LGE-KSVD: robust sparse representation classification.

The parsimonious nature of sparse representations has been successfully exploited for the development of highly accurate classifiers for various scientific applications. Despite the successes of Sparse Representation techniques, a large number of dictionary atoms as well as the high dimensionality of the data can make these classifiers computationally demanding. Furthermore, sparse classifiers are subject to the adverse effects of a phenomenon known as coefficient contamination, where, for example, variations in pose may affect identity and expression recognition. We analyze the interaction between dimensionality reduction and sparse representations, and propose a technique, called Linear extension of Graph Embedding K-means-based Singular Value Decomposition (LGE-KSVD) to address both issues of computational intensity and coefficient contamination. In particular, the LGE-KSVD utilizes variants of the LGE to optimize the K-SVD, an iterative technique for small yet over complete dictionary learning. The dimensionality reduction matrix, sparse representation dictionary, sparse coefficients, and sparsity-based classifier are jointly learned through the LGE-KSVD. The atom optimization process is redefined to allow variable support using graph embedding techniques and produce a more flexible and elegant dictionary learning algorithm. Results are presented on a wide variety of facial and activity recognition problems that demonstrate the robustness of the proposed method.