Topological data analysis

Abstract

Classical data processing uses pattern recognition methods such as classification for categorizing data. Such a method may involve a learning process. Modern data science also uses topological methods to find the structural features of data sets. In fact, topological methods should be the first step before the classification method is applied in most cases. Persistent homology is the most successful method for finding the topological structure of a discrete data set. This chapter deals with topological data processing. We first introduce space triangulations and decompositions. Then, we discuss manifold learning and focus on persistent analysis.We give an overviewof all topological methods but will focus on persistent data analysis.