Learning Kernels via Statistical Dependence Maximization

Learning kernels from a data is one of the central interests in kernel methods since the success of kernel methods is very much dependent on the choice of kernel. In this paper, we investigate the kernel learning problem from a statistical viewpoint: given the input data (such as features) and outputs (such as labels), we aim to find a kernel such that the statistical dependence between the input data and outputs is maximized. Specifically, we first introduce a general kernel learning framework based on the Hilbert-Schmidt independence criterion (HSIC), which can directly applied to classification, clustering and other learning models. As a special case of kernel learning, we also propose an effective Gaussian kernel optimization method for classification by maximizing the HSIC, where two forms of Gaussian kernels (spherical kernel and ellipsoidal kernel) are considered Comprehensive experiments are conducted on several UCI benchmark examples and the results well demonstrate the effectiveness and efficiency of our approach.