Biconvex Biclustering

Sam Rosen; Eric C. Chi; Jason Xu

stat.MLApr 5, 2026

Biconvex Biclustering

Authors: Sam Rosen, Eric C. Chi, Jason Xu

Organizations: Department of Statistical Science, Duke University · School of Statistics, University of Minnesota · Department of Biostatistics, University of California Los Angeles

Abstract

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.

Figures & tables

Figure 1: Mean of true bicluster ARI for each algorithm under the scenario described in Section 5.1 . The standard error is used to calculate 95% confidence bands for each point.

Figure 2: Distribution of AUC scores when fit under the scenario described in Section 5.1 .

Figure 3: Results for simulations described in Section 5.2 : Mean true bicluster ARI. Metrics in bold are the best performance across all algorithms for the given noise variance and matrix size. The standard error is displayed below each mean in parenthesis.

Figure 4: Distribution of AUC scores for models under the scenario described in Section 5.2 .

Label	Size	Mean Weight	Max Weight	Highest Weight mRNA Sample
A	276	1.48	2.82	Ki-67
B	156	1.26	2.11	NM23-H1 (NDP kinase A)
C	319	1.23	2.05	Cathepsin B
D	81	1.23	2.04	Beta-actin
E	111	1.20	1.81	Ras GTPase-activating protein
F	437	1.17	1.98	MEK Kinase 1 (MEKK1)

Table 1: Top eight column clusters from fit according to mean weight. The weights in the table are normalized such that a weight of 1 is equal to the inverse of

p=4026

. mRNA sample names are found in the dataset of Alizadeh et al. (2000) .

Clustering

Clustering groups data points by shared structure, developing methods to discover, validate, and interpret groups across diverse data and constraints.

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Cluster LOCO: Feature Importance For Interpreting Clusters

Claire M. He, Genevera I. Allen

Department of Statistics · Columbia University · New York, NY 10027, USA

Clustering

Open paper AskPDF arXiv

Clustering is widely used for exploratory analysis and scientific discovery, driving insights from market segmentation to biological data analysis, but its outputs can be difficult to interpret, audit, and reproduce as modern datasets become increasingly large and complex. Reliable use of clustering requires understanding which features drive the discovered structure, yet feature-level explanations for clustering remain scarce compared with methods in supervised learning. Furthermore, existing clustering feature importance scores are often tied to specific algorithms and data assumptions. To address these challenges, we propose Cluster LOCO (Leave-One-Covariate-Out), a family of model-agnostic feature importance scores for clustering. Cluster LOCO is built on feature occlusion and clustering generalizability, defined as whether cluster labels learned on one subset of the data can be accurately predicted on held-out samples. For any chosen clustering algorithm, Cluster LOCO quantifies a feature's importance by measuring how much its removal degrades generalizability. We first introduce Cluster LOCO-Split, which relies on data splitting, and then extend it to Cluster LOCO-MP, a minipatch ensemble-based version designed for large-scale data. Across synthetic simulations and an application to cell-type discovery in single-cell transcriptomics, we show that Cluster LOCO more reliably recovers informative features than existing clustering feature importance methods.

Abstract

Clustering

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