Structure preserving non-negative matrix factorization for dimensionality reduction

作     者：Li, Zechao Liu, Jing Lu, Hanqing 

作者机构：Chinese Acad Sci Natl Lab Pattern Recognit Inst Automat Beijing 100190 Peoples R China 

出 版 物：《COMPUTER VISION AND IMAGE UNDERSTANDING》 (计算机视觉与图像理解)

年 卷 期：2013年第117卷第9期

页      面：1175-1189页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：973 Program [2010CB327905] National Natural Science Foundation of China [61272329, 61070104, 61202325] 

主　　题：Dimensionality reduction Non-negative matrix factorization Structure preserving Basis compactness Multiplicative update algorithm 

摘      要：The problem of dimensionality reduction is to map data from high dimensional spaces to low dimensional spaces. In the process of dimensionality reduction, the data structure, which is helpful to discover the latent semantics and simultaneously respect the intrinsic geometric structure, should be preserved. In this paper, to discover a low-dimensional embedding space with the nature of structure preservation and basis compactness, we propose a novel dimensionality reduction algorithm, called Structure Preserving Non-negative Matrix Factorization (SPNMF). In SPNMF, three kinds of constraints, namely local affinity, distant repulsion, and embedding basis redundancy elimination, are incorporated into the NMF framework. SPNMF is formulated as an optimization problem and solved by an effective iterative multiplicative update algorithm. The convergence of the proposed update solutions is proved. Extensive experiments on both synthetic data and six real world data sets demonstrate the encouraging performance of the proposed algorithm in comparison to the state-of-the-art algorithms, especially some related works based on NMF. Moreover, the convergence of the proposed updating rules is experimentally validated. (C) 2013 Elsevier Inc. All rights reserved.