# Latent structure blockmodels for Bayesian spectral graph clustering

arXiv: https://arxiv.org/abs/2107.01734 · HTML: https://mlsanity.com/paper/2107.01734/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 64 references that are in the map.
- First posted on arXiv 4 Jul 2021.

## Builds on (most cited first, 19 of 19)

- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [A statistical interpretation of spectral embedding: the generalised random dot product graph](https://mlsanity.com/paper/1709.05506/) (2017)
- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [On a 'Two Truths' Phenomenon in Spectral Graph Clustering](https://mlsanity.com/paper/1808.07801/) (2018)
- [Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embedding](https://mlsanity.com/paper/1310.0532/) (2013)
- [Variational Inference for Gaussian Process Models with Linear Complexity](https://mlsanity.com/paper/1711.10127/) (2017)
- [The multilayer random dot product graph](https://mlsanity.com/paper/2007.10455/) (2020)
- [Manifold structure in graph embeddings](https://mlsanity.com/paper/2006.05168/) (2020)
- [Spectral clustering in the dynamic stochastic block model](https://mlsanity.com/paper/1705.01204/) (2017)
- [The Geometry of Continuous Latent Space Models for Network Data](https://mlsanity.com/paper/1712.08641/) (2017)
- [On estimation and inference in latent structure random graphs](https://mlsanity.com/paper/1806.01401/) (2018)
- [Spectral clustering on spherical coordinates under the degree-corrected stochastic blockmodel](https://mlsanity.com/paper/2011.04558/) (2020)
- [Exchangeable Random Measures for Sparse and Modular Graphs with Overlapping Communities](https://mlsanity.com/paper/1602.02114/) (2016)
- [Spectral clustering under degree heterogeneity: a case for the random walk Laplacian](https://mlsanity.com/paper/2105.00987/) (2021)
- [Learning 1-Dimensional Submanifolds for Subsequent Inference on Random Dot Product Graphs](https://mlsanity.com/paper/2004.07348/) (2020)
- [Semiparametric spectral modeling of the Drosophila connectome](https://mlsanity.com/paper/1705.03297/) (2017)
- [Simultaneous Dimensionality and Complexity Model Selection for Spectral Graph Clustering](https://mlsanity.com/paper/1904.02926/) (2019)
- [Bayesian estimation of the latent dimension and communities in stochastic blockmodels](https://mlsanity.com/paper/1904.05333/) (2019)
- [Improving Spectral Clustering using the Asymptotic Value of the Normalised Cut](https://mlsanity.com/paper/1703.09975/) (2017)

## Abstract (arXiv)

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.