Physical Sciences and Mathematics Commons^™

Understanding Data Through The Lens Of Topology, Quang Truong

Dartmouth College Master’s Theses

Machine learning depends on the ability to learn insightful representations from data. Topology of data offers a rich source of information for constructing such representations, yet its potential remains under-explored by the broader machine learning community. This work investigates the power of applied topology through two complementary projects: Topological Message Passing with Path Complexes and Persistent Homology for Anomaly Detection. In the first project, we extend the topological message passing framework by introducing a novel approach centered on path complexes, where paths form the fundamental building blocks. Our theoretical analysis demonstrates that this model generalizes existing topological deep learning and …