General subspace constrained non-negative matrix factorization for data representation

Abstract

Nonnegative matrix factorization (NMF) has been proved to be a powerful data representation method, and has shown success in applications such as data representation and document clustering. However, the non-negative constraint alone is not able to capture the underlying properties of the data. In this paper, we present a framework to enforce general subspace constraints into NMF by augmenting the original objective function with two additional terms. One on constraints of the basis, the other on preserving the structural properties of the original data. This framework is general as it can be used to regularize NMF with a wide variety of subspace constraints that can be formulated into a certain form such as PCA, Fisher LDA and LPP. In addition, we present an iterative optimization algorithm to solve the general subspace constrained non-negative matrix factorization (GSC NMF). We show that the resulting subspace has enriched representation power as shown in our experiments.