Generalization capacity of multi-class SVM based on Markovian resampling

The generalization performance of “All-in-one” Multi-class SVM (AIO-MSVM) based on uniformly ergodic Markovian chain (u.e.M.c.) samples is considered. We establish the fast learning rate of AIO-MSVM algorithm with u.e.M.c. samples and prove that AIO-MSVM algorithm with u.e.M.c. samples is consistent. We also propose a novel AIO-MSVM algorithm based on q-times Markovian resampling (AIO-MSVM-MR), and show the numerical investigation on the learning performance of AIO-MSVM-MR based on public datasets. The experimental studies indicate that compared to the classical AIO-MSVM algorithm and other MSVM algorithms, the proposed AIO-MSVM-MR algorithm has not only smaller misclassification rate, but also less sampling and training total time. We present some discussions on the case of unbalanced training samples, the choices of q and two technical parameters, and present some explanations on the learning performance of the proposed algorithm.