不完全非负矩阵分解的加速算法

Accelerated Algorithm to Incomplete Nonnegative Matrix Factorization

非负矩阵分解(NMF)已成为数据分析与处理的一种日益流行的方法.当数据矩阵不完全时,可用加权非负矩阵分解(WNMF)来分解矩阵.但是在WNMF算法中,对于给定的搜索方向,步长的选取一般来说不是最优的.本文研究了不完全非负矩阵分解(INMF)问题,提出了加速算法(AINMF).首先,将INMF问题转化为交替地求解两个非负最小二乘(NNLS)问题.对于每个NNLS问题,在搜索方向上采用精确的步长.接着,分析了NNLS问题的算法复杂度.最后,试验结果证实了AINMF优于WNMF.

Nonnegative matrix factorization（NMF） is an increasingly popular technique for data processing and analysis.For an incomplete data matrix,the weighted nonnegative matrix factorization（WNMF） is employed to decompose it.But the searching step size in WNMF is not optimal along the given searching direction.This paper studies the incomplete nonnegative matrix factorization（INMF） and proposes an accelerated algorithm.First,INMF is transformed into solving alternatively two nonnegative least squares（NNLS） problems.For each NNLS problem,the exact step size is chosen along the searching direction.Then,the complexity of NNLS problems is analyzed.Finally,experimental results show that the proposed method outperforms WNMF.