# Sparse Subspace Clustering in Diverse Multiplex Network Model

arXiv: https://arxiv.org/abs/2206.07602 · HTML: https://mlsanity.com/paper/2206.07602/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 56 references that are in the map.
- First posted on arXiv 15 Jun 2022.

## Builds on (most cited first, 25 of 25)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [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)
- [A Review of Stochastic Block Models and Extensions for Graph Clustering](https://mlsanity.com/paper/1903.00114/) (2019)
- [Achieving Optimal Misclassification Proportion in Stochastic Block Model](https://mlsanity.com/paper/1505.03772/) (2015)
- [Layer aggregation and reducibility of multilayer interconnected networks](https://mlsanity.com/paper/1405.0425/) (2014)
- [Implicit differentiation of Lasso-type models for hyperparameter optimization](https://mlsanity.com/paper/2002.08943/) (2020)
- [Mind the duality gap: safer rules for the Lasso](https://mlsanity.com/paper/1505.03410/) (2015)
- [Statistical clustering of temporal networks through a dynamic stochastic block model](https://mlsanity.com/paper/1506.07464/) (2015)
- [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)
- [Robust subspace clustering](https://mlsanity.com/paper/1301.2603/) (2013)
- [Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit](https://mlsanity.com/paper/2012.09996/) (2020)
- [Noisy Sparse Subspace Clustering](https://mlsanity.com/paper/1309.1233/) (2013)
- [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)
- [Producing a Unified Graph Representation from Multiple Social Network Views](https://mlsanity.com/paper/1301.5809/) (2013)
- [ALMA: Alternating Minimization Algorithm for Clustering Mixture Multilayer Network](https://mlsanity.com/paper/2102.10226/) (2021)
- [Clustering of Diverse Multiplex Networks](https://mlsanity.com/paper/2110.05308/) (2021)
- [General Community Detection with Optimal Recovery Conditions for Multi-relational Sparse Networks with Dependent Layers](https://mlsanity.com/paper/2004.03480/) (2020)
- [Bayesian Learning of Dynamic Multilayer Networks](https://mlsanity.com/paper/1608.02209/) (2016)
- [Sparse Popularity Adjusted Stochastic Block Model](https://mlsanity.com/paper/1910.01931/) (2019)

## Built on by (most cited first, 4 of 4)

- [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)
- [Asymptotically perfect seeded graph matching without edge correlation (and applications to inference)](https://mlsanity.com/paper/2506.02825/) (2025)
- [Simultaneous estimation of connectivity and dimensionality in samples of networks](https://mlsanity.com/paper/2508.12483/) (2025)

## Abstract (arXiv)

The paper considers the DIverse MultiPLEx (DIMPLE) network model, introduced in Pensky and Wang (2021), where all layers of the network have the same collection of nodes and are equipped with the Stochastic Block Models. In addition, all layers can be partitioned into groups with the same community structures, although the layers in the same group may have different matrices of block connection probabilities. The DIMPLE model generalizes a multitude of papers that study multilayer networks with the same community structures in all layers, as well as the Mixture Multilayer Stochastic Block Model (MMLSBM), where the layers in the same group have identical matrices of block connection probabilities. While Pensky and Wang (2021) applied spectral clustering to the proxy of the adjacency tensor, the present paper uses Sparse Subspace Clustering (SSC) for identifying groups of layers with identical community structures. Under mild conditions, the latter leads to the strongly consistent between-layer clustering. In addition, SSC allows to handle much larger networks than methodology of Pensky and Wang (2021), and is perfectly suitable for application of parallel computing.