Faster SVM Training via Conjugate SMO

We propose an improved version of the SMO algorithm for training classification and regression SVMs, based on a Conjugate Descent procedure. This new approach only involves a modest increase on the computational cost of each iteration but, in turn, usually results in a substantial decrease in the number of iterations required to converge to a given precision. Besides, we prove convergence of the iterates of this new Conjugate SMO as well as a linear rate when the kernel matrix is positive definite. We have implemented Conjugate SMO within the LIBSVM library and show experimentally that it is faster for many hyper-parameter configurations, being often a better option than second order SMO when performing a grid-search for SVM tuning.