Joint optimization of manifold learning and sparse representations

Abstract

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.

A Novel Face Recognition Method using Nearest Line Projection

“…) By substituting (5) to D(α), we have the distance of a data point y i to one of its nearest L jk (α) in (6). We hope to learn a projection matrix W so that the distance between each data point to its nearest lines could be minimized, so we obtain the following objective function in (7),…”