An introduction to an algorithm of persistent homology groups

Abstract

Persistent homology computes the change of the homology groups of a shape growing as a parameter increases. Persistent homology groups are defined for filtrations, which are increasing sequence of simplicial complexes. Vietoris-Rips complexes are filtrations constructed from point clouds. Persistent homology groups are computed with a variation of a reduction algorithm in linear algebra. An example of the computation is given in this article.