Research 1: A Generator-Tracking Algorithm for Representative Cycles in Time-Evolution Data

Research Theme

We are researching a method known as Topological Data Analysis (TDA). TDA is a method for extracting the topological structures (holes and voids) inherent in images and point cloud data as algebraic objects; it is applied to areas such as the analysis of molecular structures in chemical materials and the analysis of the physical properties of proteins.

In this research, we are developing an algorithm that uses TDA to extract changes in the topological structure of data whose shape changes over time as fixed-length vectors.

Abstract

The objective of this study is to construct an algorithm that extracts changes in the topological structure of time-varying data as fixed-length vectors, with mathematical justification. The output of TDA for time-varying data is a set with variable-length vectors, and a key challenge is that it cannot be directly incorporated into machine learning or statistical inference models, which assume fixed-length vectors. Therefore, in this study, we have developed a method that describes these changes as fixed-length vectors by tracking the formation and disappearance of topological structures.