NONNEGATIVE MATRIX FACTORIZATION WITH BAND CONSTRAINT

作     者：Xiangxiang Zhu Jicheng Li Zhuosheng Zhang 

作者机构：School of Mathematics and Statistics Xi'an Jiaotong University Xi'an 710049 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2018年第36卷第6期

页      面：761-775页

核心收录：

学科分类：0810[工学-信息与通信工程] 07[理学] 08[工学] 080401[工学-精密仪器及机械] 0804[工学-仪器科学与技术] 080402[工学-测试计量技术及仪器] 070104[理学-应用数学] 0835[工学-软件工程] 081002[工学-信号与信息处理] 0701[理学-数学] 

主　　题：Nonnegative matrix factorization Band structure Subspace clustering Sparserepresentation Image compression 

摘      要：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 signifi- cant 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.