# Signature-Kernel One-Class Learning with Manifold Regularisation for Multivariate Time Series Anomaly Detection

arXiv: https://arxiv.org/abs/2507.23449 · HTML: https://mlsanity.com/paper/2507.23449/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 31 Jul 2025.

## Builds on (most cited first, 11 of 11)

- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2201.07284/) (2022)
- [A Multimodal Anomaly Detector for Robot-Assisted Feeding Using an LSTM-based Variational Autoencoder](https://mlsanity.com/paper/1711.00614/) (2017)
- [Multivariate Time-series Anomaly Detection via Graph Attention Network](https://mlsanity.com/paper/2009.02040/) (2020)
- [DCdetector: Dual Attention Contrastive Representation Learning for Time Series Anomaly Detection](https://mlsanity.com/paper/2306.10347/) (2023)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [The Signature Kernel is the solution of a Goursat PDE](https://mlsanity.com/paper/2006.14794/) (2020)
- [Accelerated Graph Learning from Smooth Signals](https://mlsanity.com/paper/2110.09677/) (2021)

## Abstract (arXiv)

One-class learning is an effective methodology for time series anomaly detection, yet kernel one-class approaches often compare sequences in a pointwise fashion and ignore the geometry of normal data. In this work, we present a manifold-regularised, large-margin ℓp-support vector data description (ℓp-SVDD) method that analyses sequences as paths via the signature kernel. By incorporating a a graph-Laplacian penalty into the ℓp-SVDD objective function and utilising the representer theorem for manifold regularisation, we illustrate that the dual task retains the functional form of the original one with a modified kernel matrix. As such, existing Frank--Wolfe solvers can be applied unchanged. We show that this new modified kernel is a valid kernel matrix and under a generic norm bound on the discriminant, the proposed model yields a smaller Rademacher-complexity bound than the baseline. Furthermore, the signature kernel which is computed through a Goursat partial differential equation and can handle irregularly sampled data and is invariant to reparametrisation has not previously been used for one-class time series anomaly detection to the best of our knowledge. Our experiments on five widely used benchmarks, evaluated without point adjustment, demonstrate that the proposed approach compares very favourably with the state of the art approaches.