# Convex Biclustering

arXiv: https://arxiv.org/abs/1408.0856 · HTML: https://mlsanity.com/paper/1408.0856/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2014.

## Built on by (most cited first, 10 of 10)

- [Computational Lower Bounds for Graphon Estimation via Low-degree Polynomials](https://mlsanity.com/paper/2308.15728/) (2023)
- [Convex Clustering through MM: An Efficient Algorithm to Perform Hierarchical Clustering](https://mlsanity.com/paper/2211.01877/) (2022)
- [Kernel Biclustering algorithm in Hilbert Spaces](https://mlsanity.com/paper/2208.03675/) (2022)
- [Network Clustering for Latent State and Changepoint Detection](https://mlsanity.com/paper/2111.01273/) (2021)
- [Optimal Variable Clustering for High-Dimensional Matrix Valued Data](https://mlsanity.com/paper/2112.12909/) (2021)
- [Robust convex biclustering with a tuning-free method](https://mlsanity.com/paper/2212.03122/) (2022)
- [Clusterpath Gaussian Graphical Modeling](https://mlsanity.com/paper/2407.00644/) (2024)
- [Tree-Guided L1-Convex Clustering](https://mlsanity.com/paper/2503.24012/) (2025)
- [Sparse Convex Biclustering](https://mlsanity.com/paper/2601.01757/) (2026)
- [Biconvex Biclustering](https://mlsanity.com/paper/2604.03936/) (2026)

## Abstract (arXiv)

In the biclustering problem, we seek to simultaneously group observations and features. While biclustering has applications in a wide array of domains, ranging from text mining to collaborative filtering, the problem of identifying structure in high dimensional genomic data motivates this work. In this context, biclustering enables us to identify subsets of genes that are co-expressed only within a subset of experimental conditions. We present a convex formulation of the biclustering problem that possesses a unique global minimizer and an iterative algorithm, COBRA, that is guaranteed to identify it. Our approach generates an entire solution path of possible biclusters as a single tuning parameter is varied. We also show how to reduce the problem of selecting this tuning parameter to solving a trivial modification of the convex biclustering problem. The key contributions of our work are its simplicity, interpretability, and algorithmic guarantees - features that arguably are lacking in the current alternative algorithms. We demonstrate the advantages of our approach, which includes stably and reproducibly identifying biclusterings, on simulated and real microarray data.