The support vector machine learning using the second order cone programming

We propose a data dependent learning method for the support vector machine. This method is based on the technique of second order cone programming. We reformulate the SVM quadratic problem into the second order cone problem. The proposed method requires decomposing the kernel matrix of SVM optimization problem. In this paper we apply Cholesky decomposition method. Since the kernel matrix is positive semi definite, some columns of the decomposed matrix diminish. The performance of the proposed method depends on the reduction of dimensionality of the decomposed matrix. Computational results show that when the columns of decomposed matrix are small enough, the proposed method is much faster than the quadratic programming solver LOQO.