RadViz Extensions with Applications

1. RadViz Extensions with Applications Dissertation Defense John Sharko October 26, 2009

2. Committee • Prof. Georges Grinstein (Advisor) • Prof. Kenneth Marx • Prof. Haim Levkowitz • Dr. Patrick Hoffman • Dr. Alex Gee

3. Outline • Introduction • RadViz • Cluster Ensembles • Fuzzy Clusters • Methodology • Contributions • Recommendations

4. RadViz Example

5. Description of Traditional RadViz Each dimension in a dataset is represented by a point, called an anchor point, on the circumference of a circle. Each record in the dataset is positioned as if it were being pulled by a spring attached to each anchor point where the strength of the spring is proportional to that record’s coordinate or value for the dimension related to that anchor point.

6. RadViz ExampleAll Coordinate Values Equal

7. RadViz ExampleTwo Coordinate Values Equal

8. RadViz ExampleRange of Coordinates Values

9. RadViz ExampleRange of Coordinates Values

10. Terminology • Dimensional Anchor (Anchor Point) – point on the circle representing a dimension • Point • representation of record(s) within the circle

11. RadViz Mathematical Formulation where: xi and yi are the resulting transformed coordinates for record i θj is the angular position on the circle corresponding to dimension j ai,j is the value for dimension j for record i d is the number of dimensions and n the number of records.

12. Impact of Exchanging Dimensional Anchors A A B C (1, 0, 1, 0) D D C B

13. Example of Repositioning Anchor Points Using Layout Algorithm Before repositioning After repositioning

15. Multiple Clustered Datasets • Clustering algorithms are heuristic, not optimal • Different clustering algorithms tend to generate different clusters

16. Sample Multiple Clustered Dataset

17. Stable Group of Records

18. Uniquely Clustered Record

19. Fuzzy Clusters • A record belongs to multiple clusters • Varying strengths of association

20. Cluster Ensemble vs. Fuzzy Clustering

21. Using RadViz to Analyze Multiple Clustered Datasets • RadViz typically deals with real numbers • Cluster number just does not work • How do you produce a meaningful RadViz visualization?

22. Flattening of Categorical Data • Break up each original dimension into multiple dimensions • Each new dimension represents a value of the original dimension

23. Flattening a Dimension Flattened Manufacturer Model Small Large Sporty Van Price Original Manufacturer Model Type Price Original Record: (Cadillac, Deville, Large, 33) Flattened Record: (Cadillac, Deville, 0, 1, 0, 0, 33)

24. Flattening Multi Cluster Dataset Flattened Dimensions 1 2 1 2 3 1 2 3 4 Original Dimensions Algorithm A Algorithm B Algorithm C { { A B C A B C { Sample Record: (2, 1, 4) (0, 1, 1, 0, 0, 0, 0, 0, 1 )

25. Simple Example • Iris dataset • Three cluster sets • KM1: K-means clustering with 1000 iterations • KM2: K-means clustering with 100,000 iterations • HC: hierarchical clustering • Ten clusters per cluster set

26. Flattened Multi-cluster Iris Dataset KM1 Color Scale 10 9 8 7 6 5 4 3 2 1 HC-6

27. Flattened Multi-cluster Iris Dataset - Jittered KM1 Color Scale 10 9 8 7 6 5 4 3 2 1 HC-6

28. Flattened Multi-cluster Iris Dataset KM1 Color Scale 10 9 8 7 6 5 4 3 2 1 HC-6

29. Repositioning Dimensional Anchors • Move points away from the center • Separate points • Increase displayed information content

30. Class Discrimination Layout Algorithm • Select a dimension that classifies the records • Assign each dimension to the class with the highest values with respect to the other classes • Move the dimensional anchors assigned to the same class next to each other to form a classification sector

31. Example of Class Discrimination Layout Algorithm Before After Class Classification Sector 1 1 2 Classification Sector 2

32. After Repositioning Dimensional Anchors KM1 Cluster Size 30 records 20 records 10 records 5 records

33. After Repositioning Dimensional Anchors KM1-2 KM1 Cluster Size 30 records 20 records 10 records 5 records

34. After Repositioning Dimensional Anchors KM1 Cluster Size 30 records 20 records 10 records 5 records

35. After Repositioning Dimensional Anchors KM1 Cluster Size 30 records 20 records 10 records 5 records

36. After Repositioning Dimensional Anchors KM1 Cluster Size 30 records 20 records 10 records 5 records

37. After Repositioning Dimensional Anchors KM1 Cluster Size 30 records 20 records 10 records 5 records

38. After Repositioning Dimensional Anchors KM1 Cluster Size 30 records 20 records 10 records 5 records

39. Moving Similar Classification Sectors Close to Each Other -Dimensions have been grouped together into classification sectors -Determine which record classes are most similar to each other using Euclidean distances -Move those dimension sectors closer to each other using greedy algorithm -Records will tend to be moved away from the center

40. Repositioning Classification Sectors KM1 Color Scale KM2-5 KM1-7 KM1-3 HC-9 10 9 8 7 6 5 4 3 2 1 KM2-10 KM1-4 HC-5 7 HC-3 4 3 KM1-2 KM1-8 8 2 HC-6 HC-2 1 5 KM1-1 KM2-4 KM2-2 6 KM1-5 9 10 KM2-6 HC-8, HC-7 KM2-3, KM2-8 KM2-1, HC-10 KM2-9, KM1-6 HC-1 KM1-9 KM1-10 HC-4 KM2-7

41. Interpreting Vectorized RadViz Petal length Setosa Virsicolor Virginica Sepal length

42. Interpreting VRV Petal length Setosa Virsicolor Virginica Sepal length

43. Interpreting VRV Petal length Setosa Virsicolor Virginica Sepal length

44. Interpreting VRV Petal length Setosa Virsicolor Virginica Sepal length

45. Interpreting VRV Petal length Setosa Virsicolor Virginica Sepal length

46. Salamander Gene Expression Levels Expression Levels Time

47. Salamander Class 9 Genes Nvg00226 Nvg00111 Nvg00155 Nvg00091

48. Salamander Class 9 Genes • Nvg00111 • “Key” gene • CXC chemokine, ligand 10 • Nvg00226 • No homology • Nvg00155 • Keratin type II cytoskeletal • Nvg00091 • Annexin

49. Fuzzy Clusters

50. Description of Fuzzy Clusters • K-means clustering algorithm used • Four clusters • Applied to Iris dataset