Generative Models for Periodicity Detection in Noisy Signals

Area of Science:

• Signal Processing
• Computational Neuroscience
• Data Analysis

Background:

• Detecting periodicity in binary time series is crucial for understanding event-based phenomena.
• Existing methods may struggle with complex periodicities or high noise levels.

Purpose of the Study:

• To introduce a novel algorithm, the Gaussian Mixture Periodicity Detection Algorithm (GMPDA), for robust periodicity detection.
• To present two new generative models for periodic event data: the Clock Model and the Random Walk Model.

Main Methods:

• The GMPDA infers parameters from generative models to identify periodicities.
• The algorithm was tested on simulated data with varying periodicities and noise levels.
• Real-world data from sleep leg movements was used for evaluation.

Main Results:

• The GMPDA demonstrated robust performance in detecting single and multiple periodicities across different noise conditions.
• The algorithm successfully identified known periodicities in noisy sleep movement data.
• The developed generative models provide a comprehensive framework for periodic phenomena.

Conclusions:

• The GMPDA offers a highly accurate and robust method for detecting multiple periodicities in binary time series.
• This algorithm is effective even in the presence of significant noise, as shown in real-world applications.
• The novel generative models contribute to a better understanding of periodic event behaviors.