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Persistence of directed graphs via Hochschild and reachability homology

组织者

马修·伯菲特 , 李京艳 , 吴杰

演讲者

Henri Riihimaki

时间

2025年11月27日 14:00 至 15:00

地点

A3-4-101

线上

Zoom 928 682 9093 (BIMSA)

摘要

There is currently an active interest in homotopy and homology theories in the world of graphs and directed graphs; discrete homotopy theory, magnitude homology and path homology are few prominent themes. Many of these also have incarnations in topological data analysis and persistent homology as tools for network analysis. We extend the use of Hochschild homology of directed graphs in persistence setting. We "lift" Hochschild homology to higher degrees via so called connectivity structures, of which I will present functorial examples. To get an efficiently computable pipeline we have to resort to non-functorial constructions. To remedy this leads to defining the reachability category of a directed graph, and associated persistent reachability homology. Our recent machine learning results on epilepsy detection show that this pipeline performs better than traditional simplicial homology of the directed flag complexes. This is a joint work with Luigi Caputi and Nicholas Meadows.