Sparse Least Squares Low Rank Kernel Machines

Abstract--A general framework of least squares support vector machine with low rank kernels, referred to as LR-LSSVM, is introduced in this paper . The special structure of low rank kernels with a controlled model size brings sparsity as well as computational efficiency to the proposed model. Meanwhile, a two-step optimization algorithm with three different criteria is proposed and various experiments are carried out using the example of the so-call robust RBF kernel to validate the model. The experiment results show that the performance of the proposed algorithm is comparable or superior to several existing kernel machines. With the proliferation of big data in scientific and business research, in practical nonlinear modeling approaches, one wishes to build sparse models with more efficient algorithms. Kernel machines (KMs) have attracted great attention since the support vector machines (SVM), a well linear binary classification model under the principle of risk minimization, was introduced in earlier 1990s [1]. In fact, KMs have extended SVM by implementing the linearity in the so-called high dimensional feature space under a feature mapping implicitly determined by a Mercer kernel function.