Non-negative Matrix Factorization on Manifold

Recently Non-negative Matrix Factorization (NMF) has received a lot of attentions in information retrieval, computer vision and pattern recognition. NMF aims to find two non-negative matrices whose product can well approximate the original matrix. The sizes of these two matrices are usually smaller than the original matrix. This results in a compressed version of the original data matrix. The solution of NMF yields a natural parts-based representation for the data. When NMF is applied for data representation, a major disadvantage is that it fails to consider the geometric structure in the data. In this paper, we develop a graph based approach for parts-based data representation in order to overcome this limitation. We construct an affinity graph to encode the geometrical information and seek a matrix factorization which respects the graph structure. We demonstrate the success of this novel algorithm by applying it on real world problems.

• Type: Conference
• Year: 2008
• Where: ICDM
• Authors: Deng Cai, Xiaofei He, Xiaoyun Wu, Jiawei Han
• Keywords: Data Mining, ICDM 2008, Matrix Factorization, Non-Negative Matrix Factorization, Original Matrix