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Volume 36, Issue 6
Nonnegative Matrix Factorization with Band Constraint

Xiangxiang Zhu, Jicheng Li & Zhuosheng Zhang

DOI: 10.4208/jcm.1704-m2016-0657

J. Comp. Math., 36 (2018), pp. 761-775.

Published online: 2018-08

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  • Abstract

In this paper, we study a band constrained nonnegative matrix factorization (band NMF) problem: for a given nonnegative matrix $Y$, decompose it as $Y ≈ AX$ with $A$ a nonnegative matrix and $X$ a nonnegative block band matrix. This factorization model extends a single low rank subspace model to a mixture of several overlapping low rank subspaces, which not only can provide sparse representation, but also can capture significant grouping structure from a dataset. Based on overlapping subspace clustering and the capture of the level of overlap between neighbouring subspaces, two simple and practical algorithms are presented to solve the band NMF problem. Numerical experiments on both synthetic data and real images data show that band NMF enhances the performance of NMF in data representation and processing.

  • Keywords

Nonnegative matrix factorization, Band structure, Subspace clustering, Sparse representation, Image compression.

  • AMS Subject Headings

15A23, 65F30, 90C59

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhuxiangxiang@stu.xjtu.edu.cn (Xiangxiang Zhu)

jcli@mail.xjtu.edu.cn (Jicheng Li)

zszhang@mail.xjtu.edu.cn (Zhuosheng Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-761, author = {Zhu , XiangxiangLi , Jicheng and Zhang , Zhuosheng}, title = {Nonnegative Matrix Factorization with Band Constraint}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {6}, pages = {761--775}, abstract = {

In this paper, we study a band constrained nonnegative matrix factorization (band NMF) problem: for a given nonnegative matrix $Y$, decompose it as $Y ≈ AX$ with $A$ a nonnegative matrix and $X$ a nonnegative block band matrix. This factorization model extends a single low rank subspace model to a mixture of several overlapping low rank subspaces, which not only can provide sparse representation, but also can capture significant grouping structure from a dataset. Based on overlapping subspace clustering and the capture of the level of overlap between neighbouring subspaces, two simple and practical algorithms are presented to solve the band NMF problem. Numerical experiments on both synthetic data and real images data show that band NMF enhances the performance of NMF in data representation and processing.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1704-m2016-0657}, url = {http://global-sci.org/intro/article_detail/jcm/12601.html} }
TY - JOUR T1 - Nonnegative Matrix Factorization with Band Constraint AU - Zhu , Xiangxiang AU - Li , Jicheng AU - Zhang , Zhuosheng JO - Journal of Computational Mathematics VL - 6 SP - 761 EP - 775 PY - 2018 DA - 2018/08 SN - 36 DO - http://doi.org/10.4208/jcm.1704-m2016-0657 UR - https://global-sci.org/intro/article_detail/jcm/12601.html KW - Nonnegative matrix factorization, Band structure, Subspace clustering, Sparse representation, Image compression. AB -

In this paper, we study a band constrained nonnegative matrix factorization (band NMF) problem: for a given nonnegative matrix $Y$, decompose it as $Y ≈ AX$ with $A$ a nonnegative matrix and $X$ a nonnegative block band matrix. This factorization model extends a single low rank subspace model to a mixture of several overlapping low rank subspaces, which not only can provide sparse representation, but also can capture significant grouping structure from a dataset. Based on overlapping subspace clustering and the capture of the level of overlap between neighbouring subspaces, two simple and practical algorithms are presented to solve the band NMF problem. Numerical experiments on both synthetic data and real images data show that band NMF enhances the performance of NMF in data representation and processing.

Zhu , XiangxiangLi , Jicheng and Zhang , Zhuosheng. (2018). Nonnegative Matrix Factorization with Band Constraint. Journal of Computational Mathematics. 36 (6). 761-775. doi:10.4208/jcm.1704-m2016-0657
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