L_(3/2)正则化图非负矩阵分解算法

L_(3/2) Regularized Graph Non-negative Matrix Factorization

基于图正则化非负矩阵分解算法(GNMF),提出一种基于凸光滑的L3/2范数正则化图非负矩阵分解算法.该算法用非负矩阵分解算法对数据进行低维非负分解时,根据流形学习的图框架理论,构建邻接矩阵保持数据局部几何结构,并对数据的低维表示特征进行凸光滑的L3/2范数稀疏性约束,在给出算法更新迭代规则的同时,从理论上证明了所给算法的收敛性.通过人脸数据库ORL、手写体数据库USPS和图像库COIL20的仿真实验表明,相对于非负矩阵分解算法及其基于稀疏表示的改进算法,所给算法均具有更高的聚类精度.

This paper presents a novel algorithm called L3/2 regularized graph non-negative matrix factorization,which was based on the convex and smooth L3/2 norm.When original data is factorized in lower dimensional space by non-negative matrix factorization,L3/2 regularized graph non-negative matrix factorization preserves the local structure and intrinsic geometry of data,with the aid of the convex and smooth L3/2 norm as sparse constrain for the low dimensional feature.An efficient multiplicative updating procedure was produced along with its theoretic j ustification of the algorithm convergence.Compared with non-negative matrix factorization and its improved algorithms based on sparse representation,the proposed method achieves better clustering results,which is shown by experiment results on ORL face database,USPS handwrite database,and COIL20 image database.