# Community Detection on Mixture Multi-layer Networks via Regularized Tensor Decomposition

arXiv: https://arxiv.org/abs/2002.04457 · HTML: https://mlsanity.com/paper/2002.04457/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2020.

## Built on by (most cited first, 30 of 30)

- [Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition](https://mlsanity.com/paper/2106.16042/) (2021)
- [Community Detection in General Hypergraph via Graph Embedding](https://mlsanity.com/paper/2103.15035/) (2021)
- [ALMA: Alternating Minimization Algorithm for Clustering Mixture Multilayer Network](https://mlsanity.com/paper/2102.10226/) (2021)
- [Estimating Higher-Order Mixed Memberships via the ℓ2,∞ Tensor Perturbation Bound](https://mlsanity.com/paper/2212.08642/) (2022)
- [Optimal Estimation and Computational Limit of Low-rank Gaussian Mixtures](https://mlsanity.com/paper/2201.09040/) (2022)
- [Average-Case Complexity of Tensor Decomposition for Low-Degree Polynomials](https://mlsanity.com/paper/2211.05274/) (2022)
- [Optimal Clustering by Lloyd Algorithm for Low-Rank Mixture Model](https://mlsanity.com/paper/2207.04600/) (2022)
- [Covariate-assisted Sparse Tensor Completion](https://mlsanity.com/paper/2103.06428/) (2021)
- [Sparse Subspace Clustering in Diverse Multiplex Network Model](https://mlsanity.com/paper/2206.07602/) (2022)
- [Consensus Knowledge Graph Learning via Multi-view Sparse Low Rank Block Model](https://mlsanity.com/paper/2209.13762/) (2022)
- [Community detection by spectral methods in multi-layer networks](https://mlsanity.com/paper/2403.12540/) (2024)
- [Clustering multilayer graphs with missing nodes](https://mlsanity.com/paper/2103.03235/) (2021)
- [Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorization](https://mlsanity.com/paper/2205.00626/) (2022)
- [Privacy-Preserving Community Detection for Locally Distributed Multiple Networks](https://mlsanity.com/paper/2306.15709/) (2023)
- [Sharp Analysis of Power Iteration for Tensor PCA](https://mlsanity.com/paper/2401.01047/) (2024)
- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [rMultiNet: An R Package For Multilayer Networks Analysis](https://mlsanity.com/paper/2302.04437/) (2023)
- [Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Model](https://mlsanity.com/paper/2307.00575/) (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)
- [Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges](https://mlsanity.com/paper/2405.18412/) (2024)
- [Statistical Inference in Tensor Completion: Optimal Uncertainty Quantification and Statistical-to-Computational Gaps](https://mlsanity.com/paper/2410.11225/) (2024)
- [Mixture of multilayer stochastic block models for multiview clustering](https://mlsanity.com/paper/2401.04682/) (2024)
- [VEC-SBM: Optimal Community Detection with Vectorial Edges Covariates](https://mlsanity.com/paper/2402.18805/) (2024)
- [Estimating mixed memberships in multi-layer networks](https://mlsanity.com/paper/2404.03916/) (2024)
- [Asymptotically perfect seeded graph matching without edge correlation (and applications to inference)](https://mlsanity.com/paper/2506.02825/) (2025)
- [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)
- [T-GINEE: A Tensor-Based Multilayer Graph Representation Learning](https://mlsanity.com/paper/2605.28300/) (2026)

## Abstract (arXiv)

We study the problem of community detection in multi-layer networks, where pairs of nodes can be related in multiple modalities. We introduce a general framework, i.e., mixture multi-layer stochastic block model (MMSBM), which includes many earlier models as special cases. We propose a tensor-based algorithm (TWIST) to reveal both global/local memberships of nodes, and memberships of layers. We show that the TWIST procedure can accurately detect the communities with small misclassification error as the number of nodes and/or the number of layers increases. Numerical studies confirm our theoretical findings. To our best knowledge, this is the first systematic study on the mixture multi-layer networks using tensor decomposition. The method is applied to two real datasets: worldwide trading networks and malaria parasite genes networks, yielding new and interesting findings.