multi-dimensional visualization - unc charlottebasic idea: visualization of the data values as...

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Information Visualization

Jing YangSpring 2007

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Multi-dimensional Visualization

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Multi-dimensional (Multivariate) Dataset

Slide courtesy of John Stasko

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Data Item (Object, Record, Case)

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Dimension (Variable, Attribute)

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Multidimensional DataExample: Iris Data

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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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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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

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(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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Parallel Coordinates VariationPaper: An interactive 3D integration of Parallel Coordinates and Star Glyphs [Fanea:05]

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Parallel Coordinates VariationPaper: An interactive 3D integration of Parallel Coordinates and Star Glyphs [Fanea:05]

Video

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Parallel Sets: Visual Analysis of Categorical Data. F. Bendix, R. Kosara, H. Hauser. Infovis 2005

Parallel Coordinates Parallel SetsVideo

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Scatterplot Matrix

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Scatterplot Matrix

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VaR Display

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


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Fix one block!

Expand the block

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Fix another block

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Dimensional stacking!

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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


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Stick Figures

Black background White background


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More


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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


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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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Major Challenge

Patterns <-the texture of the subwindows

How to order the pixels to get informative textures?

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Pixel-Oriented Techniques


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Query-Independent Techniques

Space-Filling Curve Arrangements


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Space-Filling Curve Arrangements


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Recursive pattern arrangements


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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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Spiral technique

Arrangement The m+1 dimension (overall distance)

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Spiral technique

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Dynamic Reordering

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Dynamic Reordering

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Circular Arrangement

Circle segments


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Pixel-Oriented Technique

Circle segments


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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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Value and Relation displays [yang:2004]

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Value and Relation displays [yang:2006]

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Table-Based Techniques

Basic idea: Visualization that improves the existing spreadsheet table format

HeatMapTable Lens [RC 94]

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77This 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

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Group Discussion 1

Assume that you are the users of the datasets. What questions will you ask?Write each question on a note

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Group Discussion 2

Please find out how to solve each category of questions.

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Homework1. Present a multi-dimensional visualization paper next Thursday (each student, 10 minutes)

2. XMDV Competitionhttp://davis.wpi.edu/~xmdv/downloadxmdv.htmlBinary Release, Microsoft Windows, Xmdv 7.0http://davis.wpi.edu/~xmdv/documents.html

Winner: the two students who show the largest number of features of Xmdv (can from demo or from paper)

from demo: show how to use the function, the meaning of the interaction and display, such as “parallel coordinates in xmdv”

from paper: several slidesPrize: a waiver of one week’s homework (any week you choose,

except the project)