Discriminative Nonnegative Matrix Factorization for dimensionality reduction

Nonnegative Matrix Factorization (NMF) has been widely used for different purposes such as feature learning, dictionary leaning and dimensionality reduction in data mining and computer vision. In this work, we present a label constrained NMF, namely Discriminative Nonnegative Matrix Factorization (DNMF), which utilizes the label information of a fraction of the data as a discriminative constraint. The labeled samples are used in a regularization term, which is a linear regression based on the samples, coupled with the main objective function of NMF. In contrast to recently proposed semi-supervised NMF techniques, the proposed approach does not merge the samples with the same label into a single point. However, the algorithm enforces the samples with the same label to be aligned on the same axis in the new representation. The performed experiments on synthetic and real datasets expose the strength of our proposed method compared to the state-of-the-art methods.