拓扑数据分析理论应用研究进展

Research progress on application of topological data analysis theory

随着科学技术的发展,人们每天都面对海量数据,而且数据也正以一种前所未有的速率发展.在生活中,如何从庞大的数据中提取信息,是人们面临的一大难题.拓扑数据分析通过持久同调计算复形,有效量化数据的形状,能够通过观察数据形状的变化有效提取数据信息.近年来,拓扑数据分析受到了不同领域专家的广泛关注,在医学、经济学、机器学习等方面都取得了很好的应用.文章系统介绍了拓扑数据分析的理论知识,分析了拓扑数据分析的优势所在,并对其在不同领域的应用和发展前景进行了详细的介绍.

With the development of science and technology,people are faced with massive data every day,and the data is also developing at an unprecedented rate.In life,how to extract information from huge data is a big problem that people face.Topological data analysis can effectively quantify the shape of data by calculating the complex through persistent homology,and can effectively extract data information by observing the change of data shape.In recent years,topological data analysis has been widely focused by experts in different fields.And it has achieved good applications in medicine,economics,machine learning and so on.This paper systematically introduces the theoretical knowledge of topological data analysis,analyzes the advantages of topological data analysis,and introduces its application and development prospect in different fields in detail.