# Biconvex Biclustering

arXiv: https://arxiv.org/abs/2604.03936 · HTML: https://mlsanity.com/paper/2604.03936/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 54 references that are in the map.
- First posted on arXiv 5 Apr 2026.

## Builds on (most cited first, 16 of 16)

- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Splitting Methods for Convex Clustering](https://mlsanity.com/paper/1304.0499/) (2013)
- [Convex Clustering: Model, Theoretical Guarantee and Efficient Algorithm](https://mlsanity.com/paper/1810.02677/) (2018)
- [Statistical Properties of Convex Clustering](https://mlsanity.com/paper/1503.08340/) (2015)
- [Provable Convex Co-clustering of Tensors](https://mlsanity.com/paper/1803.06518/) (2018)
- [Convex Biclustering](https://mlsanity.com/paper/1408.0856/) (2014)
- [Dynamic Visualization and Fast Computation for Convex Clustering via Algorithmic Regularization](https://mlsanity.com/paper/1901.01477/) (2019)
- [Integrative Generalized Convex Clustering Optimization and Feature Selection for Mixed Multi-View Data](https://mlsanity.com/paper/1912.05449/) (2019)
- [Biconvex Clustering](https://mlsanity.com/paper/2008.01760/) (2020)
- [Splitting Methods for Convex Bi-Clustering and Co-Clustering](https://mlsanity.com/paper/1901.06075/) (2019)
- [The Why and How of Convex Clustering](https://mlsanity.com/paper/2507.09077/) (2025)
- [SUBIC: A Supervised Bi-Clustering Approach for Precision Medicine](https://mlsanity.com/paper/1709.09929/) (2017)
- [A Multiscale Scan Statistic for Adaptive Submatrix Localization](https://mlsanity.com/paper/1906.08884/) (2019)
- [A New Algorithm for Convex Biclustering and Its Extension to the Compositional Data](https://mlsanity.com/paper/2011.12182/) (2020)
- [Low Rank Convex Clustering For Matrix-Valued Observations](https://mlsanity.com/paper/2412.17328/) (2024)
- [Robust convex biclustering with a tuning-free method](https://mlsanity.com/paper/2212.03122/) (2022)

## Abstract (arXiv)

This article proposes a biconvex modification to convex biclustering in order to improve its performance in high-dimensional settings. In contrast to heuristics that discard a subset of noisy features a priori, our method jointly learns and accordingly weighs informative features while discovering biclusters. Moreover, the method is adaptive to the data, and is accompanied by an efficient algorithm based on proximal alternating minimization, complete with detailed guidance on hyperparameter tuning and efficient solutions to optimization subproblems. These contributions are theoretically grounded; we establish finite-sample bounds on the objective function under sub-Gaussian errors, and generalize these guarantees to cases where input affinities need not be uniform. Extensive simulation results reveal our method consistently recovers underlying biclusters while weighing and selecting features appropriately, outperforming peer methods. An application to a gene microarray dataset of lymphoma samples recovers biclusters matching an underlying classification, while giving additional interpretation to the mRNA samples via the column groupings and fitted weights.