A modified non-negative matrix factorization algorithm for face recognition

In this paper, we propose a new variation of the Nonnegative Matrix Factorization (NMF) for face recognition. The original NMF algorithm is distinguished from the other methods of pattern recognition by its non-negativity constraints which lead to a parts-based representation because they allow only additive combinations. However, it should be considered as an unsupervised method since class information in the training set is not used. To take advantage of more information in the training images and improve the performance for classification problem, we integrate the Fisher Linear Discriminant Analysis into the NMF algorithm, which results in a novel Modified Non-negative Matrix Factorization algorithm. Our new update rule guarantees the non-negativity for all the coefficients and hence preserve the intuitive meaning for the base vectors and weight vectors while facilitating the supervised learning of within-class information. Our new technique is tested on a well-known face database: the ORL Face Database. The experimental results are very encouraging and outperformed traditional techniques including the original NMF and the Eigenface method.