Persistent Homology through Image Segmentation (Student Abstract)

Abstract

The efficacy of topological data analysis (TDA) has been demonstrated in many different machine learning pipelines, particularly those in which structural characteristics of data are highly relevant. However, TDA's usability in large scale machine learning applications is hindered by the significant computational cost of generating persistence diagrams. In this work, a method that allows this computationally expensive process to be approximated by deep neural networks is proposed. Moreover, the method's practicality in estimating 0-dimensional persistence diagrams across a diverse range of images is shown.