Transcript Robust nonnegative matrix factorization using L21-norm

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
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
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Optimization
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Experimental results-1 A case study
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Experimental results 2Face clustering on Yale
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Experimental results 3Face 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.
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Future works-2
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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 nonnegative 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..
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Thanks! Q&A
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