Supervised kernel nonnegative matrix factorization for face recognition

Nonnegative matrix factorization (NMF) is a promising algorithm for dimensionality reduction and local feature extraction. However, NMF is a linear and unsupervised method. The performance of NMF would be degraded when dealing with the complicated nonlinear distributed data, such as face images with variations of pose, illumination and facial expression. Also, the available labels could potentially improve the discriminant power of NMF. To overcome the aforementioned limitations of NMF, this paper proposes a novel supervised and nonlinear approach to enhance the classification power of NMF. By mapping the input data into a reproducing kernel Hilbert space (RKHS), we can discover the nonlinear relations between the data. This is known as the kernel methods. At the same time, we make use of discriminant analysis to force the within-class scatter small and between-class scatter large in the RKHS. It theoretically shows that the proposed approach can guarantee the non-negativity of the decomposed components and the objective function is non-increasing under the update rules. The proposed method is applied to face recognition. Compared with some state-of-the-art algorithms, experimental results demonstrate the superior performance of our method.