Orthogonal Dual Graph Regularized Nonnegative Matrix Factorization.

Nonnegative matrix factorization (NMF) is a classical low-rank approximation method of data matrix, which decomposes a high-dimensional data matrix into two nonnegative low-rank matrices, namely basis matrix and coefficient matrix. In order to capture the local geometric structure of original dataset, manifold learning methods are incorporated into NMF framework. Motivated by recent progress in dual graph regularization, by considering the geometric structures of both the data manifold and the feature manifold, Orthogonal Dual-graph NMF (ODNMF) algorithms were proposed, which imposed orthogonality constraints on basis matrix or coefficient matrix. Since the projection directions were mutually orthogonal, the representation power of data samples was enhanced, thus ODNMF methods are more robust for data clustering. The extensive experimental results on UCI, text and face image data sets have demonstrated the superiority of the proposed methods.