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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. - PowerPoint PPT Presentation
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Robust Nonnegative Matrix Factorization
Yining Zhang 04-27-2012
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Outline
Review of nonnegative matrix factorization
Robust nonnegative matrix factorization using L21-norm
Robust nonnegative matrix factorization through sparse learning
Further works
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Outline
Review of nonnegative matrix factorization
Robust nonnegative matrix factorization using L21-norm
Robust nonnegative matrix factorization through sparse learning
Further works
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Review of nonnegative matrix factorization
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Clustering Interpretation
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Outline
Review of nonnegative matrix factorization
Robust nonnegative matrix factorization using L21-norm
Robust nonnegative matrix factorization through sparse learning
Further works
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Robust nonnegative matrix factorization using L21-norm
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Shortcoming of Standard NMF
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L21-norm
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From Laplacian noise to L21 NMF
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Illustration of robust NMF on toy data
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Illustration of robust NMF on real data
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Computation algorithm for L21NMF
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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.
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Updating G
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Correctness of the algorithm
Theorem 7. At convergence, the converged solution rule of Eq.(17) satisfies the KKT condition of the optimization theory.
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A general trick about the NMF
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KKT condition
Updating formula
Auxiliary function
Prove monotonicity
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Experiments on clustering
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Outline
Review of nonnegative matrix factorization
Robust nonnegative matrix factorization using L21-norm
Robust nonnegative matrix factorization through sparse learning
Further works
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Robust nonnegative matrix factorization through sparse learning
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Motivation
Motivated by robust pca
Optimization
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Experimental results-1 A case study
Experimental results 2-Face clustering on Yale
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Experimental results 3-Face recognition on AR
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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
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Future works-1
(1) Direct robust matrix factorization for anomaly detection. 2011 ICDM.
Future works-2
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[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
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Thanks! Q&A