Generative Models for Periodicity Detection in Noisy Signals

TL;DR

This paper presents GMPDA, a novel algorithm for detecting multiple periodicities in noisy binary event data, using two new generative models, achieving high accuracy in both synthetic and real sleep movement data.

Contribution

Introduction of two new generative models for periodic event behavior and the GMPDA algorithm for accurate multiple periodicity detection in noisy signals.

Findings

GMPDA accurately detects multiple periodicities in synthetic data.

GMPDA successfully identifies periodicities in noisy sleep movement data.

The models effectively describe different periodic phenomena.

Abstract

We introduce a new periodicity detection algorithm for binary time series of event onsets, the Gaussian Mixture Periodicity Detection Algorithm (GMPDA). The algorithm approaches the periodicity detection problem to infer the parameters of a generative model. We specified two models - the Clock and Random Walk - which describe two different periodic phenomena and provide a generative framework. The algorithm achieved strong results on test cases for single and multiple periodicity detection and varying noise levels. The performance of GMPDA was also evaluated on real data, recorded leg movements during sleep, where GMPDA was able to identify the expected periodicities despite high noise levels. The paper's key contributions are two new models for generating periodic event behavior and the GMPDA algorithm for multiple periodicity detection, which is highly accurate under noise.