Robust Graph Regularized Nonnegative Matrix Factorization

In the 21 st century,it has entered the information age of rapid development.We are faced with the vast amounts of data every day which contains large amounts of information.It has brought about a broad range of serious challenges in machine learning,data mining and computer vision communities.Cluster analysis is one of basic learning techniques in data mining research and Nonnegative Matrix Factorization(NMF)is one of the important methods in clustering.Recently,Nonnegative Matrix Factorization has received considerable attention in image processing,computer vision,and pattern recognition.NMF can decrease the dimensions of the data and clear some kind of underlying structure of data.Nonnegative constraints can lead to local,sparse representation,which has a better inhibitory effect on the outside noise.An important variant of NMF is Graph Regularized Nonnegative Matrix Factorization(GNMF).The algorithm aims at making the low dimensional factor obtained by the matrix factorization characterize and maintain the manifold structure of the data points reflected by the neighbor graph as accurately as possible.However,due to the presence of noisy data,errors and outliers in real world application,GNMF may fail to reflect the intrinsic structure of the data accurately,which makes it difficult to cluster analysis.In order to solve the problem of data quality,in this paper,we propose a new nonnegative matrix factorization algorithm: Robust Graph Regularized Nonnegative Matrix Factorization.The algorithm improves the robustness of GNMF by using 1,2? norm instead of 2? norm.We develop elegant multiplicative updating rules and provide a rigorous convergence analysis.Experiments on ORL and Yale face database demonstrate the effectiveness of the RGNMF algorithm.