Extending Persistent Homology Through Zigzag Modules

Zigzag persistence is a variant of the ordinary persistence in topological data analysis, which can be used to extract topological features from datasets. It was introduced by Carlsson and Silva [1] as a generalization of the original persistence algorithm for sequence of topological spaces, that are not related by only an increasing filtration, but also have inclusions and exclusions. The aim of this thesis is to present a survey of zigzag persistence by presenting its mathematical foundations and elaborating the key tools and algorithms used for its computation.

Subject Keywords

Topological Data Analysis, Zigzag Module, Zigzag Persistence, The Diamond Principle