# Signed Diverse Multiplex Networks: Clustering and Inference

arXiv: https://arxiv.org/abs/2402.10242 · HTML: https://mlsanity.com/paper/2402.10242/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 69 references that are in the map.
- First posted on arXiv 14 Feb 2024.

## Builds on (most cited first, 30 of 30)

- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [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)
- [Tensor SVD: Statistical and Computational Limits](https://mlsanity.com/paper/1703.02724/) (2017)
- [Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics](https://mlsanity.com/paper/1605.00353/) (2016)
- [Inference for multiple heterogeneous networks with a common invariant subspace](https://mlsanity.com/paper/1906.10026/) (2019)
- [Community Detection in Degree-Corrected Block Models](https://mlsanity.com/paper/1607.06993/) (2016)
- [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)
- [SPONGE: A generalized eigenproblem for clustering signed networks](https://mlsanity.com/paper/1904.08575/) (2019)
- [Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit](https://mlsanity.com/paper/2012.09996/) (2020)
- [The multilayer random dot product graph](https://mlsanity.com/paper/2007.10455/) (2020)
- [ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise](https://mlsanity.com/paper/2009.12297/) (2020)
- [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 embedding of weighted graphs](https://mlsanity.com/paper/1910.05534/) (2019)
- [Recovering shared structure from multiple networks with unknown edge distributions](https://mlsanity.com/paper/1906.07265/) (2019)
- [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)
- [Joint Spectral Clustering in Multilayer Degree-Corrected Stochastic Blockmodels](https://mlsanity.com/paper/2212.05053/) (2022)
- [Estimating Higher-Order Mixed Memberships via the ℓ2,∞ Tensor Perturbation Bound](https://mlsanity.com/paper/2212.08642/) (2022)
- [High-dimensional Mixed Graphical Models](https://mlsanity.com/paper/1304.2810/) (2013)
- [Euclidean mirrors and dynamics in network time series](https://mlsanity.com/paper/2205.06877/) (2022)
- [Balance in signed networks](https://mlsanity.com/paper/1809.05140/) (2018)
- [A Sharp Blockwise Tensor Perturbation Bound for Orthogonal Iteration](https://mlsanity.com/paper/2008.02437/) (2020)
- [Popularity Adjusted Block Models are Generalized Random Dot Product Graphs](https://mlsanity.com/paper/2109.04010/) (2021)
- [Sparse Subspace Clustering in Diverse Multiplex Network Model](https://mlsanity.com/paper/2206.07602/) (2022)
- [Testing for Balance in Social Networks](https://mlsanity.com/paper/1808.05260/) (2018)
- [SHEEP: Signed Hamiltonian Eigenvector Embedding for Proximity](https://mlsanity.com/paper/2302.07129/) (2023)

## Built on by (most cited first, 1 of 1)

- [Perfect Clustering in Very Sparse Diverse Multiplex Networks](https://mlsanity.com/paper/2507.19423/) (2025)

## Abstract (arXiv)

The paper introduces a Signed Generalized Random Dot Product Graph (SGRDPG) model, which is a variant of the Generalized Random Dot Product Graph (GRDPG), where, in addition, edges can be positive or negative. The setting is extended to a multiplex version, where all layers have the same collection of nodes and follow the SGRDPG. The only common feature of the layers of the network is that they can be partitioned into groups with common subspace structures, while otherwise matrices of connection probabilities can be all different. The setting above is extremely flexible and includes a variety of existing multiplex network models, including GRDPG, as its particular cases. By employing novel methodologies, our paper ensures strongly consistent clustering of layers and highly accurate subspace estimation, which are significant improvements over the results of Pensky and Wang (2024). All algorithms and theoretical results in the paper remain true for both signed and binary networks. In addition, the paper shows that keeping signs of the edges in the process of network construction leads to a better precision of estimation and clustering and, hence, is beneficial for tackling real world problems such as, for example, analysis of brain networks.