求解非负矩阵分解的修正非单调投影梯度法

Modified Non-monotonic Projection Gradient Method for Non-negative Matrix Factorization

非负矩阵分解(NMF)是一新的特征提取方法.十几年来,NMF备受关注,并且被成功的应用于许多数据分析问题.非负矩阵分解目前的算法大部分是基于乘性算法,交替的最小二乘算法.然而,这些算法的收敛性都不能得到保证,这归咎于聚点的存在性不清楚.本文提出了一修正的非单调投影梯度算法求解NMF.该方法能保证投影梯度算法产生的点列至少有一聚点.数据实验表明该方法要比乘性算法好.

Non-negative matrix factorization （NMF） is a new feature extraction method. NMF has attracted much attention for over a decade and has been successfully applied to mtmerous data analysis problems. Most of the current algorithms are based on multiplicative iterative algorithms and alternating least squares algorithms. However, convergence analysis of these methods can not be guaranteed, this is attributed to the existence of accumulation point is not clear. In this paper, we propose a modified non-monotonic projection gradient method for NMF. This method can ensure that the sequence generated by projection gradient method has at least one limit point. Experimental results also show that our algorithm tends to converge to better solutions than the popular multiplicative update-based algorithms.