A Novel Projective Nonnegative Matrix Factorization Based on Fisher Discriminant Analysis

Nonnegative matrix factorization (NMF) is a popular tool for data analysis in the non-negative quadrant. However, NMF has undesirable performance in classification tasks due to using unlabeled data for training and its basis matrix cannot be directly utilized as a projection matrix. To overcome the limitations of NMF, this paper proposes a novel Fisher criterion-based projective nonnegative matrix factorization (FDPNMF) approach. Our FDPNMF model is established using the loss of decomposition and the loss of projection, which is incorporated with Fisher discriminant analysis. We solve the optimization problem of the FDPNMF model via gradient descent method and construct auxiliary functions to prove the convergence of the proposed algorithm. The proposed algorithm is evaluated on facial images for classification. Experimental results demonstrate the effectiveness and the surpassing performance of our FDPNMF method when compared with other representative methods.