基于SVD的双线性非负矩阵集分解

Decomposition based on SVD bilinear non-negative matrix set

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。基于双线性型的非负矩阵集分解(bilinear form-based non-negative matrix set factorization,BFBNMSF)是对NMF的扩展,处理数据矩阵集时,BFBNMSF比NMF描述力强、推广性好。但BFBNMSF在初始化时使用随机分布,为使BFBNMSF更快收敛,该文提出一种基于奇异值分解(Singular value decomposition,SVD)初始化的BFBNMSF,即SVD-BFBNMSF,对系数矩阵进行初始化,已达到快速收敛的目的。实验结果表明:与传统BFBNMSF比较,该方法在收敛速度确有所改善。

The non-negative matrix factorization is a commonly used non-negative multivariate data description. Processing the data matrix set of NMF description is not strong, and poor promotion. Based on the bilinear form a non-negative matrix set decomposition is the extension of NMF, process the data matrix set, BFBNMSF compares with the NMF,it describes strong, has good promotion. But BFBNMSF randomly distributed at initialization time, to make BFBNMSF faster convergence, this paper proposed based on singular value decomposition to initialize the BFBNMSF, namely the SVD-BFBNMSF, the coefficient matrix of the early initialization has reached the goal of fast convergence. The experimental results show that compared with the traditional BFBNMSF the convergence speed is indeed improved.