View
127
Download
0
Category
Tags:
Preview:
DESCRIPTION
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
Citation preview
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
6
7
Clustering Interpretation
8
Outline
Review of nonnegative matrix factorization
Robust nonnegative matrix factorization using L21-norm
Robust nonnegative matrix factorization through sparse learning
Further works
9
Robust nonnegative matrix factorization using L21-norm
10
Shortcoming of Standard NMF
11
L21-norm
12
From Laplacian noise to L21 NMF
13
Illustration of robust NMF on toy data
14
15
Illustration of robust NMF on real data
16
Computation algorithm for L21NMF
17
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
Updating G
19
Correctness of the algorithm
Theorem 7. At convergence, the converged solution rule of Eq.(17) satisfies the KKT condition of the optimization theory.
20
A general trick about the NMF
21
KKT condition
Updating formula
Auxiliary function
Prove monotonicity
22
Experiments on clustering
23
24
25
Outline
Review of nonnegative matrix factorization
Robust nonnegative matrix factorization using L21-norm
Robust nonnegative matrix factorization through sparse learning
Further works
26
Robust nonnegative matrix factorization through sparse learning
27
Motivation
Motivated by robust pca
Optimization
28
29
Experimental results-1 A case study
Experimental results 2-Face clustering on Yale
30
Experimental results 3-Face recognition on AR
31
32
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
33
Future works-1
(1) Direct robust matrix factorization for anomaly detection. 2011 ICDM.
Future works-2
34
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
Thanks! Q&A
Recommended