Author ORCID Identifier

0000-0003-3640-3672

Date of Award

2024

Document Type

Thesis (Master's)

Department or Program

Engineering Sciences

First Advisor

Peter Chin

Abstract

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 graph learning methods, while benefiting from established results on simplicial and regular cell complexes. Our findings are validated via rigorous experiments on both synthetic and real-world benchmarks. Our second project leverages persistent homology, a powerful tool for analyzing topological properties of data. We apply this technique to the challenging task of human activity anomaly detection, aiming to derive topologically-informed representations that enable the robust distinction between normal and anomalous activities within spatiotemporal data. Overall, this work highlights the potential of applied topology, acknowledges limitations, and positions itself to motivate promising future research directions within the field of topological deep learning.

Original Citation

Truong, Q., & Chin, P. (2024). Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes. Proceedings of the AAAI Conference on Artificial Intelligence, 38(14), 15382-15391. https://doi.org/10.1609/aaai.v38i14.29463

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