Multidimensional Data Analysis

1. Multidimensional Data Analysis IS 247 Information Visualization and Presentation 22 February 2002 James ReffellMoryma AydelottJean-Anne Fitzpatrick

2. Problem Statement • How to effectively present more than 3 dimensions of information in a visual display with 2 (to 3) dimensions? • How to effectively visualize “inherently abstract” data? • How to effectively visualize very large, often complex data sets? • How to effectively display results – when you don’t know what those results will be?

3. Key Goals • More than 3 dimensions of data simultaneously • Support “fuzzyness” (similarity queries, vector space, tolerance ranges) • Support exploratory, opportunistic, “what-if” queries • Allow identification of “interesting data properties” through pattern recognition • Explore various dimensions without losing overview

4. Another Statement of Goals Visualization of multidimensional data • Without loss of information • With: • Minimal complexity • Any number of dimensions • Variables treated uniformly • Objects remain recognizable across transformations • Easy / intuitive conveyance of information • Mathematically / algorithmically rigorous (Adapted from Inselberg)

5. Purposes / Uses • Find clusters of similar data • Find “hot spots” (exceptional items in otherwise homogeneous regions) • Show relationships between multiple variables • Similarity retrieval rather than boolean matching, show near misses “Searching for patterns in the big picture and fluidly investigating interesting details without losing framing context” (Rao & Card)

6. Characteristics • “Data-dense displays” (large number of dimensions and/or values) • Often combine color with position / proximity representing relevance “distance” • Often provide multiple views • Build on concepts from previous weeks: • Retinal properties of marks • Gestalt concepts, e.g., grouping • Direct manipulation / interactive queries • Incremental construction of queries • Dynamic feedback • Some require specialized input devices or unique gesture vocabulary

7. Examples Warning: These visualizations are not easy to grasp at “first glance”! DON’T PANIC

8. Influence Explorer / Prosection Matrix(Tweedie et. al.) • We saw the video • Abstract one-way mathematical models: multiple parameters, multiple variables • Data through sampling • Colour coding, esp. near misses • Task: Make the red bit as big as possible!

9. Influence Explorer / Prosection Matrix(Tweedie et. al.) • Selecting performance limits

10. Influence Explorer / Prosection Matrix(Tweedie et. al.) • The colours go in two directions!

11. Influence Explorer / Prosection Matrix(Tweedie et. al.) • Fitting tolerance region (yellow box) to acceptability (red region) gives high yield for minimum cost

12. The Table Lens (Rao and Card) • - Tools: zoom, adjust, slide • - Cell contents coded by color (nominal) or bar length (interval) • - Special mouse gesture vocabulary • Search / browse (spotlighting)

13. The Table Lens (Rao and Card)

14. The Table Lens (Rao and Card) http://www.tablelens.com

15. Parallel Coordinates(Inselberg) • Transformation of multiple graphs by using parallel axes in a 2D representation. • Users attempt to recognize patterns between the axes - adding or removing parts of the data to see general patterns or more closely examine particular interactions. • Article offers suggestions on how to most effectively use this system.

16. Parallel Coordinates(Inselberg) Dataset in a Cartesian graph Same dataset in parallel coordinates Parallel Coordinates applet - http://csgrad.cs.vt.edu/~agoel/parallel_coordinates/

17. Parallel Coordinates(Inselberg) Strengths – • Works for any N • Clearly displays data characteristics of the data (without needing beaucoup explanations) • Easy to adjust or focus displays/ queries • Testing showed that it showed problems missed using other forms of process control • Can be used in decision support when used as a visual modeling tool (to see how adjusting one parameter effects others). • Weaknesses – • Formation of complex queries can be tricky (if you want to get results that are useful and easy to interpret).

18. Polaris(Stolte and Hanharan) • Extends pivot tables to generate graphic displays • Multiple graphs on one screen • Designed to “combine statistical analysis and visualization” (a pivot table) (polaris)

19. Polaris(Stolte and Hanharan) • Table algebra automatically generated via drag and drop. • Suitable graphic types are system selected based on query/result criteria. Include tables, bar charts, dot plot, gantt charts, matrices of scatterplots, maps. • Users can select marks (marks differ by shape, size, orientation and color).

20. Polaris(Stolte and Hanharan) Strengths – • Can be used with existing DB systems • Direct manipulation - drag and drop • Users can play with appearance of display • Linking and Brushing supported • Weaknesses – • User only sees aggregated (not original) data • System performs a number of functions automatically (conversion of variables, aggregation) - user may not know or not be able to control how their data is changed.

21. Worlds Within Worlds(Fiener and Beshers) • Basic approach: graph 3 dimensions, while holding “extra” dimensions constant • Visually represent “extra” dimensions as space within which graph(s) are placed • Position of “inner world” graph axis zero point equals set of constant values in “outer world” • Tools: • Dipstick • Waterline • Magnifying box The following images from: http://www-courses.cs.uiuc.edu/~cs419/multidim.ppt

26. Worlds Within Worlds • Constraints: • Uses special input device (“Data Glove”) and output device (liquid crystal stereo glasses); use without these special devices less than optimal • Technical details: • Suspend calculation of “child” details during movement • Algorithm for prioritizing overlapping objects • Need to “turn off” gesture recognition to allow normal use of hand

27. Worlds Within Worlds I/O Devices

28. Techniques for plotting multivariate functions(Mihalisin et al) • Multiples showing component dimensions, color codes for dimensions applied across multiples • Or, for categorical data, select mth category from nth dimension • Or, plot nested boxes, step values of independent variables and color-coding dependent variable

29. Techniques for plotting multivariate functions(Mihalisin et al) • Tools: • General zoom: look at smaller range of data in same amount of space • Subspace zoom: select view of particular dimension’s input to function • Decimate tool: sample fewer values within range

30. from http://www.cs.umd.edu/class/spring2001/cmsc838b/presentations/Zhijian_Pan/mdmv.ppt

31. from http://www.cs.umd.edu/class/spring2001/cmsc838b/presentations/Zhijian_Pan/mdmv.ppt

32. VisDB(Keim & Kriegel) • Mapping entries from relational database to pixels on the screen • Include “approximate” answers, with placement and color-coding based on relevance • Data points laid out in: • Rectangular spiral • Or, with axes representing positive/negative values for two selected dimensions • Or, group dimensions together (easier to interpret than very large number of dimensions)

33. from http://infovis.cs.vt.edu/cs5984/students/VisDB.ppt

34. VisDB - Relevance • Relevance calculation based on “distance” of each variable from query specification • Distance calculation depends on data type • Numeric: mathematical • String: character/substring matching, lexical, phonetic?, syntactic? • Nominal: predefined distance matrix • Possibly other “domain-specific” distance metrics

35. VisDB – Screen Resolution • Stated screen resolution seems reasonable by today’s standards:19 inch display, 1024x1280 pixels= 1.3 million data points • However, controls take up a lot of space!

36. from http://www1.ics.uci.edu/~kobsa/courses/ICS280/notes/presentations/Keim-VisDB.ppt

37. VisDB – Implementation • Requires features not available in commercial databases: • Partial query results • Incremental changes to queries • Speed? (1994 vs today)

38. Limitations and Issues • (intro to following slides and/or Tweedie’s words of wisdom?)

39. Complexity • Simplest approach to representing N dimensions is N controls, N one-dimensional outputs – but this fails to represent complex relationships • Middle ground achieved by some?

40. Abstract data • These visualizations are oriented toward abstract data • For “naturally” two or three-dimensional data (things that vary over time or space, e.g., geographic data) visualizations which exploit those properties may exist and be more effective

41. User Testing? • Many of these systems seem only appropriate for expert use

42. Future Work • Save query parameters for reference / sharing results • Automated query generation or filtering – Intelligent agents?

43. Words of wisdomfrom Tweedie et al • Trade-off between amount of information, simplicity, and accuracy • “It is often hard to judge what users will find intuitive and how [a visualization] will support a particular task”