Information Visualization. Jing Yang Spring Multi-dimensional Visualization (1)

Transcription

1 Information Visualization Jing Yang Spring Multi-dimensional Visualization (1) 2 1

2 Multi-dimensional (Multivariate) Dataset 3 Data Item (Object, Record, Case) 4 2

3 Dimension (Variable, Attribute) 5 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 $

4 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 $270k $400k $160k $600k $300k $ miles 40 miles 10 miles 13 miles 30 miles 50 miles.. miles 7 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 $270k $400k $160k $600k $ miles 40 miles 10 miles 13 miles 30 miles.. Miles Sheahome Weirland Ryan Ryan Sheahome.. 8 4

5 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 $270k $400k $160k $600k $ miles 40 miles 10 miles 13 miles 30 miles.. Miles Sheahome Weirland Ryan Ryan Sheahome.. 1 st school 50st school 20st school 1 st school 50st school... 9 Novel Examples 1. InfoCanvas 2. Dust & Manget 3. Dynamic queries 10 5

6 Classification Geometric techniques Scatterplot matrices, parallel coordinates, landscapes, Dust&Magnet Icon-based techniques glyphs, shape-coding, color icons, Hierarchical techniques Dimensional stacking, worlds-within-worlds, Pixel-oriented techniques Recursive pattern, circle segments, spiral, axes techniques, Table-based techniques HeatMap, tablelens 11 Example Dataset: Iris Scientists measured the sepal length, sepal width, petal length, petal width of many kinds of iris

7 Multidimensional Data Example: Iris Data sepal sepal petal petal length width length width Geometric Techniques Basic 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] 14 7

8 Recall 1-Dimensional Visualization (1.6) Parallel Coordinates sepal length sepal width petal length petal width

9 sepal sepal petal petal length width length width Geometry of Data Items The straight lines Pak Wong,

10 Geometry of Data Items The aircraft collision example Pak Wong, Cluster and Outlier Cluster A 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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12 Scatterplot Matrix 23 Scatterplot Matrix 24 12

13 Star Coordinates E. Kandogan, Star Coordinates: A Multi-dimensional Visualization Technique with Uniform Treatment of Dimensions, InfoVis 2000 Late-Breaking Hot Topics, Oct Landscapes Hot topics of a news collection L. Nowell, E. Hetzler, and T. Tanasse. Change Blindness in Information Visualization: A Case Study. Infovis

14 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 the Non-Visual: Spatial Analysis and Interaction with Information from Text Documents, Infovis Projection Pursuit Techniques Idea: For High-Dimensional Dataset 1. 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

15 Automatic Projection Pursuit Friedman 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. 29 Dust & Magnet Dust & Magnet: Multivariate Information Visualization using a Magnet Metaphor, Yi et al. Information Visualization (2005) (video) 30 15

16 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] 31 Dimensional Stacking Imagine each data item (4 attributes) as a small block. We place all blocks on a table

17 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 33 Dimensional Stacking Add grids in grids. Place the blocks in the grids according to their values of attribute2. According to values of attribute

18 Dimensional Stacking Add grids in grids. Place the blocks in the grids according to their values of attribute3. According to values of attribute 3 35 Dimensional Stacking Add grids in grids. Place the blocks in the grids according to their values of attribute4. According to values of attribute

19 Dimensional Stacking Fix one block! Expand the block 37 Dimensional Stacking Fix another block 38 19

20 Dimensional Stacking Dimensional stacking! 39 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 40 20

21 Worlds within Worlds Feiner S., Beshers C.: World within World: Metaphors for Exploring n-dimensional Virtual Worlds, Proc. UIST, 1990, pp 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] 42 21

22 Glyphs Profile Glyphs Each bar encodes a variable s value Max Min v1 v2 v3 v4 1 data item with 4 attributes 3 data items in the iris dataset 43 Chernoff faces (1973, Herman Chernoff) 44 22

23 Dr. Eugene Turner, Star Glyphs Space out variables at equal angles around a circle Each arm encodes a variable s value v2 v3 v1 v4 1 data item with 4 attributes 4 data items in the iris dataset 46 23

24 Glyphs 47 Stick Figures The mapping Two attributes - display axes Others - angle and/or length of limbs Texture patterns in the visualization show certain data characteristics Pickett R. M., Grinstein G. G.: Iconographic Displays for Visualizing Multidimensional Data, Proc. IEEE Conf. on Systems, Man and Cybernetics, 1988, pp Stick figure icon 48 24

25 Stick Figures 5-dim. image data from the great lake region G. Grinstein, University of Massachusetts at Lowell 49 Stick Figures Stick figure icon family Try all different mappings 12X5! = 1440 pictures Movie 50 25

26 Stick Figures The same dataset, different mapping G. Grinstein, University of Massachusetts at Lowell 51 Stick Figures Black background White background G. Grinstein, University of Massachusetts at Lowell 52 26

27 More G. Grinstein, University of Massachusetts at Lowell 53 Magnetosphere and Solar Wind Data 1. Field magnitude average 2. Average magnetic vector strength: 3. Vector Latitude: 4. Vector Longitude 5. Plasma Temperature 6. Ion Density 7. Flow Speed 8. Flow Longitude 9. Flow Latitude 10. Kp* 10: a measure of Earth's magnetic field strength and motion from the ground 11. C9: An index of activity in the 10 cm radio bandwidth. 12. r (sunspot) year/day/hour 27

28 Shape Coding Data item - small array of fields Each 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 Shape Coding Beddow J.: Shape Coding of Multidimensional Data on a Mircocomputer Display, Visualization 90, 1990, pp

29 Color Icons [Lev 91, KK94] Data item - color icon (arrays of color fields) Each field - one attribute value Arrangement is query-dependent (e.g., spiral) 6 dimensional dataset The figure is taken from Dr. D. Keim s tutorial notes in Infovis Color Icons The figure is taken from Dr. D. Keim s tutorial notes in Infovis

30 Pixel-Oriented Techniques Basic idea Each value - one colored pixel (value ranges -> fixed colormap) Values for each attribute are presented in separate subwindows Values of the same data item are at the same postions of all subwindows Keim s tutorial notes in Infovis Pixel Layout and Orders 60 30

31 Major Challenge Textures of the subwindows reflect patterns. How to order and lay the pixels out to get informative textures? 61 Pixel-Oriented Techniques The figure is taken from Dr. D. Keim s tutorial notes in Infovis

32 Query-Independent Techniques Space-Filling Curve Arrangements The figure is taken from Dr. D. Keim s tutorial notes in Infovis Query-Independent Techniques Space-Filling Curve Arrangements The figure is taken from Dr. D. Keim s tutorial notes in Infovis

33 Query-Independent Techniques Recursive pattern arrangements The figure is taken from Dr. D. Keim s tutorial notes in Infovis Query-Independent Techniques Recursive pattern arrangements The figure is taken from Dr. D. Keim s tutorial notes in Infovis

34 Query-Independent Techniques Recursive pattern arrangements The figure is taken from Dr. D. Keim s tutorial notes in Infovis Query-Dependent Techniques Basic idea: data items (a 1, a 2,..., a m ) & query (q 1, q 2,..., q m ) distances (d 1, d 2,... d m ) extend distances by overall distance (d m+1 ) determine data items with lowest overall distances map distances to color (for each attribute) visualize each distance value d i by one colored pixel The slide is taken from Dr. D. Keim s tutorial notes in Infovis

35 Query-Dependent Techniques Spiral technique Arrangement The m+1 dimension (overall distance) The figure is taken from Dr. D. Keim s tutorial notes in Infovis Query-Dependent Techniques Spiral technique The figure is taken from Dr. D. Keim s tutorial notes in Infovis

36 Circular Arrangement Circle segments The figure is taken from Dr. D. Keim s tutorial notes in Infovis Pixel-Oriented Technique Circle segments The figure is taken from Dr. D. Keim s tutorial notes in Infovis

37 Subwindow Positioning Similarity Clustering of Dimensions for an Enhanced Visualization of Multidimensional Data [Ankerst 98] 73 Subwindow Positioning Similarity Clustering of Dimensions for an Enhanced Visualization of Multidimensional Data [Ankerst 98] 74 37

38 Table-Based Techniques Basic idea: Visualization that improves the existing spreadsheet table format HeatMap Table Lens [RC 94] 75 This figure is used by Dr. M. Ward s permission 76 38

39 This figure is used by Dr. M. Ward s permission 77 This figure is used by Dr. M. Ward s permission 78 39

40 This figure is used by Dr. M. Ward s permission 79 This figure is used by Dr. M. Ward s permission 80 40

41 This figure is used by Dr. M. Ward s permission 81 This figure is used by Dr. M. Ward s permission 82 41

42 This figure is used by Dr. M. Ward s permission 83 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 94 Conf., Boston, MA, 1994, pp

43 Eureka (Table Lens) 85 Major References Colin Ware. Information Visualization, 2004 Daniel Keim. Tutorial note in InfoVis 2000 John Stasko. Course slides, Fall

44 Books 1. The Visual Display of Quantitative Information E. Tufte 2. Visual Explanations E. Tufte 87 44