# Signature Isolation Forest

arXiv: https://arxiv.org/abs/2403.04405 · HTML: https://mlsanity.com/paper/2403.04405/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 53 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Builds on (most cited first, 18 of 18)

- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [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)
- [Signature moments to characterize laws of stochastic processes](https://mlsanity.com/paper/1810.10971/) (2018)
- [Signature Methods in Machine Learning](https://mlsanity.com/paper/2206.14674/) (2022)
- [Embedding and learning with signatures](https://mlsanity.com/paper/1911.13211/) (2019)
- [When OT meets MoM: Robust estimation of Wasserstein Distance](https://mlsanity.com/paper/2006.10325/) (2020)
- [Functional Isolation Forest](https://mlsanity.com/paper/1904.04573/) (2019)
- [A Pseudo-Metric between Probability Distributions based on Depth-Trimmed Regions](https://mlsanity.com/paper/2103.12711/) (2021)
- [Unsupervised Layer-wise Score Aggregation for Textual OOD Detection](https://mlsanity.com/paper/2302.09852/) (2023)
- [DeepWriterID: An End-to-end Online Text-independent Writer Identification System](https://mlsanity.com/paper/1508.04945/) (2015)
- [DropSample: A New Training Method to Enhance Deep Convolutional Neural Networks for Large-Scale Unconstrained Handwritten Chinese Character Recognition](https://mlsanity.com/paper/1505.05354/) (2015)
- [Functional Anomaly Detection: a Benchmark Study](https://mlsanity.com/paper/2201.05115/) (2022)
- [The Area of the Convex Hull of Sampled Curves: a Robust Functional Statistical Depth Measure](https://mlsanity.com/paper/1910.04085/) (2019)
- [Enhanced Hallucination Detection in Neural Machine Translation through Simple Detector Aggregation](https://mlsanity.com/paper/2402.13331/) (2024)
- [The Signature Kernel](https://mlsanity.com/paper/2305.04625/) (2023)
- [Toward Stronger Textual Attack Detectors](https://mlsanity.com/paper/2310.14001/) (2023)
- [A Functional Data Perspective and Baseline On Multi-Layer Out-of-Distribution Detection](https://mlsanity.com/paper/2306.03522/) (2023)

## Built on by (most cited first, 1 of 1)

- [Novelty detection on path space](https://mlsanity.com/paper/2512.03243/) (2025)

## Abstract (arXiv)

Functional Isolation Forest (FIF) is a recent state-of-the-art Anomaly Detection (AD) algorithm designed for functional data. It relies on a tree partition procedure where an abnormality score is computed by projecting each curve observation on a drawn dictionary through a linear inner product. Such linear inner product and the dictionary are a priori choices that highly influence the algorithm's performances and might lead to unreliable results, particularly with complex datasets. This work addresses these challenges by introducing textitSignature Isolation Forest, a novel AD algorithm class leveraging the rough path theory's signature transform. Our objective is to remove the constraints imposed by FIF through the proposition of two algorithms which specifically target the linearity of the FIF inner product and the choice of the dictionary. We provide several numerical experiments, including a real-world applications benchmark showing the relevance of our methods.