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 - <p style="text-align: justify;">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.</p>