Nonlinear Nonnegative Matrix Factorization Based on Discriminant Analysis with Application to Face Recognition

Traditional Nonnegative Matrix Factorization (NMF) is a linear and unsupervised algorithm. This would limit the classification power of NMF for the complicated data. To overcome the above limitations of NMF, this paper proposes a novel supervised and nonlinear NMF algorithm based on kernel theory and discriminant analysis. We incorporate the class label information into the decomposition of NMF in the Reproducing Kernel Hilbert Space (RKHS). A new iterative algorithm for NMF is derived and the objective function is non-increasing under the update rules. The proposed method is evaluated on the ORL and Yale face databases. The experimental results demonstrate the the proposed method is superior to the state of-the-art algorithms.