Kernel Local Sparse Representation Based Classifier

Sparse representation-based classification (SRC) and its kernel extension methods have shown good classification performance. However, two drawbacks still exist in these classification methods: (1) These methods adopt a L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{1}$$\end{document}-minimization problem to achieve an approximate solution of sparse representation that is originally defined as a L0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{0}$$\end{document}-norm optimization problem, which may lead to an increase in the average classification error. (2) These methods employ linear programming, second-order cone programming or unconstrained quadratic programming algorithm to solve the L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{1}$$\end{document}-minimization problem, whose computing time increases rapidly with the number of training samples. In this paper, I incorporate the idea of manifold learning into kernel extension methods of SRC, and propose a novel classification approach, named kernel local sparse representation-based classifier (KLSRC). In the kernel feature space, KLSRC represents a target sample as a linear combination of merely a few nearby training samples, which is called a kernel local sparse representation (KLSR). And then the target sample is assigned to the class that minimizes the residual between itself and the partial KLSR constructed by its training neighbors from this class. Experimental results demonstrate the effectiveness of the proposed classifier.