Combinatorics

Singular homology

Topology (electrical circuits)

Persistent homology

Mathematics

Biology

Algorithm

Homology (biology)

Programming language

Topological data analysis

Software

Computer science

Computational biology

Amino acid

Genetics

Journal of the Physical Society of Japan

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.

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