2022/08/07 by Marcos Matabuena, Matabuena, Marcos, J. C Vidal +7 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Gene expression and cancer classification #Machine Learning (stat.ML) #Metabolomics and Mass Spectrometry Studies #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.ME #stat.ML #stat.TH
paper · pdf · doi:10.48550/arxiv.2208.03675
arxiv created 2022/08/07 · openalex publication_date 2022/08/07 · arxiv updated 2022/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.