提出一种动态网络嵌入新方法，保证随时间变化的稳定性与可解释性。
Unfolded Laplacian Spectral Embedding: A Theoretically Grounded Approach to Dynamic Network Representation
- 基于归一化拉普拉斯算子的展开谱嵌入，理论保障稳定性
- 在动态块模型下证明跨节点和跨时间的稳定性，且满足切比雪夫不等式
- 适用于需要稳定动态网络表示的研究者，如社交网络演化分析
动态关系数据广泛存在于机器学习应用中，但其结构随时间演变，给保持一致性和可解释性的表示学习带来挑战。现有方法常通过学习时变节点嵌入来应对，其有效性依赖于节点间及时间上的良好稳定性。本文提出展开归一化拉普拉斯谱嵌入（ULSE），是展开邻接谱嵌入在归一化拉普拉斯算子上的理论拓展，此前该场景下的稳定性保障始终未实现。我们证明了在动态随机块模型下，ULSE同时满足截面稳定性和纵向稳定性。此外，拉普拉斯形式导出了动态切比雪夫型不等式，将展开归一化拉普拉斯的谱特性与时间上最差情况的导通率联系起来，揭示了嵌入的结构性内涵。在合成数据和真实动态网络上的实验验证了理论的有效性。
原文摘要 · Abstract (English)
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 theory.
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