Supplementary Material: Jointly Learning Non-negative Projection and Dictionary with Discriminative Graph Constraints for Classification

The JNPDL model is well motivated by the current drawbacks of dictionary learning approaches, while each constraints are also well designed (the novel discriminative graph constraints are proposed, and all constrains are designed to be easily optimized). Aiming to bridge the gap between features and dictionary, we do think the proposed idea of learning a projection for features jointly with the dictionary is worth noticing. Consider that the given training data is usually not naturally discriminative, yhus the discrimination of the learned dictionary will be limited by the training data. Jointly learning the discriminative feature projection and discriminative dictionary together helps to improve each other. The key of JNPDL is to learn a discriminative projection (non-negativity is one way to discrimination) that can better work with the dictionary. In the supplementary material, we give the detailed optimization framework for the JNPDL model in Appendix A, and then provide a detailed proof in Appendix B to show the convergence of the updating rules for P and M is theoretically guaranteed. In other words, the proposed multiplicative updating algorithm for the non-negative projection P in the paper is proved to be convergent.