1. Multidimensional Data Analysis
IS 247 Information Visualization and Presentation
22 February 2002
James Reffell Moryma Aydelott Jean-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. Warning: These visualizations are not easy to grasp at “first glance”!
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)

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 -

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:

26. Worlds Within Worlds Constraints: Technical details:
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

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 wisdom from 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”