Optimization of the Weights in Multiple Kernel for Kernel Sparse Representation Based Classifier

Sparse representation based classifier (SRC) is a well-known algorithm which combines the compressive sampling and machine learning concepts. In this classifier, each sample is represented by a linear and sparse combination of the associated training samples. Following the successful application of the SRC algorithm, the kernelized version of the classifier was also presented in which the data points are implicitly mapped into a high dimensional feature space. The SRC algorithm is then applied. Selection of a proper kernel is an important issue in such a kernel based algorithm. Using multiple kernel is a proper solution for this problem. In this study, in order to increase the accuracy and speed of the KSRC algorithm, we utilize a multiple kernel function within the framework of the KSRC. The multiple kernel is created by the weighted summation of a set of basis kernels where the kernel weights are determined using a set of different approaches. In this paper, we propose a novel method of determining the weights by using an optimization algorithm which is based on minimization of the reconstruction error of the KSRC. The proposed algorithm is evaluated considering real data sets from the UCI database and also hand written digits of the MNIST data sets. Our experimental results show the superiority of the proposed algorithm in different conditions. The proposed method is also more robust against additive noises.