mlsanityData to 7 Oct 2026

Spectral embedding for dynamic networks with stability guarantees

arXiv 2106.01282 ↗First posted 2 Jun 2021stat.ML cs.LGcited by 13

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Abstract (arXiv)

We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this open-ended remit, we argue that two types of stability in the spatio-temporal positioning of nodes are desirable: to assign the same position, up to noise, to nodes behaving similarly at a given time (cross-sectional stability) and a constant position, up to noise, to a single node behaving similarly across different times (longitudinal stability). Similarity in behaviour is defined formally using notions of exchangeability under a dynamic latent position network model. By showing how this model can be recast as a multilayer random dot product graph, we demonstrate that unfolded adjacency spectral embedding satisfies both stability conditions. We also show how two alternative methods, omnibus and independent spectral embedding, alternately lack one or the other form of stability.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 27 of its 55 references that are in the map. First posted on arXiv 2 Jun 2021.

Builds on

27 of 55 references.

References · 27

  1. 2017Community Detection and Stochastic Block Modelscited by 317
  2. 2013Consistency of spectral clustering in stochastic block modelscited by 128
  3. 2017A statistical interpretation of spectral embedding: the generalised random dot product graphcited by 55
  4. 2013Spectral redemption: clustering sparse networkscited by 54
  5. 2021Dynamic Network Embedding Surveycited by 44
  6. 2020The impossibility of low rank representations for triangle-rich complex networkscited by 32
  7. 2015Statistical clustering of temporal networks through a dynamic stochastic block modelcited by 30
  8. 2020Latent Space Models for Dynamic Networkscited by 29
  9. 2013Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embeddingcited by 23
  10. 2015Multivariate Time Series Classification Using Dynamic Time Warping Template Selection for Human Activity Recognitioncited by 22
  11. 2016Latent Space Model for Road Networks to Predict Time-Varying Trafficcited by 22
  12. 2014Scalable Link Prediction in Dynamic Networks via Non-Negative Matrix Factorizationcited by 21
15 more
  1. 2014Dynamic stochastic blockmodels for time-evolving social networkscited by 20
  2. 2017A Review of Dynamic Network Models with Latent Variablescited by 18
  3. 2020The multilayer random dot product graphcited by 18
  4. 2020Manifold structure in graph embeddingscited by 17
  5. 2017Spectral clustering in the dynamic stochastic block modelcited by 12
  6. 2018Network Representation Using Graph Root Distributionscited by 12
  7. 2020A Survey on Dynamic Network Embeddingcited by 11
  8. 2020Spectral clustering on spherical coordinates under the degree-corrected stochastic blockmodelcited by 9
  9. 2013Nonparametric Bayes dynamic modeling of relational datacited by 8
  10. 2018Spectral Clustering for Multiple Sparse Networks: Icited by 8
  11. 2014Stochastic Block Transition Models for Dynamic Networkscited by 7
  12. 2020On Two Distinct Sources of Nonidentifiability in Latent Position Random Graph Modelscited by 6
  13. 2016Bayesian Learning of Dynamic Multilayer Networkscited by 5
  14. 2020Sparse and Smooth: improved guarantees for Spectral Clustering in the Dynamic Stochastic Block Modelcited by 5
  15. 2019Link prediction in dynamic networks using random dot product graphscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 4; 2025: 3; 2026: 2.

13 papers.

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  1. 2023Synergistic Graph Fusion via Encoder Embeddingcited by 6
  2. 2024Valid Conformal Prediction for Dynamic GNNscited by 6
  3. 2023Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networkscited by 5
  4. 2023A Simple and Powerful Framework for Stable Dynamic Network Embeddingcited by 5
  5. 2024Refined Graph Encoder Embedding via Self-Training and Latent Community Recoverycited by 5
  6. 2023Gradient-Based Spectral Embeddings of Random Dot Product Graphscited by 3
  7. 2025Principal Graph Encoder Embedding and Principal Community Detectioncited by 2
  8. 2024Valid Bootstraps for Network Embeddings with Applications to Network Visualisationcited by 0
  9. 2024Generalized Grade-of-Membership Estimation for High-dimensional Locally Dependent Datacited by 0
  10. 2025Unsupervised Attributed Dynamic Network Embedding with Stability Guaranteescited by 0
  11. 2025Unfolded Laplacian Spectral Embedding: A Theoretically Grounded Approach to Dynamic Network Representationcited by 0
  12. 2026Inferring Network Evolutionary History via Structure-State Coupled Learningcited by 0
1 more
  1. 2026Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunitiescited by 0