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A0298
Title: Introduction to persistent homology for graph analysis Authors:  Shizuo Kaji - Kyushu University (Japan) [presenting]
Abstract: Topological data analysis (TDA) is an emerging field in the intersection of mathematics and data science that utilises the power of algebraic topology to analyse data given in the form of point clouds, time-series, images, and graphs. TDA focuses on the shape of the data by looking at the local-global structures, quantifying the characteristics of data complementary to the ones obtained by conventional methods. Persistent homology (PH) is one of the main tools of TDA, and it provides quantification of holes and cliques together with their scales in a mathematically rigorous and computable way. We discuss the basic idea of PH and demonstrate its usability through examples of simple graph analysis. In particular, we see how similarity metrics and features of graphs are defined by PH and used for downstream tasks such as classification and regression.