1. 1 Robust Nonnegative Matrix Factorization Yining Zhang 04-27-2012

2. 2 Outline  Review of nonnegative matrix factorization  Robust nonnegative matrix factorization using L21-norm  Robust nonnegative matrix factorization through sparse learning  Further works

3. 3 Outline  Review of nonnegative matrix factorization  Robust nonnegative matrix factorization using L21-norm  Robust nonnegative matrix factorization through sparse learning  Further works

4. 4 Review of nonnegative matrix factorization

5. 5

6. 6

7. 7 Clustering Interpretation

8. 8 Outline  Review of nonnegative matrix factorization  Robust nonnegative matrix factorization using L21-norm  Robust nonnegative matrix factorization through sparse learning  Further works

9. 9 Robust nonnegative matrix factorization using L21-norm

10. 10 Shortcoming of Standard NMF

11. 11 L21-norm

12. 12 From Laplacian noise to L21 NMF

13. 13 Illustration of robust NMF on toy data

14. 14

15. 15 Illustration of robust NMF on real data

16. 16

17. Computation algorithm for L21NMF 17

18. Convergence of the algorithm  Theorem 1. (A) Updating G using the rule of Eq.(17) while fixing F, the objective function monotonically decreases. (B) Updating F using the rule of Eq.(16) while fixing G, the objective function monotonically decreases. 18

19. Updating G 19

20. Correctness of the algorithm  Theorem 7. At convergence, the converged solution rule of Eq.(17) satisfies the KKT condition of the optimization theory. 20

21. A general trick about the NMF 21 KKT condition Updating formula Auxiliary function Prove monotonicity

22. 22

23. Experiments on clustering 23

24. 24

25. 25 Outline  Review of nonnegative matrix factorization  Robust nonnegative matrix factorization using L21-norm  Robust nonnegative matrix factorization through sparse learning  Further works

26. 26 Robust nonnegative matrix factorization through sparse learning

27. 27 Motivation Motivated by robust pca

28. Optimization 28

29. 29 Experimental results-1 A case study

30. Experimental results 2- Face clustering on Yale 30

31. Experimental results 3- Face recognition on AR 31

32. 32 Outline  Review of sparse learning  Efficient and robust feature selection via joint l 2,1 -norm minimzation  Exploiting the entire feature space with sparsity for automatic image annotation  Further works

33. 33 Future works-1 (1) Direct robust matrix factorization for anomaly detection. 2011 ICDM.

34. Future works-2 34

35. 35 [1]Deguang Kong, Chris Ding, Heng Huang. Robust nonnegative matrix factorization using L21-norm. CIKM 2011. [2]Lijun Zhang, Zhengguang Chen, Miao Zheng, Xiaofei He. Robust non- negative matrix factorization. Front. Electr. Eng.China 2011. [3]Chris Ding, Tao Li, Michael I.Jordan. Convex and Semi-nonnegative matrix factorization. IEEE T.PAMI, 2010.. Reference

36. 36 Thanks! Q&A