Multidimensional (Multivariate)

Transcription

1 Multidimensional (Multivariate) Data Visualization IV Course Spring 14 Graduate Course of UCAS May 9th,

2 Data by Dimensionality 1-D (Linear, Set and Sequences) SeeSoft, Info Mural 2-D (Map) GIS, ArcView, PageMaker 3-D (Shape, the World) n-d (Relational, l Statistical) i Spotfire, Tableau Temporal LifeLines, Palantir Tree (Hierarchy) Cone/Cam/Hyperbolic Network (Graph) Pajek, JUNG CAD, Medical, Architecture 2

3 Relational Data Model Represent data as a table Each row (tuple) represents a single record Each record is a fixed-length tuple Each column (attribute) represents a single variable Each attribute has a name and a data type A database is a collection of tables 3

4 Statistical Data Model Dimensions: Nominal/Ordinal variable describing data Dates, categories of values (independent variables) Measures: Interval/Ratio that can be aggregated Numbers to be analyzed (dependent variables) Aggregate as sum, count, average, std. deviation 4

5 Data by Variable/Measurement Types N - Nominal (labels) Fruits: Apples, oranges, O -Ordinal Sanitation of restaurants: A/B/C Q - Interval (No zero measure) Date: Jan. 19, 2006; Location (LAT 33.98, LONG ) Like a geometric point. Cannot compare directly Only differences (i.e. intervals) may be compared Q -Ratio (zero fixed) Physical measurement: Length, Mass, Temp, Counts and amounts Like a geometric vector, origin i is meaningful 5

6 Multivariate Data and Analysis Definitions Multivariate analysis is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical outcome variable at a time. Multivariate statistics is a form of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. Multivariate Data: three main components Objects: Item of interests (students, courses, terms, ) Attributes: Characteristics or properties of data (name, age, GPA, number, date, ) Relations: How two or more objects relate (student takes course, course during term, ) 6

7 Objects (Entries/Cases) Example Metadata London Olympic Game Performance Attributes (Measures/Variables) Relationship among multiple objects & tables 7

8 Example 8

9 Multivariate Data Classification Number of outcome/dependent variables per entry/case 1 - Univariate data 2 - Bivariate data 3 - Trivariate data >3 - Hypervariate data 9

10 Univariate Data Visualization Put independent variable/cases (Country) on x-axis Put dependent variable/measures (#gold medal) on y- axis 10

11 Bivariate Data Visualization 11

12 Trivariate Data Visualization 12

13 Trivariate Data Visualization horsepower mileage price cases Represent each variable in separate charts 13

14 Hypervariate Data Visualization 4~20 variables/measures nd -> 2D projection (3D): in maths, MDS/PCA/ 14

15 Hypervariate Data Visualization More visual channels: ~10 variables A tensor field by tile visualization x, y, color hue, saturation, value, size, shape, orientation, rotation, texture, etc. 15

16 Hypervariate Data Visualization Separate charts, multiple views on different variables cases variables variables cases 16

17 Hypervariate Data Visualization TableLens Turn spreadsheet into statistical data graphics Leverage the basic bar and scatterplot design Change nominal values to scatterplots Change quantitative values to bars 17

18 TableLens 18

19 TableLens Focus + Context 19

20 Hypervariate Data Visualization TableLens video (0:00~5:00) InfoZoom video However, spreadsheet-like visualizations show no correlation among variables 20

21 Scatterplot Matrix 21

22 Scatterplot Matrix 22

23 Pivot Table: Flexibly aggregating spreadsheets Data Table Pivot Table 23

24 OLAP Cubes: Multidimensional analytics in BI and Data Management Slice Dice 24

25 OLAP Cubes Drill-down Pivot 25

26 OLAP Cubes 26

27 Polaris: Multi-dimensional data visualization with extended Pivot Tables 27

28 Tableau: Commercial version of Polaris: Video demo: Tableau visualization of OLAP cube 28

29 Still miss something on multidimensional data? No multidimensional relationships! 29

30 Attribute histogram Attribute Explorer All objects on all attribute scales Interaction with attributes limits 30

31 Attribute Explorer Inter-relations between attributes brushing 31

32 Attribute Explorer Color-encoded sensitivity 32

33 Attribute Explorer Old-fashioned Video Demo! 33

34 Parallel Coordinate 34

35 Parallel Coordinate Sample multivariate data 35

36 First data entry Parallel Coordinate V1 V2 V3 V4 V5 36

37 Second data entry Parallel Coordinate V1 V2 V3 V4 V5 37

38 Third data entry Parallel Coordinate V1 V2 V3 V4 V5 38

39 Case Study: VLSI Chip Dataset The Dataset: Production data for 473 batches of a VLSI chip 16 process parameters: X1: The yield: % of produced chips that are useful X2: The quality of the produced chips (speed) X3 X12: 10 types of defects (zero defects shown at top) X13 X16: 4 physical parameters The Objective: Raise the yield (X1) and maintain high quality (X2) A. Inselberg, Multidimensional Detective, Proceedings of IEEE Symposium on Information Visualization (InfoVis '97),

40 Case Study: VLSI Chip Dataset Overview 40

41 Case Study: VLSI Chip Dataset Top Yield & Quality Defects Splits 41

42 Case Study: VLSI Chip Dataset Zero Defect: not the highest yield and quality 42

43 Case Study: VLSI Chip Dataset Best quality: some defects are necessary! 43

44 Parallel Coordinate Demo 44

45 Parallel Set How about categorical data? Live Demo 45

46 Star Plot (Radar Map) Rotate coordinate from Parallel Coordinate 46

47 Star Plot (Radar Map) Single-view v.s. Multiple-view 47

48 Star Coordinate Use data point instead of polyline in Star Plots Accumulate data value along a vector parallel to the axis 48

49 Summary Multivariate Data Model Statistical and relational Unvariate, Bivariate, Trivariate, Hypervariate Multivariate Data Visualization Charts, scatterplot, spreadsheet and spreadsheet-like visualization Scatterplot matrix, pivot table, OLAP cube, Polaris and Tableau Parallel Coordinate and Parallel Set Star plot (Radar map) and star coordinate 49

50 Questions? What s Next Multivariate Data Visualization Fun Demos 50

51 Final Project Checkpoint Are you ready? Team coordinators/leaders, please find Hanpengyu now 51

52 Fun Visualizations and Demos 52

53 FLINA: Flexible Linked Axes for Multivariate Data Visualization 53

54 Chernoff Faces 54

55 Mosaic Plot 55

56 Dust & Magnet 56

57 Untangling g Euler Diagram 57