Manifold-regularised Large-Margin $\ell_p$-SVDD for Multidimensional Time Series Anomaly Detection
This work addresses anomaly detection in multidimensional time series, which is incremental as it builds on an existing ℓp-SVDD method by adding manifold regularization.
The authors tackled the problem of multidimensional time series anomaly detection by generalizing the large-margin ℓp-SVDD approach with manifold regularization to exploit data geometry, resulting in improved detection performance as validated experimentally across various datasets.
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.