Shape of Big Data Described by Topology

Although modern society is inundated with data, the true value of data is not fully exploited as seen in the black box problem of artificial intelligence. To make effective use of such big data, it is vital to describe the essential structure of the data in an appropriate mathematical language and to use that language to make sense of and understand the mechanisms behind the phenomena that generate the data. To solve this problem, topological data analysis has been actively studied in recent years. It applies topology, a mathematical field that studies shapes, to data analysis. Topology focuses on structures that hold themselves under continuous deformation, and this property is used in big data analysis for coarse graining of data and description of complex structures. Topological data analysis is rapidly developing under the slogan “Data has shape, shape has meaning, meaning drives value.” At the symposium, I will introduce basic ideas of topological data analysis with several examples from materials science and life science.