Generalization ability of online pairwise support vector machine

Pairwise classification depends on two input examples instead of one example and predicts whether the two input examples belong to the same class or to different classes. In this paper we investigate online pairwise support vector machine (OPSVM) algorithm with independently and identically distributed (i.i.d.) and non-i.i.d. samples. We first establish the convergence rates of the last iteration for OPSVM algorithm and obtain the fast convergence rates of OPSVM algorithm with strongly mixing sequence or i.i.d. samples for the case of polynomially decaying step size. We also introduce a novel OPSVM algorithm based on Markov selective sampling (OPSVM-MSS). The experimental results based on benchmark repository display that the classifier induced by OPSVM-MSS algorithm not only has smaller misclassification rate, but also the sampling and training total time is shorter compared to the classifier induced by the classical OPSVM algorithm based on randomly independent sampling (OPSVM-RIS).