Multi-Kernel Support Vector Clustering for Multi-Class Classification

Support vector clustering (SVC) has been successfully applied to solve multi-class classification problems. However, it is usually hard to determine the hyper-parameters of RBF kernel functions. A multiple kernel learning (MKL) algorithm is developed to solve this problem, by which the kernel matrix weights and Lagrange multipliers can be simultaneously obtained with semidefinite programming. However, the amount of time and space required is very demanding. We develop a two stage multiple kernel learning algorithm by incorporating sequential minimal optimization (SMO) with the gradient projection method. Experimental results on data sets from UCI and Statlog show that the proposed approach outperforms single-kernel support vector clustering.