Topological signatures of periodic-like signals

TL;DR

This paper introduces a topological method for creating robust signatures of periodic-like signals that depend only on the signal's form and are resilient to reparametrization, with convergence guarantees and estimation techniques.

Contribution

The paper proposes a novel topological signature for periodic signals that is robust to reparametrization and can be estimated from a single time series using bootstrap methods.

Findings

Signature converges with increasing periods

Method is robust to reparametrization

Can be estimated from a single time series

Abstract

We present a method to construct signatures of periodic-like data. Based on topological considerations, our construction encodes information about the order and values of local extrema. Its main strength is robustness to reparametrisation of the observed signal, so that it depends only on the form of the periodic function. The signature converges as the observation contains increasingly many periods. We show that it can be estimated from the observation of a single time series using bootstrap techniques.