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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