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[2508.12674] Unfolded Laplacian Spectral Embedding: A Theoretically Grounded Approach to Dynamic Network Representation
Summary
The paper introduces Unfolded Laplacian Spectral Embedding (ULSE), a novel method for dynamic network representation that ensures stability over time, enhancing interpretability in machine learning applications.
Why It Matters
Dynamic relational data is crucial in various machine learning contexts, yet maintaining consistent representations over time is challenging. This research provides a theoretically grounded approach to achieve stability in dynamic networks, which can significantly improve the performance of machine learning models in real-world applications.
Key Takeaways
- ULSE offers a principled extension of spectral embedding for dynamic networks.
- The method guarantees both cross-sectional and longitudinal stability.
- Empirical validation demonstrates ULSE's effectiveness on synthetic and real-world data.
Statistics > Machine Learning arXiv:2508.12674 (stat) [Submitted on 18 Aug 2025 (v1), last revised 23 Feb 2026 (this version, v2)] Title:Unfolded Laplacian Spectral Embedding: A Theoretically Grounded Approach to Dynamic Network Representation Authors:Haruka Ezoe, Hiroki Matsumoto, Ryohei Hisano View a PDF of the paper titled Unfolded Laplacian Spectral Embedding: A Theoretically Grounded Approach to Dynamic Network Representation, by Haruka Ezoe and 2 other authors View PDF HTML (experimental) Abstract:Dynamic relational data arise in many machine learning applications, yet their evolving structure poses challenges for learning representations that remain consistent and interpretable over time. A common approach is to learn time varying node embeddings, whose usefulness depends on well defined stability properties across nodes and across time. We introduce Unfolded Laplacian Spectral Embedding (ULSE), a principled extension of unfolded adjacency spectral embedding to normalized Laplacian operators, a setting where stability guarantees have remained out of reach. We prove that ULSE satisfies both cross-sectional and longitudinal stability under a dynamic stochastic block model. Moreover, the Laplacian formulation yields a dynamic Cheeger-type inequality linking the spectrum of the unfolded normalized Laplacian to worst case conductance over time, providing structural insight into the embeddings. Empirical results on synthetic and real world dynamic networks validate the th...
