# Multiway clustering via tensor block models

arXiv: https://arxiv.org/abs/1906.03807 · HTML: https://mlsanity.com/paper/1906.03807/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2019.

## Built on by (most cited first, 17 of 17)

- [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 Clustering by Lloyd Algorithm for Low-Rank Mixture Model](https://mlsanity.com/paper/2207.04600/) (2022)
- [Beyond the Signs: Nonparametric Tensor Completion via Sign Series](https://mlsanity.com/paper/2102.00384/) (2021)
- [Multiway Spherical Clustering via Degree-Corrected Tensor Block Models](https://mlsanity.com/paper/2201.07401/) (2022)
- [Bayesian community detection for networks with covariates](https://mlsanity.com/paper/2203.02090/) (2022)
- [Sparse Subspace Clustering in Diverse Multiplex Network Model](https://mlsanity.com/paper/2206.07602/) (2022)
- [Multi-Slice Clustering for 3-order Tensor Data](https://mlsanity.com/paper/2109.10803/) (2021)
- [Statistical and Computational Efficiency for Smooth Tensor Estimation with Unknown Permutations](https://mlsanity.com/paper/2111.04681/) (2021)
- [Identifiability of Nonnegative Tucker Decompositions -- Part I: Theory](https://mlsanity.com/paper/2505.12713/) (2025)
- [Optimal Variable Clustering for High-Dimensional Matrix Valued Data](https://mlsanity.com/paper/2112.12909/) (2021)
- [Multiway clustering of 3-order tensor via affinity matrix](https://mlsanity.com/paper/2303.07757/) (2023)
- [Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges](https://mlsanity.com/paper/2405.18412/) (2024)
- [MultiwayPAM: Multiway Partitioning Around Medoids for LLM-as-a-Judge Score Analysis](https://mlsanity.com/paper/2603.10287/) (2026)
- [Statistical and computational rates in high rank tensor estimation](https://mlsanity.com/paper/2304.04043/) (2023)
- [Parallel Computation of Multi-Slice Clustering of Third-Order Tensors](https://mlsanity.com/paper/2309.17383/) (2023)
- [Mixture of multilayer stochastic block models for multiview clustering](https://mlsanity.com/paper/2401.04682/) (2024)

## Abstract (arXiv)

We consider the problem of identifying multiway block structure from a large noisy tensor. Such problems arise frequently in applications such as genomics, recommendation system, topic modeling, and sensor network localization. We propose a tensor block model, develop a unified least-square estimation, and obtain the theoretical accuracy guarantees for multiway clustering. The statistical convergence of the estimator is established, and we show that the associated clustering procedure achieves partition consistency. A sparse regularization is further developed for identifying important blocks with elevated means. The proposal handles a broad range of data types, including binary, continuous, and hybrid observations. Through simulation and application to two real datasets, we demonstrate the outperformance of our approach over previous methods.