ANAPT: Additive Noise Analysis for Persistence Thresholding

TL;DR

ANAPT is a new method that uses statistical analysis of noise in time series to accurately identify significant features in persistence diagrams, applicable across various noise models and demonstrated with simulations and real data.

Contribution

This paper introduces ANAPT, a novel, efficient approach for noise-based feature detection in persistence diagrams that does not require pre-filtering and is applicable to multiple noise types.

Findings

Effective separation of significant features from noise in persistence diagrams.

Applicable to Gaussian, uniform, exponential, and Rayleigh noise models.

Provides an open-source implementation and demonstrates success on simulated and real data.

Abstract

We introduce a novel method for Additive Noise Analysis for Persistence Thresholding (ANAPT) which separates significant features in the sublevel set persistence diagram of a time series based on a statistics analysis of the persistence of a noise distribution. Specifically, we consider an additive noise model and leverage the statistical analysis to provide a noise cutoff or confidence interval in the persistence diagram for the observed time series. This analysis is done for several common noise models including Gaussian, uniform, exponential and Rayleigh distributions. ANAPT is computationally efficient, does not require any signal pre-filtering, is widely applicable, and has open-source software available. We demonstrate the functionality ANAPT with both numerically simulated examples and an experimental data set. Additionally, we provide an efficient $\Theta(n\log(n))$ algorithm for calculating the zero-dimensional sublevel set persistence homology.