1. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Structuring Interactive Cluster Analysis Wayne Oldford University of Waterloo

2. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Overview ill-defined problem high-interaction desirable explore partitions recast algorithms problems resources interactive clustering partition moves implications Content by example:Argument:

3. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Problem … geometric/visual structure

4. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Problem … context matters

5. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Problem … structure in context … image source … segmentation in MRI

6. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Problem … context specific structure … image source

7. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Problem … some specific some not … image source

8. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Problem … some specific some not … image source

9. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Problem –What do you mean similar? Find groups in data – –Similar objects are together – –Groups are separated Problem is ill defined: – –Can we believe it? E.g. what is contiguous structure? – –When are groups separate?

10. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Computational resources 1. Processing 2. Memory 3. Display

11. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Computational resources 1. Processing 2. Memory 3. Display “computationally intensive” problem constrained optimality sought

12. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Computational resources 1. Processing 2. Memory 3. Display GBs, TBs, disk GBs ram to processor more data

13. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Computational resources 1. Processing 2. Memory 3. Display high resolution, large graphics processors, digital video more data, more visual detail

14. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Computational resources 1. Processing 2. Memory 3. Display Balance and integrate

15. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland High interaction integrate computational resources multiple displays software design?

16. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Example: image analysis

17. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Example: context and function plots

18. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Example: mutual support and shapes

19. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Example: exploratory data analysis

20. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interactive clustering visual grouping –location, motion, shape, texture,... –linking across displays manual –selection cases, variates, groups,... –colouring –focus immediate and incremental –context can be used to form groups multiple partitions

21. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Automated clustering: typical software resources dedicated to numerical computation –teletype interaction –runs to completion –graphical “output” don’t always work so well (no universal solution) confirm via exploratory data analysis Must be integrated with interactive methods

22. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Example: K-means clustering

23. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Example: VERI Visual Empirical Regions of Influence join points if no third point falls in this region

24. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Example: VERI

25. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Integrating automatic methods: Move about the space of partitions: P a --> P b --> P c --> …. Which operators f f(P a ) --> P b are of interest?

26. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Refine Reduce

27. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Reassign

28. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Refinement sequence: 1-> 2-> 3-> 4-> 5

29. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Reassign, reduce sequence: 5-> 5

30. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Reassign, reduce sequence: 5-> 5-> 4-> 3 -> 2

31. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Moves: examples: refine (P old ) --> P new break minimal spanning tree reduce (P old ) --> P new join near centres reassign (P old ) --> P new k-means maximize F partition (graphic) --> P new colours from point cloud

32. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Challenges: varying focus subsets (selected manually and at random) merging new data into partition interface design control panels, options interaction exploring multiple partitions interactive display and comparison resolving many to one

33. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interface

34. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interface - reduce

35. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interface - refine

36. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interface - reassign

37. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interaction

38. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interaction - refine 2

39. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interaction - refine 3

40. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interaction -save partition movie

41. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interaction -refine 4

42. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interaction - refine 5

43. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interaction - refine 5 dendrogram

44. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interaction - reassign

45. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Interaction - cluster plot movie

46. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Creation: partition (Data ;...) --> P new “manually” from colours k-means, random start, mst, veri, etc from existing classifier. partition-path (Data ; …) --> {P 1, P 2, …, P n } partition-path (P old ;...) --> {P old, P 1, P 2, …, P n } e.g. nested sequence from hierarchical clustering

47. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Composition: merge (P a, P b ; …) --> P + new combine non-overlapping partitions merge (Data, P old ; …) --> P + new classify additional points resolve (P 1,..., P m ; …) --> P new combine different partitions of the same data

48. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Other operators dissimilarity (P i, P j ) --> d i,j display (P 1,..., P m ) – –dendrogram if P 1 < …< P m – –mds plot of all clusters in P 1, …, P m – –mds plot of all partitions P 1, …, P m

49. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Implications: Algorithms (re)cast in terms of moves: –refine, reduce –reassign –partition, partition-path –easily understandable (e.g. geometric structures) –specify required data structures e.g. ms tree, triangulation, var-cov matrix, …

50. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland New problems: interface design multiple partitions –comparison and/or resolution –multiple display inference

51. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Summary Cluster analysis is naturally exploratory and needs integration with modern interactive data analysis. Enlarging the problem to partitions: –simplifies and gives structure –encourages exploratory approach –integrates naturally –introduces new possibilities (analysis and research)

52. June 26, 2003 Dept. of Computer Science Memorial University of Newfoundland Acknowledgements: Catherine Hurley, Erin McLeish, Rayan Yahfoufi, Natasha Wiebe U(W) students in statistical computing Quail: Quantitative Analysis in Lisp http://www.stats.uwaterloo.ca/Quail