Persistent Homology Analysis for Materials Research and Persistent Homology Software: HomCloud
Ippei Obayashi, Takenobu Nakamura, Yasuaki Hiraoka
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.
Topics & Concepts
Persistent homologyHomology (biology)Topological data analysisSoftwareComputer scienceSingular homologyComputational biologyTopology (electrical circuits)Programming languageBiologyGeneticsMathematicsAlgorithmAmino acidCombinatoricsTopological and Geometric Data AnalysisAdvanced Neuroimaging Techniques and ApplicationsHomotopy and Cohomology in Algebraic Topology