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

TL;DR

This paper introduces a novel convex biclustering algorithm, bi-ADMM, that efficiently handles general data and microbiome compositional constraints, improving visualization and analysis capabilities.

Contribution

The paper presents a new bi-ADMM algorithm for convex biclustering, extending it to compositional data with a Sylvester Equation-based approach, enhancing microbiome data analysis.

Findings

bi-ADMM guarantees global optimality in biclustering.

The method effectively handles microbiome compositional constraints.

Numerical experiments demonstrate superior performance and visualization.

Abstract

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.