A Novel Enhanced Nonnegative Matrix Factorization Method for Face Recognition

Nonnegative matrix factorization (NMF), distinguished from the approaches for holistic feature representation, is able to acquire meaningful basis images for parts-based representation. However, NMF does not utilize the data-label information and usually achieves undesirable performance in classification. To address the above-mentioned problem of NMF, this paper proposes a new enhanced NMF (ENMF) method for facial image representation and recognition. We seek to learn powerfully discriminative feature by a label-based regularizer which describes the relationship between the data. It is desired that minimizing the regularizer makes the data from the same class have high similarity and the data from different classes have low similarity. This good property will contribute to improving the performance of NMF. Therefore, we propose an objective function of ENMF by incorporating the label-based regularizer into the loss function. Subsequently, we find the stationary point of the constructed auxiliary function by means of Cardano's formula and derive the update rules of our ENMF algorithm. The convergence of the proposed ENMF is both theoretically sound and empirically validated. Finally, the proposed ENMF method is successfully applied to face recognition. Four publicly available face datasets, namely AR, Caltech 101, Yale, and CMU PIE, are chosen for evaluations. Compared with the state-of-the-art NMF-based algorithms, the experimental results illustrate that the proposed ENMF algorithm achieves superior performance.