Year: 2018
Author: Xiangxiang Zhu, Jicheng Li, Zhuosheng Zhang
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 6 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1704-m2016-0657
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 6 : pp. 761–775
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Nonnegative matrix factorization Band structure Subspace clustering Sparse representation Image compression.
Author Details
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Two fast vector-wise update algorithms for orthogonal nonnegative matrix factorization with sparsity constraint
Li, Wenbo
Li, Jicheng
Liu, Xuenian
Dong, Liqiang
Journal of Computational and Applied Mathematics, Vol. 375 (2020), Iss. P.112785
https://doi.org/10.1016/j.cam.2020.112785 [Citations: 6]