Multi-Dimensional Data Visualization

1. Multi-Dimensional Data Visualization CS 5764: Information Visualization Chris North

2. Review • What is the Visualization Pipeline? • What are the 2 steps of Visual Mapping? • What is Shneiderman’s Info Vis Mantra? • What are Cleveland’s rules?

3. Where are we? Tabular (multi-dimensional) Spatial & Temporal 1D / 2D 3D Networks Trees Graphs Text & Documents Fundamentals Navigation strategies Overview strategies Interaction techniques Design Development Evaluation

4. The Simple Stuff • Univariate • Bivariate • Trivariate

5. Univariate • Dot plot • Bar chart (item vs. attribute) • Tukey box plot • Histogram

6. Bivariate • Scatterplot

7. Trivariate • 3D scatterplot, spin plot • 2D plot + size (or color…)

8. Multi-Dimensional Data • Each attribute defines a dimension • Small # of dimensions easy • Data mapping, Cleveland’s rules • What about many dimensional data? n-D What does 10-D space look like?

9. Map n-D space onto 2-D screen • Visual representations: • Complex glyphs • E.g. star glyphs, faces, embedded visualization, … • Multiple views • E.g. plot matrices, brushing histograms, Spotfire, … • Non-orthogonal axes • E.g. Parallel coords, star coords, … • Tabular layout • E.g. TableLens, … • Interactions: • Dynamic Queries • Brushing & Linking • Selecting for details, …

10. Glyphs: Chernoff Faces • 10 Parameters: • Head Eccentricity • Eye Eccentricity • Pupil Size • Eyebrow Slope • Nose Size • Mouth Vertical Offset • Eye Spacing • Eye Size • Mouth Width • Mouth Openness • http://hesketh.com/schampeo/projects/Faces/chernoff.html

11. Glyphs: Stars d1 d2 d7 d3 d6 d4 d5

12. Multiple Views withBrushing-and-linking

13. Scatterplot Matrix • All pairs of attributes • Brushing and linking • http://noppa5.pc.helsinki.fi/koe/3d3.html

14. … on steroids

15. Different Arrangements of Axes • Axes are good • Lays out all points in a single space • “position” is 1st in Cleveland’s rules • Uniform treatment of dimensions • Space > 3D ? • Must trash orthogonality

16. Parallel Coordinates • Inselberg, “Multidimensional detective” (parallel coordinates)

17. Parallel Coordinates • Forget about Cartesian orthogonal axes • (0,1,-1,2)= x y z w 0 0 0 0

18. Star Plot 1 8 2 7 3 4 6 5 Parallel Coordinates with axes arranged radially

19. Star Coordinates • Kandogan, “Star Coordinates”

20. Star Coordinates CartesianStar Coordinates P=(v1,v2,v3,v4,v5,v6,v7,v8) P=(v1, v2) d1 d1 d8 d2 v3 v4 p v2 v1 v5 v2 d7 d3 d2 p v1 v8 v6 v7 d6 • Mapping: • Items → dots • Σ attribute vectors → (x,y) d4 d5

21. Analysis

22. Table Lens • Rao, “Table Lens”

23. FOCUS / InfoZoom • Spenke, “FOCUS”

24. VisDB & Pixel Bar Charts • Keim, “VisDB”

25. Comparison of Techniques

26. Comparison of Techniques • ParCood: <1000 items, <20 attrs • Relate between adjacent attr pairs • StarCoord: <1,000,000 items, <20 attrs • Interaction intensive • TableLens: similar to par-coords • more items with aggregation • Relate 1:m attrs (sorting), short learn time • Visdb: 100,000 items with 10 attrs • Items*attrs = screenspace, long learn time, must query • Spotfire: <1,000,000 items, <10 attrs (DQ many) • Filtering, short learn time

27. Scaling up further • Beyond 20 dimensions? • Interaction • E.g. Offload some dims to Dynamic Query sliders, … • Reduce dimensionality of the data • E.g. Multi-dimensional scaling (MDS) …later • Visualize features of the dimensions, instead of the data • E.g. rank-by-feature

28. Rank-by-Feature • Seo, et al.

29. Combining multiple data types • Multi-Dimensional + GeoSpatial • DataMaps, Virginia Tech

30. Exercise • Demographics data: • Multi-Dimensional attributes(multiple measures over time) • Geospatial map • Static visual representation, no interaction(must visually relate all attributes to geospatial) • Design choices?

31. 1. Small Multiples Multiple views: 1 attribute / map 1976

32. 2. Embedded Visualizations Complex glyphs: For each location, show vis of all attributes

33. Multi-DimensionalFunctions cs5764: Information Visualization Chris North

34. Multi-Dimensional Functions • y = f(x1, x2, x3, …, xn) • Continuous: • E.g. y = x13 + 2x22 - 9x3 • Discrete: • xi are uniformly sampled in a bounded region • E.g. xi = [0,1,2,…,100] • E.g. measured density in a 3D material under range of pressures and room temperatures.

35. Relations vs. Functions • Relations: • R(A, B, C, D, E, F) • All dependent variables (1 ind.var.?) • Sparse points in multi-d dep.var. space • Functions: • R(A, B, C, D, E, F, Y) : Y=f(A, B, C, D, E, F) • Many independent variables • Defined at every point in multi-d ind.var. space (“onto”) • Huge scale: 6D with 10 samples/D = 1,000,000 data points

36. Multi-D Relation Visualizations… • Don’t work well for multi-D functions • Example: • Parallel coords • 5D func sampled on 1-9 for all ind.vars.

37. Typically want to encode ind.vars. as spatial attrs

38. 1-D: Easy • b = f(a) • a  x • b  y b a

39. 2-D: Easy • c = f(a, b) • Height field: • a  x • b  y • c  z c b a

40. 2-D: Easy • c = f(a, b) • Heat map: • a  x • b  y • c  color b a c

41. 3-D: Hard • d = f(a, b, c) • Color volume: • a  x • b  y • c  z • d  color • What’s inside? c b a

42. 4D: Really Hard • y = f(x1, x2, x3, x4, …, xn) • What does a 5D space look like? • Approaches: • Hierarchical axes (Mihalisin) • Nested coordinate frames (Worlds within Worlds) • Slicing (HyperSlice) • Radial Focus+Context (PolarEyez, Sanjini)

43. Hierarchical Axes • 1D view of 3D function: (Mihalisin et al.) f(x1, x2, x3) x3 x2 x1

44. as in TableLens 5D 9 samp/D

46. Hierarchical Axes • 2D view of 4D function (using heat maps) • y = f(x1, x2, x3, x4) • Discrete: xi = [0,1,2,3,4] x3 x1 x2 y = f(x1,x2,0,0) as color x4

47. Hierarchical Axes • Scale? • 6d = 3 levels in the 2d approach • 10 samples/d = 1,000,000 data points = 1 screen • For more dimensions: • zoom in on “blocks” • reorder dimensions

48. 5D9 sample/D

49. Nested Coordinate Frames • Feiner, “Worlds within Worlds”

50. Slicing • Van Wijk, “HyperSlice”