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Robust Nonnegative Matrix Factorization

Robust Nonnegative Matrix Factorization. Yining Zhang 04-27-2012. Outline. Review of nonnegative matrix factorization Robust nonnegative matrix factorization using L21-norm Robust nonnegative matrix factorization through sparse learning Further works. Outline.

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Robust Nonnegative Matrix Factorization

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

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

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

  4. Review of nonnegative matrix factorization

  5. Clustering Interpretation

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

  7. Robust nonnegative matrix factorization using L21-norm

  8. Shortcoming of Standard NMF

  9. L21-norm

  10. From Laplacian noise to L21 NMF

  11. Illustration of robust NMF on toy data

  12. Illustration of robust NMF on real data

  13. Computation algorithm for L21NMF

  14. 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.

  15. Updating G

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

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

  18. Experiments on clustering

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

  20. Robust nonnegative matrix factorization through sparse learning

  21. Motivation Motivated by robust pca

  22. Optimization

  23. Experimental results-1 A case study

  24. Experimental results 2-Face clustering on Yale

  25. Experimental results 3-Face recognition on AR

  26. Outline • Review of sparse learning • Efficient and robust feature selection via joint l2,1-norm minimzation • Exploiting the entire feature space with sparsity for automatic image annotation • Further works

  27. Future works-1 • Direct robust matrix factorization for anomaly detection. 2011 ICDM.

  28. Future works-2

  29. Reference • [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..

  30. Thanks! Q&A

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