Orthogonal Nonnegative Matrix Factorization by Sparsity and Nuclear Norm Optimization

Junjun Pan; Michael K. Ng

doi:10.1137/16M1107863

Orthogonal Nonnegative Matrix Factorization by Sparsity and Nuclear Norm Optimization

Junjun Pan, Michael K. Ng^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

17 Citations (Scopus)

283 Downloads (Pure)

Abstract

In this paper, we study orthogonal nonnegative matrix factorization. We demonstrate the coefficient matrix can be sparse and low-rank in the orthogonal nonnegative matrix factorization. By using these properties, we propose to use a sparsity and nuclear norm minimization for the factorization and develop a convex optimization model for finding the coefficient matrix in the factorization. Numerical examples including synthetic and real-world data sets are presented to illustrate the effectiveness of the proposed algorithm and demonstrate that its performance is better than other testing methods.

Original language	English
Pages (from-to)	856-875
Number of pages	20
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	39
Issue number	2
DOIs	https://doi.org/10.1137/16M1107863
Publication status	Published - 22 May 2018

Scopus Subject Areas

Analysis

User-Defined Keywords

Convex optimization
Document clustering
Hyperspectral image unmixing
Nuclear norm
Orthogonal nonnegative matrix factorization
Sparsity

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abstract = "In this paper, we study orthogonal nonnegative matrix factorization. We demonstrate the coefficient matrix can be sparse and low-rank in the orthogonal nonnegative matrix factorization. By using these properties, we propose to use a sparsity and nuclear norm minimization for the factorization and develop a convex optimization model for finding the coefficient matrix in the factorization. Numerical examples including synthetic and real-world data sets are presented to illustrate the effectiveness of the proposed algorithm and demonstrate that its performance is better than other testing methods.",

keywords = "Convex optimization, Document clustering, Hyperspectral image unmixing, Nuclear norm, Orthogonal nonnegative matrix factorization, Sparsity",

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N2 - In this paper, we study orthogonal nonnegative matrix factorization. We demonstrate the coefficient matrix can be sparse and low-rank in the orthogonal nonnegative matrix factorization. By using these properties, we propose to use a sparsity and nuclear norm minimization for the factorization and develop a convex optimization model for finding the coefficient matrix in the factorization. Numerical examples including synthetic and real-world data sets are presented to illustrate the effectiveness of the proposed algorithm and demonstrate that its performance is better than other testing methods.

AB - In this paper, we study orthogonal nonnegative matrix factorization. We demonstrate the coefficient matrix can be sparse and low-rank in the orthogonal nonnegative matrix factorization. By using these properties, we propose to use a sparsity and nuclear norm minimization for the factorization and develop a convex optimization model for finding the coefficient matrix in the factorization. Numerical examples including synthetic and real-world data sets are presented to illustrate the effectiveness of the proposed algorithm and demonstrate that its performance is better than other testing methods.

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KW - Document clustering

KW - Hyperspectral image unmixing

KW - Nuclear norm

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KW - Sparsity

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Orthogonal Nonnegative Matrix Factorization by Sparsity and Nuclear Norm Optimization

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