Bidirectional Nonnegative Deep Model and Its Optimization in Learning

Abstract

Nonnegative matrix factorization (NMF) has been successfully applied in signal processing as a simple two-layer nonnegative neural network. Projective NMF (PNMF) with fewer parameters was proposed, which projects a high-dimensional nonnegative data onto a lower-dimensional nonnegative subspace. Although PNMF overcomes the problem of out-of-sample of NMF, it does not consider the nonlinear characteristic of data and is only a kind of narrow signal decomposition method. In this paper, we combine the PNMF with deep learning and nonlinear fitting to propose a bidirectional nonnegative deep learning (BNDL) model and its optimization learning algorithm, which can obtain nonlinear multilayer deep nonnegative feature representation. Experiments show that the proposed model can not only solve the problem of out-of-sample of NMF but also learn hierarchical nonnegative feature representations with better clustering performance than classical NMF, PNMF, and Deep Semi-NMF algorithms.