Persistent Homology Analysis for Materials Research and Persistent Homology Software: HomCloud

TL;DR

This paper explains persistent homology, a topological data analysis method, reviews its applications in materials research, and introduces HomCloud, a software tool for persistent homology data analysis.

Contribution

It provides a comprehensive introduction to persistent homology, reviews its applications in materials science, and presents HomCloud software for data analysis.

Findings

Persistent homology effectively characterizes data shape.

HomCloud software facilitates persistent homology analysis.

Applications demonstrate usefulness in materials research.

Abstract

This paper introduces persistent homology, which is a powerful tool to characterize the shape of data using the mathematical concept of topology. We explain the fundamental idea of persistent homology from scratch using some examples. We also review some applications of persistent homology to materials researches and software for persistent homology data analysis. HomCloud, one of persistent homology software, is especially featured in this paper.