Chapter 9

Persistent homology

Abstract

Statistics is the analysis of data to infer properties of the original data set. Persistent Homology is the analysis of the shape of the original data set. We discuss the definition of point cloud and methods to give the set an underlying structure. This is done by covering Delaunay triangulations, Voronoi shapes, convex hulls, and alpha shapes. The definition of homology is given and is used to create Persistent Homology. The underlying goal of Persistent Homology is to enumerate persistent holes in the data. Visualizations for Persistent Homology are given as well.

Keywords

Delaunay triangulation; Alpha shapes; Persistent homology; Holes

Statistics teaches us how to ask predictive questions about the ...

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