Newton Method-based Subspace Support Vector Data Description

TL;DR

This paper introduces a Newton's method-based optimization approach for Subspace Support Vector Data Description, improving the efficiency and accuracy of one-class classification by surpassing traditional gradient descent methods.

Contribution

It adapts Newton's method for S-SVDD, providing a more effective optimization technique for subspace learning in one-class classification tasks.

Findings

Newton's method enhances optimization efficiency.

Proposed method outperforms gradient descent in experiments.

Applicable to both linear and nonlinear S-SVDD formulations.

Abstract

In this paper, we present an adaptation of Newton's method for the optimization of Subspace Support Vector Data Description (S-SVDD). The objective of S-SVDD is to map the original data to a subspace optimized for one-class classification, and the iterative optimization process of data mapping and description in S-SVDD relies on gradient descent. However, gradient descent only utilizes first-order information, which may lead to suboptimal results. To address this limitation, we leverage Newton's method to enhance data mapping and data description for an improved optimization of subspace learning-based one-class classification. By incorporating this auxiliary information, Newton's method offers a more efficient strategy for subspace learning in one-class classification as compared to gradient-based optimization. The paper discusses the limitations of gradient descent and the advantages of using Newton's method in subspace learning for one-class classification tasks. We provide both linear and nonlinear formulations of Newton's method-based optimization for S-SVDD. In our experiments, we explored both the minimization and maximization strategies of the objective. The results demonstrate that the proposed optimization strategy outperforms the gradient-based S-SVDD in most cases.