Two-Dimensional Non-negative Matrix Factorization for Face Representation and Recognition

Non-negative matrix factorization (NMF) is a recently developed method for finding parts-based representation of non-negative data such as face images. Although it has successfully been applied in several applications, directly using NMF for face recognition often leads to low performance. Moreover, when performing on large databases, NMF needs considerable computational costs. In this paper, we propose a novel NMF method, namely 2DNMF, which stands for 2-D non-negative matrix factorization. The main difference between NMF and 2DNMF is that the former first align images into 1D vectors and then represents them with a set of 1D bases, while the latter regards images as 2D matrices and represents them with a set of 2D bases. Experimental results on several face databases show that 2DNMF has better image reconstruction quality than NMF under the same compression ratio. Also the running time of 2DNMF is less, and the recognition accuracy higher than that of NMF.