非负矩阵分解的分层最小二乘快速算法研究

摘要

非负矩阵分解是对于代价函数近似非线性优化问题,考虑均方误差值作为代价函数,通过对分层交替非负最小二乘算法的迭代运算量进行分析,对运算耗费大的矩阵运算提出利用限制更新的方法对分层交替非负最小二乘算法进行修改,达到加速收敛的目的.通过仿真,与原倍乘更新算法、投射梯度算法比较,验证算法的有效性和稳定性和高效性.%Nonnegative matrix factorization( NMF) is typically formulated as a nonlinear optimization problem with a cost function measuring the quality of the low-rank approximation. In this paper, we considered the sum of squared errors as a cost function. We proposed a simple modifcation of Hierarchical alternating leasts quares (HALS) to speed up their convergence signifcantly based on the analysis of matrix computational cost. The proposed organization of the different matrix computations (in particular the ordering of the matrix products) minimizes the total computational cost. The experimental results confirm the validity and high performance of the developed algorithms by compa-ration with the original HALS and the projected gradient method of Lin ( PG).