  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.
