# Kernel Biclustering algorithm in Hilbert Spaces

arXiv: https://arxiv.org/abs/2208.03675 · HTML: https://mlsanity.com/paper/2208.03675/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 77 references that are in the map.
- First posted on arXiv 7 Aug 2022.

## Builds on (most cited first, 13 of 13)

- [Interpretable Distribution Features with Maximum Testing Power](https://mlsanity.com/paper/1605.06796/) (2016)
- [Deep Knockoffs](https://mlsanity.com/paper/1811.06687/) (2018)
- [Selective Inference for Hierarchical Clustering](https://mlsanity.com/paper/2012.02936/) (2020)
- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [Co-clustering through Optimal Transport](https://mlsanity.com/paper/1705.06189/) (2017)
- [Implicit Kernel Learning](https://mlsanity.com/paper/1902.10214/) (2019)
- [Functional Models for Time-Varying Random Objects](https://mlsanity.com/paper/1907.10829/) (2019)
- [Distributional data analysis of accelerometer data from the NHANES database using nonparametric survey regression models](https://mlsanity.com/paper/2104.01165/) (2021)
- [Convex Biclustering](https://mlsanity.com/paper/1408.0856/) (2014)
- [Kernel k-Groups via Hartigan's Method](https://mlsanity.com/paper/1710.09859/) (2017)
- [Learning Data-adaptive Nonparametric Kernels](https://mlsanity.com/paper/1808.10724/) (2018)
- [More Powerful Selective Kernel Tests for Feature Selection](https://mlsanity.com/paper/1910.06134/) (2019)
- [Biclustering with Alternating K-Means](https://mlsanity.com/paper/2009.04550/) (2020)

## Built on by (most cited first, 3 of 3)

- [Variable Selection Methods for Multivariate, Functional, and Complex Biomedical Data in the AI Age](https://mlsanity.com/paper/2501.06868/) (2025)
- [Distributional Random Forests for Complex Survey Designs](https://mlsanity.com/paper/2512.08179/) (2025)
- [Gaussian mixture models in Hilbert spaces via kernel methods](https://mlsanity.com/paper/2605.05996/) (2026)

## Abstract (arXiv)

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.