Unfolded Laplacian Spectral Embedding: A Theoretically Grounded Approach to Dynamic Network Representation

• URL: http://arxiv.org/abs/2508.12674v1
• Date: Mon, 18 Aug 2025 07:13:53 GMT
• Title: Unfolded Laplacian Spectral Embedding: A Theoretically Grounded Approach to Dynamic Network Representation
• Abstract summary: A common approach is to learn time-varying node embeddings, whose effectiveness depends on satisfying key stability properties.<n>We propose Unfolded Laplacian Spectral Embedding, a new method that extends the Unfolded Adjacency Spectral Embedding framework to normalized Laplacians.<n>As a bonus, we establish a new Cheeger-style inequality that connects the embeddings to the conductance of the underlying dynamic graphs.
• Score: 1.4747234049753448
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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