Spectral embedding and the latent geometry of multipartite networks

• URL: http://arxiv.org/abs/2202.03945v3
• Date: Fri, 24 Oct 2025 15:22:34 GMT
• Title: Spectral embedding and the latent geometry of multipartite networks
• Authors: Alexander Modell, Ian Gallagher, Joshua Cape, Patrick Rubin-Delanchy,
• Abstract summary: Many networks are multipartite, meaning that they contain nodes of fundamentally different types.<n>This paper demonstrates that the node representations obtained via spectral embedding lie near type-specific low-dimensional subspaces of a higher-dimensional ambient space.<n>We propose a follow-on step after spectral embedding, to recover node representations in their intrinsic rather than ambient dimension.
• Score: 47.18054692085814
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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