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Latent structure blockmodels for Bayesian spectral graph clustering

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Title: Latent structure blockmodels for Bayesian spectral graph clustering
Authors: Sanna Passino, F
Heard, N
Item Type: Journal Article
Abstract: Spectral embedding of network adjacency matrices often produces node representations living approximately around low-dimensional submanifold structures. In particular, hidden substructure is expected to arise when the graph is generated from a latent position model. Furthermore, the presence of communities within the network might generate community-specific submanifold structures in the embedding, but this is not explicitly accounted for in most statistical models for networks. In this article, a class of models called latent structure block models (LSBM) is proposed to address such scenarios, allowing for graph clustering when community-specific one dimensional manifold structure is present. LSBMs focus on a specific class of latent space model, the random dot product graph (RDPG), and assign a latent submanifold to the latent positions of each community. A Bayesian model for the embeddings arising from LSBMs is discussed, and shown to have a good performance on simulated and real world network data. The model is able to correctly recover the underlying communities living in a one-dimensional manifold, even when the parametric form of the underlying curves is unknown, achieving remarkable results on a variety of real data.
Issue Date: 16-Feb-2022
Date of Acceptance: 20-Jan-2022
URI: http://hdl.handle.net/10044/1/95621
DOI: 10.1007/s11222-022-10082-6
ISSN: 0960-3174
Publisher: Springer
Journal / Book Title: Statistics and Computing
Volume: 32
Copyright Statement: © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Keywords: stat.ML
Statistics & Probability
0104 Statistics
0802 Computation Theory and Mathematics
Publication Status: Published
Open Access location: https://link.springer.com/article/10.1007/s11222-022-10082-6
Article Number: ARTN 22
Appears in Collections:Statistics

This item is licensed under a Creative Commons License Creative Commons