AbstractPersistent homology provides essential topological insights into datasets, representing eachtopological feature with an interval whose length, known as the feature's lifetime, represents itspersistence. Features with short lifetimes are typically regarded as noise, while those with longellifetimes are considered meaningful characteristics of the dataset. We introduce a novel filteringme...
PrerequisiteThe elementary theory about algebraic topologyAbstractIn applied mathematics, topological based data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. In this course we will concentrate mainly on two such techniques: persistent homology and GLMY-homology. Persistent homology is an algebraic tool for measuring topological features of shapes and...