arXiv subjects

Brittany T. Fasy

Publications and source records attributed to Brittany T. Fasy.

2 recordsLinked to original sources

arXiv2022

ANAPT: Additive Noise Analysis for Persistence Thresholding

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 $Θ(n\log(n))$ algorithm for calculating the zero-dimensional sublevel set persistence homology.

math.AT↗

arXiv2014

Robust Topological Inference: Distance To a Measure and Kernel Distance

Let P be a distribution with support S. The salient features of S can be quantified with persistent homology, which summarizes topological features of the sublevel sets of the distance function (the distance of any point x to S). Given a sample from P we can infer the persistent homology using an empirical version of the distance function. However, the empirical distance function is highly non-robust to noise and outliers. Even one outlier is deadly. The distance-to-a-measure (DTM), introduced by Chazal et al. (2011), and the kernel distance, introduced by Phillips et al. (2014), are smooth functions that provide useful topological information but are robust to noise and outliers. Chazal et al. (2014) derived concentration bounds for DTM. Building on these results, we derive limiting distributions and confidence sets, and we propose a method for choosing tuning parameters.

math.ST↗