P-packSVM: Parallel Primal grAdient desCent Kernel SVM

It is an extreme challenge to produce a nonlinear SVM classifier on very large scale data. In this paper we describe a novel P-packSVM algorithm that can solve the Support Vector Machine (SVM) optimization problem with an arbitrary kernel. This algorithm embraces the best known stochastic gradient descent method to optimize the primal objective, and has 1\/ϵ dependency in complexity to obtain a solution of optimization error ϵ. The algorithm can be highly paralleled with a special packing strategy, and experiences sub-linear speed-up with hundreds of processors. We demonstrate that P-packSVM achieves accuracy sufficiently close to that of SVM-light, and overwhelms the state-of-the-art parallel SVM trainer PSVM in both accuracy and efficiency. As an illustration, our algorithm trains CCAT dataset with 800k samples in 13 minutes and 95% accuracy, while PSVM needs 5 hours but only has 92% accuracy. We at last demonstrate the capability of P-packSVM on 8 million training samples.