Non-negative matrix factorization via discriminative label embedding for pattern classification

As one of the most commonly used dimension reduction approaches, discriminant non-negative matrix factorization (NMF) has been widely used for data representation in the pattern classification task. However, the previous discriminant NMFs emphasize the Fisher criterion or maximum margin criterion which has high requirement to the distribution of data. Therefore, this work proposes a discriminative label embedded NMF (LENMF) algorithm. LENMF takes into account the discriminative label embedding to obtain the low-dimensional projected data and orthogonal property of the non-negative basis to strength the ability of parts-based representation. Besides, LENMF is extended in the kernel space to explore the nonlinear relations of data. By integrating the non-negative constraint, discriminative label embedding, and the orthogonal property into the proposed objective, the multiplicative updating rules have been given in this work. Experiment results on the challenging face, object, document, and digit databases illustrate the performance of the proposed algorithm.