K-means*: Clustering by Gradual Data Transformation

1. K-means*: Clustering by Gradual Data Transformation Mikko Malinen and Pasi Fränti • Speech and Image Processing Unit • School of Computing • University of Eastern Finland

2. K-means* clustering Gradual transformation of data Fit the data to a model Model Intermediate Final Data

3. K-means clustering Iterate between two steps: 1. Assignment step Assign the points to the nearest centroids 2. Update step Update the location of centroids

4. K-means* clustering

5. Example of clustering (s2 dataset)

6. 0% done

7. 10% done

8. 20% done

9. 30% done

10. 40% done

11. 50% done

12. 60% done

13. 70% done

14. 80% done

15. 90% done

16. 100% done

17. Empty clusters problem

18. Time Complexity

19. Time Complexity Fixedk-means

20. s1 d = 2 n = 5000 k = 15 s2 d = 2 n = 5000 k = 15 s3 d = 2 n = 5000 k = 15 s4 d = 2 n = 5000 k = 15 bridge d = 16 n = 4096 k= 256 missa d = 16 n = 6480 k= 256 house d = 3 n=34000 k=256 thyroid d = 5 n = 215 k = 2 iris d = 4 n = 150 k = 2 wine d = 13 n = 178 k = 3 Datasets

21. Mean square error

22. Mean square error vs.number of steps

23. Mean square error vs.number of steps

24. Mean square error vs.number of steps

25. Mean square error vs.number of steps

26. Mean square error vs.number of steps

27. Mean square error vs.number of steps

28. Mean square error vs.number of steps

29. Number of incorrect clusters All correct: proposed:36% k-means:14%

30. Number of incorrect clusters 1 incorrect: proposed:64% k-means:38%

31. Number of incorrect clusters 2 incorrect: proposed: 0% k-means:34%

32. Number of incorrect clusters 3 incorrect: proposed: 0% k-means:10%

33. Summary We have presented a clustering method based on gradual transformation of data and k-means. Instead of fitting the model to data, we fit the data to a model. The proposed method gives better mean square error than k-means.