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

Abstract: We generalise the recently introduced large-margin $\ell_p$-SVDD approach to exploit the geometry of data distribution via manifold regularising and a signature kernel representation 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 and show that it can benefit from the signature kernel to capture time series complexities for anomaly detection. 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.