Reliable data clustering with Bayesian community detection

We develop a model-free, noise-aware Bayesian clustering framework that constructs a martingale posterior over clusterings from a predictive Bayesian perspective. This avoids explicit likelihood-prior model specification, expensive MCMC sampling, and mode-seeking variational approximations, while accommodating irregular cluster shapes and enabling parallel generation of posterior draws. To interpret the posterior over high-dimensional, noise-aware clusterings, we introduce a Wasserstein-type summarization method. Using a novel noise-aware loss, this approach compresses the large collection of posterior draws into a small set of weighted representatives, capturing distinct cluster structures and noise assignments. Further, we marginalise the uncertainty in the density level, avoiding reliance on a specific choice. We establish theoretical properties of the proposed loss and guarantees for the level-marginal posterior approximation. Results demonstrate the framework's effectiveness in capturing clustering and noise uncertainty.

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.

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.