Nonnegative Matrix Factorization Regularized by k-NN Graphs

Abstract

Nonnegative matrix factorization (NMF) is a widely used feature extraction method.NMF decomposes a data matrix into a basis matrix and a feature matrix with all ofthese matrices allow to have only nonnegative elements.With only non-subtractive constraints, NMF learns a sparse basis matrix,result in part-based representation.The fundamental goal of feature extraction is to exploit the more compact anddiscriminative representation of input data for further processing such asclassification or clustering.NMF is unsupervised feature extraction method, which assumes thatdata points are generated from Euclidean space.Based on this observation , we use label information to directly exploit the discriminativegeometrical structure of data points to extract more discriminative and also respectsmanifold structure of data.In this paper, we propose a novel feature extraction (subspace learning) method namedNMF regularized by k-NN graphs (KNMF).KNMF is based on two kinds of graphs:within-class k-NN graph and between-class k-NN graph.Within-class k-NN graph connects only the neighboring data points which belong tothe same class of the given data point,while between-class k-NN graph connects the neighboring data pointswhich belong to different class of the given data point.By minimizing the local regions of within-class neighborhood andmaximizing the local regions of between-class neighborhood,KNMF could exploit more discriminative hidden patterns of given data set,benefit to the following classification based on the extracted features.Experiments on several benchmark face recognition datasets and document datasetsconfirmed the useful behavior of our proposed method in the task of feature extraction.