Kernel Biclustering algorithm in Hilbert Spaces

TL;DR

This paper introduces a novel model-free biclustering algorithm in Hilbert spaces that leverages energy distance and MMD to identify complex cluster shapes in data, outperforming existing methods especially in higher-order moment differences.

Contribution

The paper develops a new biclustering method in abstract spaces using ED and MMD, capable of detecting complex cluster structures beyond mean and variance differences.

Findings

Performs well on simulated and real datasets

Outperforms state-of-the-art methods in higher-order moment detection

Provides theoretical consistency results using optimal transport tools

Abstract

Biclustering algorithms partition data and covariates simultaneously, providing new insights in several domains, such as analyzing gene expression to discover new biological functions. This paper develops a new model-free biclustering algorithm in abstract spaces using the notions of energy distance (ED) and the maximum mean discrepancy (MMD) -- two distances between probability distributions capable of handling complex data such as curves or graphs. The proposed method can learn more general and complex cluster shapes than most existing literature approaches, which usually focus on detecting mean and variance differences. Although the biclustering configurations of our approach are constrained to create disjoint structures at the datum and covariate levels, the results are competitive. Our results are similar to state-of-the-art methods in their optimal scenarios, assuming a proper kernel choice, outperforming them when cluster differences are concentrated in higher-order moments. The model's performance has been tested in several situations that involve simulated and real-world datasets. Finally, new theoretical consistency results are established using some tools of the theory of optimal transport.