Manifold-regularised Large-Margin $\ell_p$-SVDD for Multidimensional Time Series Anomaly Detection

TL;DR

This paper introduces a manifold-regularised large-margin $ ext{ell}_p$-SVDD method for multidimensional time series anomaly detection, leveraging data geometry to improve detection accuracy.

Contribution

It extends $ ext{ell}_p$-SVDD with manifold regularisation, providing a new approach that captures data structure for better anomaly detection performance.

Findings

The method outperforms existing approaches on various datasets.

Theoretical analysis confirms good generalisation properties.

Effective optimisation technique developed for the proposed model.

Abstract

We generalise the recently introduced large-margin $\ell_p$-SVDD approach to exploit the geometry of data distribution via manifold regularising for time series anomaly detection. Specifically, we formulate a manifold-regularised variant of the $\ell_p$-SVDD method to encourage label smoothness on the underlying manifold to capture structural information for improved detection performance. Drawing on an existing Representer theorem, we then provide an effective optimisation technique for the proposed method. We theoretically study the proposed approach using Rademacher complexities to analyse its generalisation performance and also provide an experimental assessment of the proposed method across various data sets to compare its performance against other methods.