Visualising Multi Dimensional Data

1. Amit Kapoor @amitkaps Visualising Multi - Dimensional Data x w z y

2. Flatland A Romance in Many Dimensions by Edwin Abbot (1884) Square

3. A square is but a line in 2d eye The Square

4. The disappearing circle The Sphere visits the 2d flatland The Sphere rising out of 2d space The Sphere on the point of vanishing eye

5. The square is a cube in 3d! eye The Square sees the world in a new way!

6. Show, not Tell

7. 70% of the sensory receptors are in the eyes 50% of the brain used for visual processing 100ms to get a sense of the visual scene Visual Wired Brain

8. Symbolic Abstraction Visual Abstraction Phenomena Source: Bret Victor

9. “Visualisation is the transformation of the symbolic into geometric”

10. Small Data Large Data Big Data Wide Data

11. Visualise Small Data Area Sales (Rs.) North 5 East 25 West 15 South 20 Central 10

12. Area Sales North 5 East 25 West 15 South 20 Central 10 Acquire Data

13. Area Sales North 5 East 25 West 15 South 20 Central 10 x y 1 5 2 25 3 15 4 20 5 10 x (C) = Area y (Q) = Sales Parse Variables Acquire Data

14. Area Sales North 5 East 25 West 15 South 20 Central 10 x y 1 5 2 25 3 15 4 20 5 10 x (C) = Area y (Q) = Sales x y 20 60 100 140 180 Encode Shape & Select Scales Parse Variables Acquire Data x - position, y - bar scale - 200 x 200

15. Area Sales North 5 East 25 West 15 South 20 Central 10 x y 1 5 2 25 3 15 4 20 5 10 x (C) = Area y (Q) = Sales x - position, y - bar scale - 200 x 200 x y 20 60 100 140 180 Parse Variables Acquire Data cartesian Render with Coordinates Encode Shape & Select Scales

16. Points Line Bar Bar - Stacked Bar - Stagger Coordinates System Create Visualisations

17. Coordinates Cartesian x y Dot Plot Line Chart Column Chart WaterfallStacked Column

18. Coordinates Cartesian - Flip Dot Plot Line Chart Bar Chart CascadeStacked Bar y x

19. Polar Coordinate - X r θ x = θ y = r Marked Radar Line Radar CoxComb Polar WaterfallBullseye

20. Polar Coordinate - Y r θ x = r y = θ Target Line Track Wind Rose Polar CascadePie Chart

21. Data Viz Process (Small Data)Acquire Data Encode Shape Select Scales Render Coordinates Parse Variables

22. gadfly bokeh ggplot2 matplotlib graphics

24. Visualise Large Data ~24,000 Pincodes e.g. Pincode : 560076 Latitude : 12.8843049° Longitude: 77.5967384° Place : Bannerghatta Pincodes in India

25. Pincode Map Scatter plot, play with alpha to show density But what if I want to show geographic nature of pincode?

26. Pincode+ Map Exploration of large data is iterative! Refine Data (Filter, Transform)

27. Data Viz Process (Large Data) Acquire Data Encode Shape Select Scales Render Coordinates Parse Variables Refine Data

29. Visualise Big Data x,y => 1,000,000 Comparable to the Number of Pixels on my MacBook Air 1400 x 900 Data

30. Data Sample Sampling can be effective (with overweighting unusual values) Require multiple plots or careful tuning parameters

31. Data Sample Model Models are great as they scale nicely. But, visualisation is required as “I don’t know, what I don’t know.”

32. Data Sample ModelBinning Binning can solve a lot of these challenges “Bin - Summarize - Smooth: A framework for visualising big data” - Hadley Wickam (2013) “imMens: Real-time Visual Querying of Big Data” - Liu, Jiang, Heer (2013)

34. Tools Matter Defaults Matter

35. “We are calling 2015 the year of the histogram” Amanda Cox

36. “Visualising big data is the process of creating generalized histograms” Amit Kapoor

37. Data Viz Process (Big Data) Acquire Data Encode Shape Select Scales Render Coordinates Parse Variables Filter Data Aggregate Data

39. Multi Dimensional Viz Standard 2d/3d Pixel Based Approach Glyph Approach Geometric Transforms Stacking Approach Scatterplot SPLOM Trellis / Facets Multiple View Star plots Stick Figure Chernoff Faces Color Icons Parallel Coord Table lens Star Coords Tours Space Filling Pixel Bar Chart Spiral Technique Treemaps Dimensional Stacking Hierarchical Axis

40. Multi Dimensional Viz Standard 2d/3d Pixel Based Approach Glyph Approach Geometric Transforms Stacking Approach Scatterplot SPLOM Trellis / Facets Multiple View Star plots Stick Figure Chernoff Faces Color Icons Parallel Coord Table lens Star Coords Tours Space Filling Pixel Bar Chart Treemaps Dimensional Stacking Hierarchical Axis Need for Interaction Ease of Interpretation Spiral Technique

41. Diamonds dataset 50K+ observations of 10 dimensions

42. Diamonds dataset 50K+ observations of 10 dimensions Price of diamonds is related to the 4C’s price in US$ carat weight (⅕ of a gram) cut 5 levels [Fair to ideal] colour 7 levels [J to D] clarity 8 levels [I1 to IF]

43. Diamonds dataset 50K+ observations of 10 dimensions z depth table width z y x x length mm y width mm z height mm depth z depth % table table width %

44. Diamonds dataset price carat cut color clarity x y z depth table 326 0.23 Ideal E SI2 3.95 3.98 2.43 61.5 55 326 0.21 Premium E SI1 3.89 3.84 2.31 59.8 61 327 0.23 Good E VS1 4.05 4.07 2.31 56.9 65 334 0.29 Premium I VS2 4.2 4.23 2.63 62.4 58 335 0.31 Good J SI2 4.34 4.35 2.75 63.3 58 336 0.24 Very Good J VVS2 3.94 3.96 2.48 62.8 57 50K+ observations of 10 dimensions

45. 2d 1d x x y

46. Chart Options Points Bars Lines Areas 1d Quantitative 1d Categorical 2d Quantitative + Categorical 2d Categorical + Categorical 2d Quantitative + Quantitative

47. Chart Options Points Bars Lines Areas 1d Quantitative Strip Plot Histogram Freq Poly Density Plots 1d Categorical Dot Plot Bar Chart Avoid Avoid 2d Quantitative + Categorical Strip Plot Box Plot Freq Poly Density Plots 2d Categorical + Categorical Avoid Bar Chart Avoid Mosaic Plot 2d Quantitative + Quantitative Scatter Plot Table Lens Slopegraph Avoid

48. 2d Scatter Plot

49. 2d Scatter Plot Interaction: Annotation (4.13, 17329) (4.50, 18531) (5.01, 18081)

50. 2d Scatter Plot log transformation

51. 2d Scatter Plot Select or Filter Area of Interest Carat > 1, Price > 10,000

52. 2d Scatter Plot Interaction: Pan & Zoom

53. 3d z x y

54. Use aesthetic for 3d Size Color Shape

55. 3d Scatter Plot Size for Quantitative Dim

56. 3d Scatter Plot Color for Categorical Dim

57. 3d Scatter Plot Shapes don’t scale well

58. 3d Scatter Plot depth persp not good

59. 3d Scatter Plot Interaction: Rotation

60. 4d to 6d z x y w v u

61. 4d Bubble Plot Color and Size

62. 5d Bubble Plot Color, Size and Time The Joy of Stat - Hans Rosling

63. Trellis / Facets Create Small Multiples

64. Trellis / Facet Grid Create Small Multiples

65. SPLOM Scatterplot Matrix Price Carat Table Depth

66. Subplots Binned Plot Distribution

67. Multiple View Create Many Small Charts

68. Multiple View Interaction: Brushing & Linking

70. 6d & more z x y w v u

71. Star Stick Chernoff Icon based Approach

72. Star Plot Matrix Layout color clarity depth cut table

73. Star Plot Plot on X-Y location color clarity depth cut table

74. Orthogonal Parallel

75. Parallel Coord Interaction: Sorting

76. Parallel Coord Interaction: Selection

77. Table Plot Interaction: Bin & Sort

78. Table Plot Interaction: Zoom & Filter

79. Stacked Interaction: Brushing Mosaic Plot cut, color and clarity Other example - Treemaps

80. Star Coordinates Tours & Projections Tourr PackageEser Kandogan Geometric Transforms

81. Spiral Pixel Curve Pixel Bar Chart Pixel Bar Chart - KeimVisDB - Keim Pixel Based Approach

82. Data Viz Process (Wide Data) Acquire Data Encode Shape Select Scales Render Algorithm Parse Variables Filter Data Aggregate Data Make Views Add Interactivity

83. Data Viz Process (Wide Data) Acquire Data Encode Shape Select Scales Render Algorithm Parse Variables Filter Data Aggregate Data Make Views Add Interactivity 1. Encode wisely 2. Use space and multiples 3. Add interactivity 4. Reduce dimensions

84. Code for these Slides https://github.com/amitkaps/multidim R libraries ❖ ggplot2 ❖ GGally ❖ ggsubplot ❖ scales ❖ iplots/Mondrian ❖ ggvis ❖ tourr ❖ rgl ❖ scatterplot3d ❖ dplyr ❖ tabplot ❖ grid ❖ gridExtra

85. “The greatest value of a picture is when it forces us to notice what we never expected to see” John Tukey

86. Amit Kapoor @amitkaps amitkaps.com narrativeviz.com Data Visual Story *

Visualising Multi Dimensional Data

Visualising Multi Dimensional Data

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