Joint optimization of manifold learning and sparse representations

Dimensionality reduction via manifold learning offers an elegant representation of data whereby the high dimensional feature space is parameterized by a lower dimensional space where the data resides. Sparse representations efficiently represent test patterns by sparse linear coefficients from a dictionary of training exemplars. Sparse representations have been adopted for classification purposes, but the resulting classifiers may have to deal with data in high dimensions and large dictionaries. This paper analyzes the interaction between dimensionality reduction and sparse representations. The proposed technique, called K-LGE, presents a unified framework which utilizes a semi-supervised variant of Linear extension of Graph Embedding with K-SVD dictionary learning. An iterative procedure optimizes the dimensionality reduction matrix, sparse representation dictionary, sparse coefficients, and linear classifier. Results are demonstrated in a wide variety of facial and activity recognition problems to demonstrate the robustness of our proposed method.