# Applications of Signature Methods to Market Anomaly Detection

arXiv: https://arxiv.org/abs/2201.02441 · HTML: https://mlsanity.com/paper/2201.02441/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 44 references that are in the map.
- First posted on arXiv 7 Jan 2022.

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

- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [Implicit Regularization of Random Feature Models](https://mlsanity.com/paper/2002.08404/) (2020)
- [The iisignature library: efficient calculation of iterated-integral signatures and log signatures](https://mlsanity.com/paper/1802.08252/) (2018)
- [Deep neural networks, generic universal interpolation, and controlled ODEs](https://mlsanity.com/paper/1908.07838/) (2019)
- [Discrete-time signatures and randomness in reservoir computing](https://mlsanity.com/paper/2010.14615/) (2020)
- [Minimum Covariance Determinant and Extensions](https://mlsanity.com/paper/1709.07045/) (2017)
- [The Anatomy of a Cryptocurrency Pump-and-Dump Scheme](https://mlsanity.com/paper/1811.10109/) (2018)
- [The Doge of Wall Street: Analysis and Detection of Pump and Dump Cryptocurrency Manipulations](https://mlsanity.com/paper/2105.00733/) (2021)
- [Dimensionless Anomaly Detection on Multivariate Streams with Variance Norm and Path Signature](https://mlsanity.com/paper/2006.03487/) (2020)

## Built on by (most cited first, 9 of 9)

- [Neural signature kernels as infinite-width-depth-limits of controlled ResNets](https://mlsanity.com/paper/2303.17671/) (2023)
- [Global universal approximation of functional input maps on weighted spaces](https://mlsanity.com/paper/2306.03303/) (2023)
- [Randomized Signature Methods in Optimal Portfolio Selection](https://mlsanity.com/paper/2312.16448/) (2023)
- [Universal randomised signatures for generative time series modelling](https://mlsanity.com/paper/2406.10214/) (2024)
- [Universal approximation with signatures of non-geometric rough paths](https://mlsanity.com/paper/2602.05898/) (2026)
- [Infinite-dimensional Mahalanobis Distance with Applications to Kernelized Novelty Detection](https://mlsanity.com/paper/2407.11873/) (2024)
- [Semi-Supervised Bayesian GANs with Log-Signatures for Uncertainty-Aware Credit Card Fraud Detection](https://mlsanity.com/paper/2509.00931/) (2025)
- [Generating Financial Time Series by Matching Random Convolutional Features](https://mlsanity.com/paper/2606.05138/) (2026)
- [Gaussian processes based data augmentation and expected signature for time series classification](https://mlsanity.com/paper/2310.10836/) (2023)

## Abstract (arXiv)

Anomaly detection is the process of identifying abnormal instances or events in data sets which deviate from the norm significantly. In this study, we propose a signatures based machine learning algorithm to detect rare or unexpected items in a given data set of time series type. We present applications of signature or randomized signature as feature extractors for anomaly detection algorithms; additionally we provide an easy, representation theoretic justification for the construction of randomized signatures. Our first application is based on synthetic data and aims at distinguishing between real and fake trajectories of stock prices, which are indistinguishable by visual inspection. We also show a real life application by using transaction data from the cryptocurrency market. In this case, we are able to identify pump and dump attempts organized on social networks with F1 scores up to 88% by means of our unsupervised learning algorithm, thus achieving results that are close to the state-of-the-art in the field based on supervised learning.