# ALMA: Alternating Minimization Algorithm for Clustering Mixture Multilayer Network

arXiv: https://arxiv.org/abs/2102.10226 · HTML: https://mlsanity.com/paper/2102.10226/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 52 references that are in the map.
- First posted on arXiv 20 Feb 2021.

## Builds on (most cited first, 22 of 22)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [Layer aggregation and reducibility of multilayer interconnected networks](https://mlsanity.com/paper/1405.0425/) (2014)
- [Community Detection on Mixture Multi-layer Networks via Regularized Tensor Decomposition](https://mlsanity.com/paper/2002.04457/) (2020)
- [Spectral and matrix factorization methods for consistent community detection in multi-layer networks](https://mlsanity.com/paper/1704.07353/) (2017)
- [Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit](https://mlsanity.com/paper/2012.09996/) (2020)
- [Multiway clustering via tensor block models](https://mlsanity.com/paper/1906.03807/) (2019)
- [Community detection in multi-relational data with restricted multi-layer stochastic blockmodel](https://mlsanity.com/paper/1506.02699/) (2015)
- [Latent space models for multiplex networks with shared structure](https://mlsanity.com/paper/2012.14409/) (2020)
- [Provable Convex Co-clustering of Tensors](https://mlsanity.com/paper/1803.06518/) (2018)
- [Spectral clustering in the dynamic stochastic block model](https://mlsanity.com/paper/1705.01204/) (2017)
- [Change Point Estimation in a Dynamic Stochastic Block Model](https://mlsanity.com/paper/1812.03090/) (2018)
- [General Community Detection with Optimal Recovery Conditions for Multi-relational Sparse Networks with Dependent Layers](https://mlsanity.com/paper/2004.03480/) (2020)
- [Multilayer Networks in a Nutshell](https://mlsanity.com/paper/1804.03488/) (2018)
- [General Tensor Spectral Co-clustering for Higher-Order Data](https://mlsanity.com/paper/1603.00395/) (2016)
- [Bayesian Learning of Dynamic Multilayer Networks](https://mlsanity.com/paper/1608.02209/) (2016)
- [Quantifying layer similarity in multiplex networks: a systematic study](https://mlsanity.com/paper/1711.11335/) (2017)
- [The Power Mean Laplacian for Multilayer Graph Clustering](https://mlsanity.com/paper/1803.00491/) (2018)
- [Layer Communities in Multiplex Networks](https://mlsanity.com/paper/1706.04147/) (2017)
- [Multiresolution Tensor Decomposition for Multiple Spatial Passing Networks](https://mlsanity.com/paper/1803.01203/) (2018)
- [Testing Changes in Communities for the Stochastic Block Model](https://mlsanity.com/paper/1812.00769/) (2018)

## Built on by (most cited first, 8 of 8)

- [Sparse Subspace Clustering in Diverse Multiplex Network Model](https://mlsanity.com/paper/2206.07602/) (2022)
- [Optimal Clustering of Discrete Mixtures: Binomial, Poisson, Block Models, and Multi-layer Networks](https://mlsanity.com/paper/2311.15598/) (2023)
- [Nested stochastic block model for simultaneously clustering networks and nodes](https://mlsanity.com/paper/2307.09210/) (2023)
- [Signed Diverse Multiplex Networks: Clustering and Inference](https://mlsanity.com/paper/2402.10242/) (2024)
- [Mixture of multilayer stochastic block models for multiview clustering](https://mlsanity.com/paper/2401.04682/) (2024)
- [Perfect Clustering in Very Sparse Diverse Multiplex Networks](https://mlsanity.com/paper/2507.19423/) (2025)
- [Simultaneous estimation of connectivity and dimensionality in samples of networks](https://mlsanity.com/paper/2508.12483/) (2025)
- [Transfer learning under latent space model](https://mlsanity.com/paper/2509.15797/) (2025)

## Abstract (arXiv)

The paper considers a Mixture Multilayer Stochastic Block Model (MMLSBM), where layers can be partitioned into groups of similar networks, and networks in each group are equipped with a distinct Stochastic Block Model. The goal is to partition the multilayer network into clusters of similar layers, and to identify communities in those layers. Jing et al. (2020) introduced the MMLSBM and developed a clustering methodology, TWIST, based on regularized tensor decomposition. The present paper proposes a different technique, an alternating minimization algorithm (ALMA), that aims at simultaneous recovery of the layer partition, together with estimation of the matrices of connection probabilities of the distinct layers. Compared to TWIST, ALMA achieves higher accuracy both theoretically and numerically.