarchical partitioning into subspaces

Dimensional Stacking [LWW90]Worlds-within-Worlds [FB 90a/b]Treemap [Shn 92, Joh 93]Cone Trees [RMC 91]InfoCube [RG93]

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Dimensional Stacking

Imagine each data item (4 attributes) as a small block. We place all blocks on a table.

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Dimensional Stacking

Add grids on the table. Place the blocks in the grids according to their values of attribute1.

According to values of attribute 1

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Dimensional Stacking

Add grids in grids. Place the blocks in the grids according to their values of attribute2.

According to values of attribute 2

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Dimensional Stacking

Add grids in grids. Place the blocks in the grids according to their values of attribute3.

According to values of attribute 3

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Dimensional Stacking

Add grids in grids. Place the blocks in the grids according to their values of attribute4.

According to values of attribute 4

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Dimensional Stacking

Fix one block!

Expand the block

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Dimensional Stacking

Fix another block

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Dimensional Stacking

Dimensional stacking!

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Dimensional Stacking

visualization of oil mining data with longitude and latitude mapped to the outer x-, y- axes and ore grade and depth mapped to the inner x-, y- axes

M. Ward, Worcester Polytechnic Institute

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Worlds within Worlds

Feiner S., Beshers C.: ‘World within World: Metaphors for Exploring n-dimensional Virtual Worlds’, Proc. UIST, 1990, pp. 76-83.

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Icon-Based Techniques

Basic idea: visualization of the data values as features of icons

Chernoff-Faces [Che 73, Tuf 83]Stick Figures [Pic 70, PG88]Shape Coding [Bed 90]Color Icons [Lev 91, KK94]TileBars [Hea 95]

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Glyphs

Profile GlyphsEach bar encodes a variable’s value

3 data items in the iris dataset

Min

Max

1 data item with 4 attributes

v1 v2 v3 v4

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Chernoff faces (1973, Herman Chernoff)

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Dr. Eugene Turner, 1979

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Star Glyphs

Space out variables at equal angles around a circleEach arm encodes a variable’s value

4 data items in the iris dataset

v1

v2

v3

v4

1 data item with 4 attributes

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Glyphs

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Stick Figures

The mappingTwo attributes - display axes Others - angle and/or length of limbs

Texture patterns in the visualization show certain data characteristics

Stick figure icon

Pickett R. M., Grinstein G. G.: ‘Iconographic Displays for Visualizing Multidimensional Data’, Proc. IEEE Conf.on Systems, Man and Cybernetics, 1988, pp. 514-519.

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Stick Figures

http://ivpr.cs.uml.edu/gallery/G. Grinstein, University of Massachusetts at Lowell

5-dim. imagedata from thegreat lake region

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Stick Figures

Stick figure icon familyTry all different mappings

12X5! = 1440 picturesMovie

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Stick Figures

The same dataset, different mapping

http://ivpr.cs.uml.edu/gallery/G. Grinstein, University of Massachusetts at Lowell

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Stick Figures

Black background White background

http://ivpr.cs.uml.edu/gallery/G. Grinstein, University of Massachusetts at Lowell

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More

http://ivpr.cs.uml.edu/gallery/G. Grinstein, University of Massachusetts at Lowell

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Magnetosphere and Solar Wind Data1. Field magnitude average2. Average magnetic vector strength: 3. Vector Latitude:4. Vector Longitude5. Plasma Temperature6. Ion Density7. Flow Speed8. Flow Longitude9. Flow Latitude10. Kp* 10: a measure of Earth's magnetic field strength and motion from the ground11. C9: An index of activity in the 10 cm radio bandwidth.12. r (sunspot) 13. year/day/hour

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Shape Coding

Data item - small array of fieldsEach field - one attribute value

Arrangement of attribute fields (e.g., 12-dimensional data):

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00

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Shape Coding

Beddow J.: ‘Shape Coding of Multidimensional Data on a Mircocomputer Display’, Visualization ‘90, 1990, pp. 238-246.

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Color Icons [Lev 91, KK94]

Data item - color icon (arrays of color fields)Each field - one attribute valueArrangement is query-dependent (e.g., spiral)

6 dimensional dataset

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00.

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Color Icons

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00

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Pixel-Oriented TechniquesBasic idea

Each value - one colored pixel (value ranges -> fixed colormap)

Values for each attribute are presented in separate subwindowsValues of the same data item are at the same postions of all subwindows

Keim’s tutorial notes in Infovis 00

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Pixel Layout and Orders

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Major Challenge

Textures of the subwindows reflect patterns. How to order and lay the pixels out to get informative textures?

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Pixel-Oriented Techniques

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00

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Query-Independent Techniques

Space-Filling Curve Arrangements

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00

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Query-Independent Techniques

Space-Filling Curve Arrangements

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00

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Query-Independent Techniques

Recursive pattern arrangements

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00

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Query-Independent Techniques

Recursive pattern arrangements

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00

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Query-Independent Techniques

Recursive pattern arrangements

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00

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Query-Dependent Techniques

Basic idea:data items (a1, a2, ..., am) & query (q1, q2, ..., qm)distances (d1, d2, ... dm)extend distances by overall distance (dm+1)determine data items with lowest overall distancesmap distances to color (for each attribute)visualize each distance value di by one colored pixel

The slide is taken from Dr. D. Keim’s tutorial notes in Infovis 00

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Query-Dependent Techniques

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00

Spiral technique

Arrangement The m+1 dimension (overall distance)

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Query-Dependent Techniques

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00

Spiral technique

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Circular Arrangement

Circle segments

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00

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Pixel-Oriented Technique

Circle segments

The figure is taken from Dr. D. Keim’s tutorial notes in Infovis 00

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Subwindow Positioning

Similarity Clustering of Dimensions for an Enhanced Visualization of Multidimensional Data [Ankerst 98]

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Subwindow PositioningSimilarity Clustering of Dimensions for an Enhanced Visualization of Multidimensional Data [Ankerst 98]

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Table-Based Techniques

Basic idea: Visualization that improves the existing spreadsheet table format

HeatMapTable Lens [RC 94]

76This figure is used by Dr. M. Ward’s permission

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77This figure is used by Dr. M. Ward’s permission

78This figure is used by Dr. M. Ward’s permission

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79This figure is used by Dr. M. Ward’s permission

80This figure is used by Dr. M. Ward’s permission

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81This figure is used by Dr. M. Ward’s permission

82This figure is used by Dr. M. Ward’s permission

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83This figure is used by Dr. M. Ward’s permission

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Eureka (Table Lens)

Rao R., Card S. K.: ‘The Table Lens: Merging Graphical and Symbolic Representation in an Interactive Focus+Context Visualization for Tabular Information’, Proc. Human Factors in Computing Systems CHI ‘94Conf., Boston, MA, 1994, pp. 318-322.

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Eureka (Table Lens)

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Major References

Colin Ware. Information Visualization, 2004Daniel Keim. Tutorial note in InfoVis 2000John Stasko. Course slides, Fall 2005

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Books

1. The Visual Display of Quantitative Information E. Tufte2. Visual Explanations E. Tufte