Online sparse passive aggressive learning with kernels

Abstract

Conventional online kernel methods often yield an unbounded large number of support vectors, making them inefficient and non-scalable for large-scale applications. Recent studies on bounded kernel-based online learning have attempted to overcome this shortcoming. Although they can bound the number of support vectors at each iteration, most of them fail to bound the number of support vectors for the final output solution which is often obtained by averaging the series of solutions over all the iterations. In this paper, we propose a novel kernel-based online learning method, Sparse Passive Aggressive learning (SPA), which can output a final solution with a bounded number of support vectors. The key idea of our method is to explore an efficient stochastic sampling s-trategy, which turns an example into a new support vector with some probability that depends on the loss suffered by the example. We theoretically prove that the proposed SPA algorithm achieves an optimal regret bound in expectation, and empirically show that the new algorithm outperforms various bounded kernel-based online learning algorithms.