Spectral embedding and the latent geometry of multipartite networks

TL;DR

This paper explores how spectral embedding reveals the latent geometry of multipartite networks, showing that node representations cluster near type-specific subspaces and proposing a method to recover intrinsic representations with proven consistency.

Contribution

It introduces a novel approach to recover intrinsic node representations in multipartite networks after spectral embedding, with theoretical guarantees and practical validation.

Findings

Node embeddings lie near type-specific low-dimensional subspaces.

Proposed method recovers intrinsic representations with uniform consistency.

Validated on a large biomedical multipartite network.

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.