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![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]](https://image.slidesharecdn.com/fifthel-visualisingmultidimensionaldata-150717064701-lva1-app6892/75/Visualising-Multi-Dimensional-Data-42-2048.jpg)
Uploaded byAmit Kapoor
Visualising Multi Dimensional Data
The document discusses the visualization of multi-dimensional data, emphasizing the importance of transforming symbolic information into geometric representations. It covers various methods for visualizing small, large, and big data, outlining processes to acquire, encode, and render data effectively. Additionally, it highlights the necessity of interactivity and different visualization techniques, such as scatter plots, treemaps, and parallel coordinates, in interpreting complex datasets.
In this document
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Introduction by Amit Kapoor on visualizing multi-dimensional data, referencing Edwin Abbot's 'Flatland' and discussions on dimensions with examples like squares and spheres.
Highlights the significance of visual processing: 70% of sensory receptors are in the eyes, emphasizing visualization transformation from symbolic to geometric.
Categorizes data into Small, Large, Big, and Wide Data with examples of area sales data across different regions.
Describes parsing variables and encoding data for visualization, including axes and scales with area sales data.
Details various visualization systems like points, lines, and bars, as well as coordinate systems—Cartesian and Polar—for plotting data.
Defines the data visualization process for Small and Large Data, emphasizing data acquisition, encoding, rendering, and refining data.
Explores Big Data visualization, the need for histograms, and the processes involved in handling large datasets including acquisition, encoding, and filtering.
Lists methods for multi-dimensional visualization, including pixel-based, glyph, and geometric transforms to enhance data interaction and interpretation.
Analyzes a diamonds dataset with over 50K observations, discussing related variables like price, carat, cut, color, clarity, and their dimensions.
Discusses various chart options for 1D and 2D data visualizations, along with interactivity techniques like zooming and annotation.
Introduces advanced techniques for visualizing 4D to 6D data, including bubble plots, trellis, parallel coordinates, and interactive features.
Details the procedure for visualizing wide data, emphasizing thoughtful encoding, interactivity, and dimensionality reduction.
Provides resources like GitHub code for examples and concludes with a quote highlighting the value of visual insights.
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Visualising Multi Dimensional Data
- 1.
- 2. Flatland A Romance inMany Dimensions by Edwin Abbot (1884) Square
- 3. A square isbut a line in 2d eye The Square
- 4. The disappearing circle TheSphere visits the 2d flatland The Sphere rising out of 2d space The Sphere on the point of vanishing eye
- 5. The square isa cube in 3d! eye The Square sees the world in a new way!
- 6.
- 7. 70% of the sensory receptorsare in the eyes 50% of the brain used for visual processing 100ms to get a sense of the visual scene Visual Wired Brain
- 8.
- 9. “Visualisation is the transformationof the symbolic into geometric”
- 10. Small Data Large Data BigData Wide Data
- 11. Visualise Small Data AreaSales (Rs.) North 5 East 25 West 15 South 20 Central 10
- 12. Area Sales North 5 East25 West 15 South 20 Central 10 Acquire Data
- 13. Area Sales North 5 East25 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 East25 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 East25 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 LineChart Column Chart WaterfallStacked Column
- 18. Coordinates Cartesian - Flip DotPlot 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 (SmallData)Acquire Data Encode Shape Select Scales Render Coordinates Parse Variables
- 22.
- 23. Small Data Large Data BigData Wide Data
- 24. Visualise Large Data ~24,000Pincodes e.g. Pincode : 560076 Latitude : 12.8843049° Longitude: 77.5967384° Place : Bannerghatta Pincodes in India
- 25. Pincode Map Scatter plot, playwith alpha to show density But what if I want to show geographic nature of pincode?
- 26. Pincode+ Map Exploration oflarge data is iterative! Refine Data (Filter, Transform)
- 27. Data Viz Process (LargeData) Acquire Data Encode Shape Select Scales Render Coordinates Parse Variables Refine Data
- 28. Small Data Large Data BigData Wide 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 canbe effective (with overweighting unusual values) Require multiple plots or careful tuning parameters
- 31. Data Sample Model Models aregreat as they scale nicely. But, visualisation is required as “I don’t know, what I don’t know.”
- 32. Data Sample ModelBinning Binning cansolve 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.
- 35. “We are calling2015 the year of the histogram” Amanda Cox
- 36. “Visualising big data isthe process of creating generalized histograms” Amit Kapoor
- 37. Data Viz Process (BigData) Acquire Data Encode Shape Select Scales Render Coordinates Parse Variables Filter Data Aggregate Data
- 38. Small Data Large Data BigData Wide Data
- 39. Multi Dimensional Viz Standard 2d/3d PixelBased 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 PixelBased 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+ observationsof 10 dimensions
- 42. Diamonds dataset 50K+ observationsof 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+ observationsof 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 caratcut 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.
- 46. Chart Options PointsBars Lines Areas 1d Quantitative 1d Categorical 2d Quantitative + Categorical 2d Categorical + Categorical 2d Quantitative + Quantitative
- 47. Chart Options PointsBars 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.
- 49. 2d Scatter Plot Interaction:Annotation (4.13, 17329) (4.50, 18531) (5.01, 18081)
- 50. 2d Scatter Plot logtransformation
- 51. 2d Scatter Plot Selector Filter Area of Interest Carat > 1, Price > 10,000
- 52. 2d Scatter Plot Interaction:Pan & Zoom
- 53.
- 54. Use aesthetic for3d Size Color Shape
- 55. 3d Scatter Plot Sizefor Quantitative Dim
- 56. 3d Scatter Plot Colorfor Categorical Dim
- 57. 3d Scatter Plot Shapesdon’t scale well
- 58. 3d Scatter Plot depthpersp not good
- 59. 3d Scatter Plot Interaction:Rotation
- 60.
- 61. 4d Bubble Plot Colorand Size
- 62. 5d Bubble Plot Color,Size and Time The Joy of Stat - Hans Rosling
- 63. Trellis / Facets CreateSmall Multiples
- 64. Trellis / FacetGrid Create Small Multiples
- 65.
- 66.
- 67. Multiple View Create ManySmall Charts
- 68. Multiple View Interaction: Brushing& Linking
- 70.
- 71. Star Stick Chernoff Iconbased Approach
- 72.
- 73. Star Plot Plot onX-Y location color clarity depth cut table
- 74.
- 75.
- 76.
- 77.
- 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 CurvePixel Bar Chart Pixel Bar Chart - KeimVisDB - Keim Pixel Based Approach
- 82. Data Viz Process (WideData) Acquire Data Encode Shape Select Scales Render Algorithm Parse Variables Filter Data Aggregate Data Make Views Add Interactivity
- 83. Data Viz Process (WideData) 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 theseSlides https://github.com/amitkaps/multidim R libraries ❖ ggplot2 ❖ GGally ❖ ggsubplot ❖ scales ❖ iplots/Mondrian ❖ ggvis ❖ tourr ❖ rgl ❖ scatterplot3d ❖ dplyr ❖ tabplot ❖ grid ❖ gridExtra
- 85. “The greatest valueof a picture is when it forces us to notice what we never expected to see” John Tukey
- 86.