  Clustering methods are popular for revealing structure in data, particularly
in the high-dimensional setting common to contemporary data science. A central
statistical question is, "are the clusters really there?" One pioneering method
in statistical cluster validation is SigClust, but it is severely underpowered
in the important setting where the candidate clusters have unbalanced sizes,
such as in rare subtypes of disease. We show why this is the case, and propose
a remedy that is powerful in both the unbalanced and balanced settings, using a
novel generalization of k-means clustering. We illustrate the value of our
method using a high-dimensional dataset of gene expression in kidney cancer
patients. A Python implementation is available at
https://github.com/thomaskeefe/sigclust.
