Information Visualization Multivariate Data Visualization Krešimir Matković

Transcription

1 Information Visualization Multivariate Data Visualization Krešimir Matković Vienna University of Technology, VRVis Research Center, Vienna

2 Multivariable >3D Data Tables have so many variables that orthogonal Visual Structures are not sufficient.

3 Multidimensional Multivariate Data Use of Color & Shape to increase dimensionality Table Lens Scatter plot matrix Chernoff faces Parallel Coordinates Star plot Star coordinates Parallel Sets Mosaic Plot Interaction and Coordinated Multiple Views, Example Application

4 Multidimensional Multivariate Data Conventional approach deals with n-dim. Euclidian spaces Each item is a point in n-dim. Space (n-tuple) Each dimension can be categorical (nominal, ordinal) or numerical Data example, meteorological stations in California Pi x,..., x,..., x i n 1 STATION AVERAGE TEMP PRESSURE ELEVATION

5 Visualizing single dimensions Each dimension (column in the table) can be visualized as 1D data Histogram, Bar Chart, Box-Plot

6 Visualizing pairs of dimensions Pairs of dimensions can be visualized as 2D data Scatter plot Widely used Shows correlation positive, negative, no correlation Shows clusters Multiple points scatter, increase size Can be used to show up to 5 dimensions (color, size, shape)

7 Visualizing pairs of dimensions

8 Visualizing pairs of dimensions

9 Visualizing many dimensions There are 2 geometric dimensions on screen For data sets with >2 dimensions, we must project data down to 2D Come up with visual mapping that locates each dimension into 2D plane A spreadsheet already does that Column -> dimension Row -> record, case, item

10 Table Lens Textual table too large Rao and Card 1994

11 Table Lens

12 (1/6) Distortion-oriented F+C vis. 5 Table lens [Rao/Card 1994] Initial view, no details

13 (1/6) Distortion-oriented F+C vis. 5 Table lens [Rao/Card 1994] Sort by 1YR

14 (1/6) Distortion-oriented F+C vis. 5 Table lens [Rao/Card 1994] Mark good 1YR Sort by 3YR

15 (1/6) Distortion-oriented F+C vis. 5 Table lens [Rao/Card 1994] Mark good 3YR Sort by 5YR Krešimir Matković An InfoVis, Interaction TU Wien, View 2016 on

16 (1/6) Distortion-oriented F+C vis. 5 Table lens [Rao/Card 1994] Open good lines

17 (1/6) Distortion-oriented F+C vis. 5 Table lens [Rao/Card 1994] Open Category

18 Multiplies Idea: use multiple single visualization many bar charts, e.g. Scatterplot matrix Show (all possible) combinations of dimensions as a scatterplot matrix Good overview of corellation for all depicted dimensions Often used in statistics Too small for many dimensions Zoom in usually possible

19 Scatter plot matrix [

20 Chernoff Faces 1 We can easily distinguish various faces Encode different variables in characteristics of human face Decreasing order of perception Area of face Shape of face Length of nose Location of mouth Curve of smile Width of mouth Location, separation, angle, shape and width of eyes Location of pupil Location, angle, width of eyebrows 20

21 Chernoff Faces 2 21

22 Chernoff Faces Example 1 [Joseph G. Spinelli and Yu Zhou] 22

23 Chernoff Faces Example 1 [Joseph G. Spinelli and Yu Zhou] 23

24 Chernoff Faces Example 2 24

25 Chernoff Faces Example 3 Comments? 25

26 Parallel Coordinates Parallel 2D axes Add/Remove data Establish Patterns Examine interactions Useful for recognizing patterns between the axes Skilled user

27 Parallel Coordinates 2 [Inselberg] Encode variables along a horizontal row Vertical line specifies single variable Blue line specifies a case

28 PC Line Point Duality 28

29 PC Line Point Duality 29

30 PC 5D Sphere! 30

31 Parallel Coordinates - Problems If many records overlapping and clutter Reorder dimensions Density Clustering Outlier preserving methods Short demo

32 Parallel Coordinates Outlier Preserving Novotny and Hauser

33 Extended Parallel Coordinates Greyscale, color Histogram information on axes Smooth brushing Angular brushing

34 Extended Parallel Coordinates Greyscale, color Histogram information on axes Smooth brushing Angular brushing

35 Extended Parallel Coordinates Greyscale, color Histogram information on axes Smooth brushing Angular brushing

36 Star Plot, Radar Chart Space out the n dimensions at equal angles around a circle Each spoke encodes a variable s value Data point is now a shape 36

37 Star Coordinates Similar idea as star plot Rather than represent point as shape, just accumulate values along a vector parallel to particular axis Data case then becomes a single point 37

38 Star Coordinates Similar idea as star plot Rather than represent point as shape, just accumulate values along a vector parallel to particular axis Data case then becomes a single point 38

39 Parallel Sets Parallel Coordinates for categorical data Axis replaced with boxes Layout similar to PC Demo! 39

40 Parallel Sets 2 Which class has the highest number of survivors? 40

41 Parallel Sets 3 Which class has the highest number of survivors? 41

42 Linewidth Illusion Playfair s chart from the Commercial and Political Atlas (1786) showing the balance of trade between England and the East Indies. 42

43 Linewidth Illusion Where is the difference highest? 43

44 Common Angle Plot a Possible Solution Heike Hofmann and Marie Vendettuoli, TVCG

45 Mosaic Plot Categorical data Not-suitable views: scatter plot, PC, Box Plot Example data: Titanic dataset Mosaic Plot Relationship between 2 or more categorical dimensions Start with a square of length 1 Divide it according to one category horizontally Divide each sub-block vertically according to another category. 45

46 Mosaic Plot [Steve Simon] [Stasko] 46

47 Mosaic Plot This and following slides on Mosaic plot adopted from Stephen Few: [Stasko] 47

48 Mosaic Plot 48

49 Mosaic Plot 49

50 Mosaic Plot 50

51 Mosaic Plot 51

52 Mosaic Plot 52

53 Mosaic Plot 53

54 Trees Visual Structures that refer to use of connection and enclosure to encode relationships among cases Desirable Features Planarity (no crossing edges) Clarity in reflecting the relationships among the nodes Clean, non-convoluted design Hierarchical relationships should be drawn directional

55 Trees

56 Treevis.net

57 ConeTree [Robertson et al, 1991]

58 Tree Maps [Johnson, Shneiderman, 1991] Outline Tree diagram Venn diagram Nested treemap Treemap

59 Tree Map

60 Tree Map

61 Tree Map

62 Tree Map

63 Tree Map

64 Tree Map

65 Networks Used to describe Communication Networks, Telephone Systems, Internet Nodes Unstructured Nominal Ordinal Quantity Links Directed Undirected [Branigan et al, 2001]

66 Networks Problems Visualizing Networks: Positioning of Nodes Managing links so they convey the actual information Handling the scale of graphs with large amounts of nodes Interaction Navigation [London Subway]

67 Dense Pixel Methods - Basic Idea Use pixel to represent one data item Number of pixels (~1M) determines number of items Relies on use of color - color mapping Value ranges are mapped to a fixed color sequence of full color (hue) scale but monotonically decreasing brightness [Butz Course Notes]

68 Horizontal arangement 8 horizontal bars correspond to 8 years Subdivisions between the bars represent 12 months within each year Example analysis results Gold price was very low in the sixth year IBM price fell quickly after the first 1 ½ month US-Dollar exchange rate was highest in the third year [Keim et al. 1995]

69 Query Dependent Arrengement

70 Pixel Bar Chart Overload typical bar chart with more information about individual elements [Keim et al.]

71 Pixel Bar Chart 1 Overload typical bar chart with more information about individual elements [Keim et al.]

72 Pixel Bar Chart 2 Make each pixel within a bar correspond to a data point in that group represented by the bar Can do millions that way Color the pixel to represent the value of one of the data point s variables [Keim et al.]

73 Pixel Bar Chart 2 Product type is x-axis divider Customers ordered by y-axis: dollar amount x-axis: number of visits Color is (a) dollar amount spent, (b) number of visits, (c) sales quantity [Keim et al.]

74 Pixel Bar Chart 3 [Keim et al.]

75 Pixel Bar Chart 4 Mapping specified by 5 tuple <Dx, Dy, Ox, Oy, C> Dx Attribute partitions x axis Dy Attribute partitions y axis Ox Attribute specifies x ordering Oy Attribute specifies y ordering C Attribute specifies color mapping [Keim et al.]

76 Pixel Bar Chart 5 [Keim et al.]

77 Pixel Bar Chart CFD Data [Martin Gasser Hannes Kiraly.]

78 Color Lines View 1 Pixel based techniqur for families of curves Interaction! [Stasko Course Notes]

79 Color Lines View 2 Demo! [Stasko Course Notes]

80 InfoVis Techniques D. Keim proposes a taxonomy of techniques Standard 2D/3D display Bar charts, scatterplots Geometrically transformed display Parallel coordinates Iconic display Needle icons, Chernoff faces Dense pixel display Pixel Bar Chart, Color Lines Stacked display Treemaps, dimensional stacking

81 Thank you! Special thanks for used materials to M.E. Gröller, H. Hauser, and colleagues from VRVis!