Presentation is loading. Please wait.

Presentation is loading. Please wait.

Multi-Dimensional Data Visualization cs5764: Information Visualization Chris North.

Similar presentations


Presentation on theme: "Multi-Dimensional Data Visualization cs5764: Information Visualization Chris North."— Presentation transcript:

1 Multi-Dimensional Data Visualization cs5764: Information Visualization Chris North

2 Review What is the Visualization Pipeline? What are the steps of Visual Mapping? What is the Info Vis Mantra?

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

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 Projection map n-D space onto 2-D screen

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

11 Glyphs: Stars d1 d2 d3 d4 d5 d6 d7

12 Multiple Views with Brushing-and-linking

13 Scatterplot Matrix All pairs of attributes Brushing and linking

14 … on steroids

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

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

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

18 Star Plot Parallel Coordinates with axes arranged radially

19 Star Coordinates Kandogan, “Star Coordinates”

20 Star Coordinates CartesianStar Coordinates d1 d2 d5 d6 d8 v1v1 v2 v3v3 v4 v5 v6v6 v7 v8v8 p d7 d3 d4 P=(v1,v2,v3,v4,v5,v6,v7,v8) P=(v1, v2) v1v1 v2 d1 d2 p Mapping: Items → dots Σ attribute vectors → (x,y)

21 Analysis

22 Table Lens Rao, “Table Lens”

23 FOCUS / InfoZoom Spenke, “FOCUS”

24 VisDB Keim, “VisDB”

25 Pixel Bar Charts Keim

26 Comparison of Techniques

27 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

28 Multi-Dimensional Functions cs5764: Information Visualization Chris North

29 Multi-Dimensional Functions y = f(x 1, x 2, x 3, …, x n ) Continuous: E.g. y = x x x 3 Discrete: x i are uniformly sampled in a bounded region E.g. x i = [0,1,2,…,100] E.g. measured density in a 3D material under range of pressures and room temperatures.

30 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

31 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.

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

33 1-D: Easy b = f(a) a  x b  y a b

34 2-D: Easy c = f(a, b) Height field: a  x b  y c  z b a c

35 2-D: Easy c = f(a, b) Heat map: a  x b  y c  color b a c

36 3-D: Hard d = f(a, b, c) Color volume: a  x b  y c  z d  color What’s inside? a b c

37  4D: Really Hard y = f(x 1, x 2, x 3, x 4, …, x n ) What does a 5D space look like? Approaches: Hierarchical axes (Mihalisin) Nested coordinate frames (Worlds within Worlds) Slicing (HyperSlice) Radial Focus+Context (PolarEyez, Sanjini)

38 Hierarchical Axes 1D view of 3D function: (Mihalisin et al.) f(x 1, x 2, x 3 ) x3 x2 x1

39 as in TableLens 5D 9 samp/D

40

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

42 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

43 5D 9 sample/D

44 Nested Coordinate Frames Feiner, “Worlds within Worlds”

45 Slicing Van Wijk, “HyperSlice”

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

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

48 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

49 Dynamic Queries cs5764: Information Visualization Chris North

50 HomeFinder

51 Spotfire

52 Limitations Scale: Scatterplot screen space: 10,000 – 1,000,000 Data structures & algorithms: < 50,000 –Poor screen drawing on Filter-out A Solution: Query Previews! “AND” queries only Arbitrary boolean queries? A solution: Filter Flow

53 DQ Algorithm Idea: incremental algorithm only deal with data items that changed state When slider moves: Calculate slider delta Search in data structure for data items in the delta region If slider moved inward (filter out): –Erase data items from visualization Else slider moved outward (filter in): –Draw data items on visualization Problem! Overlapped items, erases items underneath too

54 DQ Data Structures (1) Sorted array of the data for each slider Need counter for each data item = # sliders that filter it Attribute Explorer visualizes these counters too! O(delta) Year: Delta

55 DQ Data Structures (2) Multi-dimensional data structure E.g.: K-d tree, quad-tree, … Recursively split space, store in tree structure Enables fast range search, O()

56 DQ Data Structures (2) Multi-dimensional data structure E.g.: K-d tree, quad-tree, … Recursively split space, store in tree structure Enables fast range search, O(logn) Delta

57 Erasure Problem Each pixel has counter = number of items Can visualize this for density! Z-buffer? Redraw local area only

58 Filter-Flow Betty Catherine Edna Freda Grace Hilda Judy Marcus Tom

59 Influence/Attribute Explorer Tweedie, Spence, “Externalizing Abstract Mathematical Models” (Influence/Attribute Explorer)

60 Query Previews Doan, “Query Previews”


Download ppt "Multi-Dimensional Data Visualization cs5764: Information Visualization Chris North."

Similar presentations


Ads by Google