Dissertation Information

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

Program: Computing Ph.D. Data Science emphasis

Advisor: Dr. Edoardo Serra

Committee Members: Dr. Francesco Gullo, Dr. Oliviero Andreussi

Abstract:

Graphs furnish a general model for relational data across a broad range of scientific domains, including molecular chemistry, biological interaction networks, transportation systems, brain connectomics, and social platforms. A central problem in modern graph analytics is graph representation learning (GRL), whose purpose is to assign numerical vector embeddings to graph objects in such a way that proximity in the embedding space reflects a meaningful notion of similarity in the graph. In many applications, however, the graph is not merely combinatorial. Nodes may be embedded in Euclidean space, edges may evolve through time, and directions may encode flow, causation, or other physically meaningful asymmetries. In such settings, the central difficulties are no longer purely representational. They concern invariance, scalability, and the principled construction of features.

This dissertation advances GRL for spatial and temporal graphs along three connected directions. First, for static spatial graphs, we develop a linear-time transformation that converts node coordinates into canonical edge features that are provably invariant to rotation and translation, thereby separating invariance preservation from downstream representation learning. Second, we develop a spectral framework for spatial graphs that combines local diffusion coordinates on $r$-hop patches with an optional magnetic Laplacian formulation, together with canonical-frame resolution for degenerate eigenspaces, adaptive local charge, and spectral-gap truncation, yielding node- and graph-level embeddings that jointly encode geometric, structural, and directional information. Third, for temporal graphs, we extend the Temporal SIR-GN framework from first-order pairwise transitions to arbitrary-order transitions between structural roles, while preserving linear-time scalability through an exact factorization of the temporal aggregation.

Taken together, these contributions address three persistent difficulties in graph representation learning: the preservation of invariance in spatial settings, the extraction of principled spectral information from geometric and directed graphs, and the efficient encoding of higher-order temporal structure. Each approach is supported by theoretical guarantees, evaluated on benchmark datasets spanning classification and regression tasks, and designed to compose naturally with existing GRL pipelines.