Using Topological Data Analysis to Process Time-series Data: A Persistent Homology Way

Abstract Topological Data Analysis (TDA) is a novel new and strong-growing method to deal with various data in most areas. And Persistent Homology is one of the most pivotal tools in Topological Data Analysis to acquire topological properties of the data. This article is based on the main mathematics behind Topological and Topological Data Analysis. And it describes how to use the above theories and methods to do the analysis job for time-series data. Moreover, it discusses the further applications of TDA to other domains and the combination of machine learning with Topological Data Analysis. The article outlines the TDA model and principle behind the data set and provides insights into the function of TDA for time-series analysis as well as opportunities for future work.