Subspace Newton method for sparse SVM

Abstract

Kernel-based methods for support vector machines (SVM) have seen a great advantage in various applications. However, they may incur prohibitive computational costs when the involved sample size is on a large scale. Therefore, reducing the number of support vectors (or say sample reduction) appears to be necessary, which gives rise to the topic of the sparse SVM. Motivated by this, we aim at solving a sparsity constrained kernel SVM optimization, which is capable of controlling the number of the support vectors. Based on the established optimality conditions associated with the stationary equations, a subspace Newton method is cast to tackle the sparsity constrained problem and enjoys one-step convergence property if the starting point is close to a local region of a stationary point, leading to a super-fast computational speed. Numerical comparisons with some other excellent solvers demonstrate that the proposed method performs exceptionally well, especially for datasets with large numbers of samples, in terms of a much fewer number of support vectors and shorter computational time.

More information

Identifiers

ORCID for Shenglong Zhou: orcid.org/0000-0003-2843-1614

Catalogue record

Export record