Kernel Sparse Representation-Based Classifier

Abstract

Sparse representation-based classifier (SRC), a combined result of machine learning and compressed sensing, shows its good classification performance on face image data. However, SRC could not well classify the data with the same direction distribution. The same direction distribution means that the sample vectors belonging to different classes distribute on the same vector direction. This paper presents a new classifier, kernel sparse representation-based classifier (KSRC), based on SRC and the kernel trick which is a usual technique in machine learning. KSRC is a nonlinear extension of SRC and can remedy the drawback of SRC. To make the data in an input space separable, we implicitly map these data into a high-dimensional kernel feature space by using some nonlinear mapping associated with a kernel function. Since this kernel feature space has a very high (or possibly infinite) dimensionality, or is unknown, we have to avoid working in this space explicitly. Fortunately, we can indeed reduce the dimensionality of the kernel feature space by exploiting kernel-based dimensionality reduction methods. In the reduced subspace, we need to find sparse combination coefficients for a test sample and assign a class label to it. Similar to SRC, KSRC is also cast into an ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -minimization problem or a quadratically constrained ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -minimization problem. Extensive experimental results on UCI and face data sets show KSRC improves the performance of SRC.