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