Unfolded Laplacian Spectral Embedding: A Theoretically Grounded Approach to Dynamic Network Representation
This work addresses the problem of dynamic network representation for AI tasks, offering a theoretically grounded method that is incremental in nature.
The paper tackled the challenge of creating stable and interpretable representations for dynamic networks by proposing Unfolded Laplacian Spectral Embedding, which extends an existing framework to normalized Laplacians and provides formal proofs of stability conditions, with empirical evaluations supporting its performance.
Dynamic relational structures play a central role in many AI tasks, but their evolving nature presents challenges for consistent and interpretable representation. A common approach is to learn time-varying node embeddings, whose effectiveness depends on satisfying key stability properties. In this paper, we propose Unfolded Laplacian Spectral Embedding, a new method that extends the Unfolded Adjacency Spectral Embedding framework to normalized Laplacians while preserving both cross-sectional and longitudinal stability. We provide formal proof that our method satisfies these stability conditions. In addition, as a bonus of using the Laplacian matrix, we establish a new Cheeger-style inequality that connects the embeddings to the conductance of the underlying dynamic graphs. Empirical evaluations on synthetic and real-world datasets support our theoretical findings and demonstrate the strong performance of our method. These results establish a principled and stable framework for dynamic network representation grounded in spectral graph theory.