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Spectral embedding and the latent geometry of multipartite networks

arXiv 2202.03945 ↗First posted 8 Feb 2022stat.ME stat.MLcited by 0

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Abstract (arXiv)

Spectral embedding finds vector representations of the nodes of a network, based on the eigenvectors of a properly constructed matrix, and has found applications throughout science and technology. Many networks are multipartite, meaning that they contain nodes of fundamentally different types, e.g. drugs, diseases and proteins, and edges are only observed between nodes of different types. When the network is multipartite, this paper demonstrates that the node representations obtained via spectral embedding lie near type-specific low-dimensional subspaces of a higher-dimensional ambient space. For this reason we propose a follow-on step after spectral embedding, to recover node representations in their intrinsic rather than ambient dimension, proving uniform consistency under a low-rank, inhomogeneous random graph model. We demonstrate the performance of our procedure on a large 6-partite biomedical network relevant for drug discovery.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 25 of its 71 references that are in the map. First posted on arXiv 8 Feb 2022.

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25 of 71 references.

References · 25

  1. 2016node2vec: Scalable Feature Learning for Networkscited by 1,913
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  12. 2020The multilayer random dot product graphcited by 18
13 more
  1. 2016Limit theorems for eigenvectors of the normalized Laplacian for random graphscited by 17
  2. 2020Manifold structure in graph embeddingscited by 17
  3. 2018Understanding Regularized Spectral Clustering via Graph Conductancecited by 14
  4. 2021On the Power of Edge Independent Graph Modelscited by 13
  5. 2018On estimation and inference in latent structure random graphscited by 9
  6. 2016Exchangeable Random Measures for Sparse and Modular Graphs with Overlapping Communitiescited by 8
  7. 2020On Two Distinct Sources of Nonidentifiability in Latent Position Random Graph Modelscited by 6
  8. 2020Learning 1-Dimensional Submanifolds for Subsequent Inference on Random Dot Product Graphscited by 6
  9. 2021Spectral clustering under degree heterogeneity: a case for the random walk Laplaciancited by 6
  10. 2021Matrix factorisation and the interpretation of geodesic distancecited by 6
  11. 2021Estimating Graph Dimension with Cross-validated Eigenvaluescited by 6
  12. 2021Root and community inference on the latent growth process of a networkcited by 4
  13. 2017Consistency of adjacency spectral embedding for the mixed membership stochastic blockmodelcited by 2

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