A general framework for testing clustering significance and variable-level inference in high-dimensional data.

Clustering is a fundamental tool for uncovering heterogeneity in data, but two challenges remain: determining whether observed clusters reflect genuine structure rather than sampling variability, and identifying the variables that drive any significant clustering pattern. Statistical significance of clustering (SigClust) addresses the first problem by assessing clustering significance using the cluster index under a Gaussian null model, with the null distribution estimated by Monte Carlo simulation in high dimensions. We propose SigClust-DE, a method that improves null covariance estimation in SigClust and extends the framework to variable-level inference for identifying features associated with cluster separation. In this way, SigClust-DE provides a joint framework for clustering significance testing and differential expression analysis, a central task in RNA-seq studies. Through extensive simulations and an application to RNA-seq data, we show that SigClust-DE controls Type I error in clustering significance testing, controls the false discovery rate in variable-level inference, and achieves strong power for detecting differentially expressed features.