Facial Expression Recognition based on Graph-Preserving Sparse Non-Negative Matrix Factorization

In this paper, we present a novel algorithm for representing fa-cial expressions. The algorithm is based on the non-negative matrix factorization (NMF) algorithm, which decomposes the original facial image matrix into two non-negative matrices, namely the coefficient matrix and the basis image matrix. We call the novel algorithm graph-preserving sparse non-negative matrix factorization (GSNMF). GSNMF utilizes both sparse and graph-preserving constraints to achieve a non-negative factorization. The graph-preserving criterion preserves the structure of the original facial images in the embedded sub-space while considering the class information of the facial im-ages. Therefore, GSNMF has more discriminant power than NMF. GSNMF is applied to facial images for the recogni-tion of six basic facial expressions. Our experiments show that GSNMF achieves on average a recognition rate of 93.5% compared to that of discriminant NMF with 91.6%. Index Terms — Facial expression recognition, non-negative matrix factorization, graph-preserving constraint, sparse representations 1