Noise robustness of persistent homology on greyscale images, across filtrations and signatures.

ABSTRACT: Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the last decade. Often cited as the most favourable property of PH and the main reason for practical success are the stability theorems that give theoretical results about noise robustness, since real data is typically contaminated with noise or measurement errors. However, little attention has been paid to what these stability theorems mean in practice. To gain some insight into this question, we evaluate the noise robustness of PH on the MNIST dataset of greyscale images. More precisely, we investigate to what extent PH changes under typical forms of image n

SUBMITTER: Turkes R 

PROVIDER: S-EPMC8462731 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature