Sparse Algorithm for Robust LSSVM in Primal Space

TL;DR

This paper introduces a sparse, robust LSSVM algorithm in primal space that effectively handles outliers, achieves sparsity, and is computationally efficient for large-scale classification and regression tasks.

Contribution

The paper proposes a novel sparse R-LSSVM model using low-rank kernel approximation and entropy smoothing, improving efficiency and robustness over existing dense solutions.

Findings

Achieves sparse solutions with low-rank kernel approximation.

Outperforms existing algorithms in training speed for large-scale problems.

Maintains or improves classification/regression accuracy.

Abstract

As enjoying the closed form solution, least squares support vector machine (LSSVM) has been widely used for classification and regression problems having the comparable performance with other types of SVMs. However, LSSVM has two drawbacks: sensitive to outliers and lacking sparseness. Robust LSSVM (R-LSSVM) overcomes the first partly via nonconvex truncated loss function, but the current algorithms for R-LSSVM with the dense solution are faced with the second drawback and are inefficient for training large-scale problems. In this paper, we interpret the robustness of R-LSSVM from a re-weighted viewpoint and give a primal R-LSSVM by the representer theorem. The new model may have sparse solution if the corresponding kernel matrix has low rank. Then approximating the kernel matrix by a low-rank matrix and smoothing the loss function by entropy penalty function, we propose a convergent sparse R-LSSVM (SR-LSSVM) algorithm to achieve the sparse solution of primal R-LSSVM, which overcomes two drawbacks of LSSVM simultaneously. The proposed algorithm has lower complexity than the existing algorithms and is very efficient for training large-scale problems. Many experimental results illustrate that SR-LSSVM can achieve better or comparable performance with less training time than related algorithms, especially for training large scale problems.