Path Signatures for Feature Extraction. An Introduction to the Mathematics Underpinning an Efficient Machine Learning Technique

TL;DR

This paper introduces path signatures as a mathematically grounded method for feature extraction from data streams in machine learning, emphasizing conceptual understanding over technical proofs.

Contribution

It provides an accessible introduction to the mathematical theory of path signatures for feature extraction, bridging theory and practical application.

Findings

Highlights the mathematical foundation of path signatures

Explains the conceptual advantages for feature extraction

Serves as an educational resource for students

Abstract

We provide an introduction to the topic of path signatures as means of feature extraction for machine learning from data streams. The article stresses the mathematical theory underlying the signature methodology, highlighting the conceptual character without plunging into the technical details of rigorous proofs. These notes are based on an introductory presentation given to students of the Research Experience for Undergraduates in Industrial Mathematics and Statistics at Worcester Polytechnic Institute in June 2024.