Subclass discriminant Nonnegative Matrix Factorization for facial image analysis

Nonnegative Matrix Factorization (NMF) is among the most popular subspace methods, widely used in a variety of image processing problems. Recently, a discriminant NMF method that incorporates Linear Discriminant Analysis inspired criteria has been proposed, which achieves an efficient decomposition of the provided data to its discriminant parts, thus enhancing classification performance. However, this approach possesses certain limitations, since it assumes that the underlying data distribution is unimodal, which is often unrealistic. To remedy this limitation, we regard that data inside each class have a multimodal distribution, thus forming clusters and use criteria inspired by Clustering based Discriminant Analysis. The proposed method incorporates appropriate discriminant constraints in the NMF decomposition cost function in order to address the problem of finding discriminant projections that enhance class separability in the reduced dimensional projection space, while taking into account subclass information. The developed algorithm has been applied for both facial expression and face recognition on three popular databases. Experimental results verified that it successfully identified discriminant facial parts, thus enhancing recognition performance. ► Certain limitations arise form LDA optimality assumptions. ► Real data samples distribution is multimodal thus, CDA is more appropriate. ► Impose CDA discriminant constraints in NMF cost function proposing SDNMF method. ► Derived update rules consider both samples class labels and their subclass origins. ► Experiments for face and facial expression recognition verified SDNMF superiority.