# A New Algorithm for Convex Biclustering and Its Extension to the Compositional Data

arXiv: https://arxiv.org/abs/2011.12182 · HTML: https://mlsanity.com/paper/2011.12182/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2020.

## Built on by (most cited first, 2 of 2)

- [Sparse Convex Biclustering](https://mlsanity.com/paper/2601.01757/) (2026)
- [Biconvex Biclustering](https://mlsanity.com/paper/2604.03936/) (2026)

## Abstract (arXiv)

Biclustering is a powerful data mining technique that allows simultaneously clustering rows (observations) and columns (features) in a matrix-format data set, which can provide results in a checkerboard-like pattern for visualization and exploratory analysis in a wide array of domains. Multiple biclustering algorithms have been developed in the past two decades, among which the convex biclustering can guarantee a global optimum by formulating in as a convex optimization problem. On the other hand, the application of biclustering has not progressed in parallel with the algorithm techniques. For example, biclustering for increasingly popular microbiome research data is under-applied possibly due to its compositional constraints for each sample. In this manuscript, we propose a new convex biclustering algorithm, called the bi-ADMM, under general setups based on the ADMM algorithm, which is free of extra smoothing steps to visualize informative biclusters required by existing convex biclustering algorithms. Furthermore, we tailor it to the algorithm named biC-ADMM specifically to tackle compositional constraints confronted in microbiome data. The key step of our methods utilizes the Sylvester Equation to derive the ADMM algorithm, which is new to the clustering research. The effectiveness of the proposed methods is examined through a variety of numerical experiments and a microbiome data application.