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Object Orie’d Data Analysis, Last Time

Object Orie’d Data Analysis, Last Time. DiProPerm Test Direction – Projection – Permutation HDLSS hypothesis testing NCI 60 Data Particulate Matter Data Perou 500 Breast Cancer Data OK for subpop’ns found by clustering??? Started Investigation of Clustering Simple 1-d examples.

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Object Orie’d Data Analysis, Last Time

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  1. Object Orie’d Data Analysis, Last Time • DiProPerm Test • Direction – Projection – Permutation • HDLSS hypothesis testing • NCI 60 Data • Particulate Matter Data • Perou 500 Breast Cancer Data • OK for subpop’ns found by clustering??? • Started Investigation of Clustering • Simple 1-d examples

  2. Clustering Important References: • McQueen (1967) • Hartigan (1975) • Gersho and Gray (1992) • Kaufman and Rousseeuw (2005),

  3. K-means Clustering Notes on Cluster Index: • CI = 0 when all data at cluster means • CI small when gives tight clustering (within SS contains little variation) • CI big when gives poor clustering (within SS contains most of variation) • CI = 1 when all cluster means are same

  4. K-means Clustering Clustering Goal: • Given data • Choose classes • To miminize

  5. 2-means Clustering Study CI, using simple 1-d examples • Varying Standard Deviation

  6. 2-means Clustering

  7. 2-means Clustering

  8. 2-means Clustering Study CI, using simple 1-d examples • Varying Standard Deviation • Varying Mean

  9. 2-means Clustering

  10. 2-means Clustering

  11. 2-means Clustering Study CI, using simple 1-d examples • Varying Standard Deviation • Varying Mean • Varying Proportion

  12. 2-means Clustering

  13. 2-means Clustering

  14. 2-means Clustering

  15. 2-means Clustering

  16. 2-means Clustering

  17. 2-means Clustering

  18. 2-means Clustering

  19. 2-means Clustering

  20. 2-means Clustering

  21. 2-means Clustering

  22. 2-means Clustering

  23. 2-means Clustering

  24. 2-means Clustering

  25. 2-means Clustering

  26. 2-means Clustering

  27. 2-means Clustering Study CI, using simple 1-d examples • Over changing Classes (moving b’dry)

  28. 2-means Clustering

  29. 2-means Clustering

  30. 2-means Clustering

  31. 2-means Clustering

  32. 2-means Clustering

  33. 2-means Clustering

  34. 2-means Clustering

  35. 2-means Clustering

  36. 2-means Clustering

  37. 2-means Clustering

  38. 2-means Clustering Study CI, using simple 1-d examples • Over changing Classes (moving b’dry) • Multi-modal data  interesting effects • Multiple local minima (large number) • Maybe disconnected • Optimization (over ) can be tricky… (even in 1 dimension, with K = 2)

  39. 2-means Clustering

  40. 2-means Clustering Study CI, using simple 1-d examples • Over changing Classes (moving b’dry) • Multi-modal data  interesting effects • Can have 4 (or more) local mins (even in 1 dimension, with K = 2)

  41. 2-means Clustering

  42. 2-means Clustering Study CI, using simple 1-d examples • Over changing Classes (moving b’dry) • Multi-modal data  interesting effects • Local mins can be hard to find • i.e. iterative procedures can “get stuck” (even in 1 dimension, with K = 2)

  43. 2-means Clustering Study CI, using simple 1-d examples • Effect of a single outlier?

  44. 2-means Clustering

  45. 2-means Clustering

  46. 2-means Clustering

  47. 2-means Clustering

  48. 2-means Clustering

  49. 2-means Clustering

  50. 2-means Clustering

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