基于约束图正则的块稀疏对称非负矩阵分解  

Block Sparse Symmetric Nonnegative Matrix Factorization Based on Constrained Graph Regularization

作　　者：刘威[1] 邓秀勤[1] 刘冬冬 刘玉兰 LIU Wei;DENG Xiuqin;LIU Dongdong;LIU Yulan(School of Mathematics and Statistics,Guangdong University of Technology,Guangzhou 510000,China)

机构地区：[1]广东工业大学数学与统计学院,广州510000

出　　处：《计算机科学》2023年第7期89-97,共9页Computer Science

基　　金：国家自然科学基金(12101136);广东省研究生教育创新计划项目(2021SFKC030);广州市科技基金(202102020273);广东省区域联合基金(2020A1515110967);重庆师范大学数学学科省部级重点实验室开放课题(CSSXKFKTQ202002)。

摘　　要：现有的基于对称非负矩阵因式分解(Symmetric Nonnegative matrix Factorization, SymNMF)算法大都仅依赖初始数据构造亲和矩阵,并且一定程度上忽视了样本有限的成对约束信息,无法有效区分不同类别的相似样本以及学习样本的几何特征。针对以上问题,提出了基于约束图正则的块稀疏对称非负矩阵分解(Block Sparse Symmetric Nonnegative Matrix Factorization Based on Constrained Graph Regularization, CGBS-SymNMF)。首先,通过先验信息构造约束图矩阵,用于指导类别指示矩阵区分高相似度的不同类别样本;然后,引入PCP-SDP(Pairwise Constraint Propagation by Semi-definite Programming)方法,利用成对约束学习一个新的样本图映射矩阵;最后,利用“勿连”约束构造不相似矩阵,用于引导一个块稀疏正则项,以增强模型抗噪能力。实验结果表明,所提算法具有更高的聚类精确度和稳定性。The existing algorithms based on symmetric nonnegative matrix factorization(SymNMF)are mostly rely on initial data to construct affinity matrices,and neglect the limited pairwise constraints,so these methods are unable to effectively distinguish similar samples of different categories or learn the geometric features of samples.To solve the above problems,this paper proposes a block sparse symmetric nonnegative matrix factorization based on constrained graph regularization(CGBS-SymNMF).Firstly,the constrained graph matrix is constructed by prior information,which is used to guide the clustering indicator matrix to distinguish different clusters of samples with high similarity.Secondly,pairwise constraint propagation by semidefinite programming(PCP-SDP)is introduced to learn a new sample graph mapping matrix by using pairwise constraints.Finally,a dissimilarity matrix is constructed by cannot-link constraints,which is used to guide a block sparse regular term for enhancing the anti-noise capability of the model.Experimental results demonstrate a higher clustering accuracy and stability of the proposed algorithm.

关 键 词：对称非负矩阵因式分解 亲和矩阵 成对约束 图正则 块稀疏 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]