Two Classes Of Efficient Methods For Symmetric Nonnegative Matrix Factorization Problem

Symmetric nonnegative matrix factorization(SymNMF)is a powerful tool for data dimension reduction,which is widely used in text clustering,data mining and other fields.Its solutions are generally divided into two categories,one is nonsymmetric relaxations,the other is direct solvers.This paper puts forward two methods to solve SymNMF problem.The first chapter describes the research background and research status quo of SymNMF problem.In Chapter 2,an alternate rank-k nonnegative least square augmented Lagrange(ARkNLSAL)method is proposed,this method is based on the framework of approximately augmented Lagrange method(AALM)to solve the nonsymmetric relaxation problem of SymNMF,the augmented Lagrange(AL)subproblem is solved column by column by block coordinate descent(BCD)method,and the exact solution of nonnegative least squares(NLS)subproblem in BCD framework is given.In Chapter3,an accelerated Bregman proximal gradient method(ABPGM)is proposed to solve SymNMF problem directly based on the structure of SymNMF problem,this method by introducing kernel function and using Bregman distance overcomes the difficulty caused by non-Lipschitz continuous gradient of objective function in SymNMF problem,and enables it to be solved using the accelerated proximal gradient method(APG).Experiments on synthetic data and real data show that the ARkNLSAL method has advanced performance in terms of running time and clustering accuracy compared with the existing methods.Experiments on real data show that the clustering accuracy of ABPGM method is similar to the existing methods.The fourth chapter summarizes the thesis and gives the future research direction.