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Topological Data Analysis(TDA) is a new and fast growing field in data science. TDA provides an approach to analyze data sets and derive their relevant feature out of complex high-dimensional data, which greatly improves the working efficiency in many fields. In this paper, the author mainly discusses some mathematics concepts about topology, methods in TDA and the relation between these topological concepts and data sets (how to apply topological concepts on data). The problems of TDA, mathematical algorithm using in TDA and two application-examples are introduced in this paper. In addition, the advantages, limitations, and the direction of future development of TDA are discussed.

The Application of Topological Data Analysis in Practice and Its Effectiveness