# Splitting Methods for Convex Bi-Clustering and Co-Clustering

arXiv: https://arxiv.org/abs/1901.06075 · HTML: https://mlsanity.com/paper/1901.06075/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2019.

## Built on by (most cited first, 3 of 3)

- [Network Clustering for Latent State and Changepoint Detection](https://mlsanity.com/paper/2111.01273/) (2021)
- [Simple and Scalable Algorithms for Cluster-Aware Precision Medicine](https://mlsanity.com/paper/2211.16553/) (2022)
- [Biconvex Biclustering](https://mlsanity.com/paper/2604.03936/) (2026)

## Abstract (arXiv)

Co-Clustering, the problem of simultaneously identifying clusters across multiple aspects of a data set, is a natural generalization of clustering to higher-order structured data. Recent convex formulations of bi-clustering and tensor co-clustering, which shrink estimated centroids together using a convex fusion penalty, allow for global optimality guarantees and precise theoretical analysis, but their computational properties have been less well studied. In this note, we present three efficient operator-splitting methods for the convex co-clustering problem: a standard two-block ADMM, a Generalized ADMM which avoids an expensive tensor Sylvester equation in the primal update, and a three-block ADMM based on the operator splitting scheme of Davis and Yin. Theoretical complexity analysis suggests, and experimental evidence confirms, that the Generalized ADMM is far more efficient for large problems.