# Sinkhorn Divergence of Topological Signature Estimates for Time Series Classification

## TL;DR

This paper introduces a non-parametric classifier for time series classification that leverages topological signatures and Sinkhorn divergences, effectively distinguishing chaotic system states even with noise and unknown models.

## Contribution

It proposes a novel approach combining persistent homology, kernel density estimates, and Sinkhorn divergences for robust, model-free time series classification.

## Key findings

- Accurately discriminates between similar chaotic system states.
- Robust performance in noisy conditions.
- Effective in classifying long, complex signals.

## Abstract

Distinguishing between classes of time series sampled from dynamic systems is a common challenge in systems and control engineering, for example in the context of health monitoring, fault detection, and quality control. The challenge is increased when no underlying model of a system is known, measurement noise is present, and long signals need to be interpreted. In this paper we address these issues with a new non parametric classifier based on topological signatures. Our model learns classes as weighted kernel density estimates (KDEs) over persistent homology diagrams and predicts new trajectory labels using Sinkhorn divergences on the space of diagram KDEs to quantify proximity. We show that this approach accurately discriminates between states of chaotic systems that are close in parameter space, and its performance is robust to noise.