Dissertation Defense: Derek Bagagem

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Title: Graph Representation Learning for Spatial and Temporal Graphs: Invariance, Spectral Structure, and Higher-Order Temporal Roles

Program: Computing PhD

Committee Chair: Edoardo Serra

Committee: Edoardo Serra, Francesco Gullo, Oliviero Andreussi

Abstract: Graphs furnish a general model for relational data across the sciences, from molecular chemistry and materials to biological interaction networks, transportation systems, and social platforms. Graph representation learning (GRL) assigns vector embeddings to nodes, edges, or entire graphs so that proximity in the embedding space reflects meaningful similarity in the underlying data. Most GRL methods, however, treat the graph as a purely combinatorial object. In scientific applications this is rarely the case: nodes carry coordinates in physical space, edges carry direction and orientation, interactions unfold over time, and structure is often hierarchical rather than flat. This additional structure is what makes such data informative, yet it is also what standard methods handle least well. Representations must respect the symmetries of the setting, such as invariance to rotation and translation; they must scale to large graphs and point sets; and they must expose geometric, directional, and temporal information in a form that downstream models can use.

This dissertation develops representation learning methods for graphs that carry such structure. The unifying principle is to build the relevant structure directly into the representation, through geometric constructions, spectral operators, and role-based aggregation, rather than relying on downstream models to learn it from data. The resulting representations are invariant by construction, computable in linear or near-linear time, and supported by theoretical guarantees. They cover static spatial graphs, directed and geometric graphs, hyperbolic embeddings of hierarchical structure, and temporal graphs.

The methods are evaluated on molecular property prediction, physical simulation data, and benchmark classification and regression tasks, and are designed to compose naturally with existing GRL pipelines. Together, they argue that treating geometry, direction, and time as first-class structure, rather than as auxiliary attributes, is a principled and scalable path to graph representations for scientific data.