Multi-Dimensional Data Visualization

1. Multi-Dimensional Data Visualization

2. Information Types • Multi-dimensional: databases,… • 1D: timelines,… • 2D: maps,… • 3D: volumes,… • Hierarchies/Trees: directories,… • Networks/Graphs: web, communications,… • Document collections: digital libraries,…

3. The Simple Stuff • Univariate • Bivariate • Trivariate

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

5. Bivariate • Scatterplot

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

7. Multi-Dimensional Data • Each attribute defines a dimension • Small # of dimensions easy • What about many dimensional data? n-D What does 10-D space look like?

8. Projection • map n-D space onto 2-D screen

9. 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

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

11. Multiple Views withBrushing-and-linking

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

13. … on steroids

14. 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

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

16. Parallel Coordinates • Bag cartesian • (0,1,-1,2)= x y z w 0 0 0 0

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

18. Star Coordinates • Kandogan, “Star Coordinates”

19. 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

20. Analysis

21. Table Lens • Rao, “Table Lens”

22. FOCUS / InfoZoom • Spenke, “FOCUS”

23. VisDB • Keim, “VisDB”

24. Pixel Bar Charts • Keim

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. Multi-DimensionalFunctions

28. 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.

29. 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

30. 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.

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

32. 1-D: Easy • b = f(a) • a  x • b  y b a

33. 2-D: Easy • c = f(a, b) • Height field: • a  x • b  y • c  z c b a

34. 2-D: Easy • c = f(a, b) • Heat map: • a  x • b  y • c  color b a c

35. 3-D: Hard • d = f(a, b, c) • Color volume: • a  x • b  y • c  z • d  color • What’s inside? c b a

36. 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)

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

38. as in TableLens 5D 9 samp/D

40. 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

41. 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

42. 5D9 sample/D

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

44. Slicing • Van Wijk, “HyperSlice”

45. Radial Focus+Context • Jayaraman, “PolarEyez” • infovis.cs.vt.edu x3 x4 x2 x1 x5 -x5 -x1 -x4 -x2

46. Comparison • Hierarchical axes (Mihalisin): • Nested coordinate frames (Worlds in Worlds) • Slicing (HyperSlice): • Radial Focus+Context (PolarEyez)

47. Comparison • Hierarchical axes (Mihalisin): • < 6d by 10 samples, ALL slices, view 2d at a time • Nested coordinate frames (Worlds in Worlds) • < 5-8d, continuous, no overview, 3d hardware • Slicing (HyperSlice): • < 10d by 100 samples, 2d slices • Radial Focus+Context (PolarEyez) • < 10d by 1000 samples, overview, all D uniform, rays

48. Dynamic Queries

49. HomeFinder

50. Spotfire