基于双线性型的非负矩阵集分解

Bilinear Form-Based Non-Negative Matrix Set Factorization

非负矩阵分解(Non-negative Matrix Factorization,NMF)是一种常用的非负多元数据描述方法.处理数据矩阵集时,NMF描述力不强、推广性差.为解决这两个问题,并保留NMF的好特性,该文提出了非负矩阵集分解(Non-negative Matrix Set Factorization,NMSF)的概念,并在NMSF的框架下系统研究了基于双线性型的非负矩阵集分解(Bilinear Form-Based Non-negative Matrix Set Factorization,BFBNMSF),构造了单调下降的BFBNMSF算法.理论分析和实验结果均表明:处理数据矩阵集时,BFBNMSF比NMF描述力强、推广性好.由此可认为,此时BFBNMSF比NMF更善于抓住数据的本质特征.

Non-negative Matrix Factorization （NMF） is a popular technique for representations of non-negative multivariate data. While treating a set of matrices, NMF is confronted with two main problems （unsatisfactory accuracy of representation and bad generality）. In this paper, Non-negative Matrix Set Factorization （NMSF） is conceived to overcome the two problems and to retain NMF＇s good properties. Under the frame of NMSF, Bilinear Form-Based Non-negative Matrix Set Factorization （BFBNMSF） is systematically studied, and a monotonic algorithm of NMF.