Cluster Analysis with Resampling for Validation and Exploration (CARVE)
Authors: Kai R. Wycik, Tiffany M. Tang, Tarek M. Zikry, Genevera I. Allen
Abstract
Clustering is widely used across the sciences as the foundation for downstream data-driven scientific discoveries. However, clustering results are highly sensitive to the choice of algorithm, preprocessing, and the number of clusters k, producing scientific claims that are often not reproducible. The current state of the art for validating clustering solutions consists of clustering validation indices (CVIs) such as Silhouette, Davies-Bouldin, and Calinski-Harabasz, which rely on geometric assumptions that break down on the heavy-tailed, high-dimensional, and nonlinearly structured data encountered in biomedical research. Resampling-based alternatives - grounded in the ideas of clustering stability and generalizability - have been proposed but remain scattered across specialized tools with no unified, accessible software. We fill this gap with CARVE (Cluster Analysis with Resampling for Validation and Exploration), an open-source Python and R package that jointly evaluates multiple clustering algorithms and hyperparameters, returning stability and generalizability diagnostics at the global, cluster, and sample level together with principled selection rules and consensus-based cluster labels. Across six synthetic benchmarks CARVE consistently recovers near-optimal clusterings where classical indices degrade substantially. On experimental genomics and proteomics data sets, CARVE recovers finer biological structure when classical CVIs collapse entirely. CARVE is available with a scikit-learn-compatible Python API and an analogous R interface compatible with Seurat workflows.
Despite being ubiquitous in science, clustering lacks a unified framework for quantitatively evaluating the replicability of its results. We present evaluating replicability via iterative clustering assignments (ERICA), a method for determining whether clusters can be identified reproducibly in a dataset. The pipeline computes a statistic that determines whether reproducible cluster structure is present in a dataset. Quantitative visualization methods are also introduced to characterize similarities between clusters and identify observations that may represent outliers or unstable assignments. Experiments on synthetic datasets demonstrate that ERICA successfully identifies reproducible cluster structure. In contrast, application of ERICA to three breast cancer gene-expression datasets reveals instances in which clustering solutions are not reproducible. The study underscores the importance of rigorously evaluating clustering solutions and provides a practical framework for doing so.
Siamak K. Sorooshyari, Manuel A. Rivas, Robert Tibshirani
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.
Although some very common test beds exist for assessing the performance of clustering methods, large scale benchmarking is typically limited to relatively simplistic simulation set-ups. Here we describe the production and curation of close to 3000 synthetic data sets, derived from more than 200 publicly available data sets; the majority of which arose from real-world applications. By fitting a flexible non-parametric distribution to each base data set we are able to retain much of the nuance in real-world data which is difficult to reproduce in standard simulations, while also producing data sets whose sizes are sometimes substantially greater than the data sets from which they are derived. The synthetic data sets, plus an accompanying R package, are available for download from https://github.com/DavidHofmeyr/ClusBench.