Nonparametric Hypothesis Testing of High-dimensional Clustering With Application to Single-cell RNA Data

Single-cell RNA sequencing studies routinely use clustering to define putative cell types and cell states, yet the observed separation may arise from sampling variability rather than genuine biological heterogeneity. This paper studies formal significance testing of such clustering structure in high-dimensional data. Existing SigClust methods assess clustering significance through Monte Carlo simulation under a Gaussian single-cluster null, but this assumption can be unreliable for normalized gene expression data and other non-Gaussian settings. We propose SigClust-LCP, a nonparametric extension that models a single cluster by a log-concave distribution. To make this approach computationally feasible in moderate to high dimensions, we develop a score-matching estimator for log-concave projection inspired by recent generative modeling ideas. We establish theoretical guarantees for the estimator and for its use in clustering significance testing. Simulations show that SigClust-LCP controls Type-I error more reliably than existing methods across a range of unimodal and mixture distributions while retaining competitive power. In a single-cell RNA sequencing analysis of Hydra cells, the method avoids spurious subclusters within annotated cell populations and supports biologically meaningful separation across lineages and body-axis regions.