  Unsupervised clustering of feature matrix data is an indispensible technique
for exploratory data analysis and quality control of experimental data.
However, clusters are difficult to assess for statistical significance in an
objective way. We prove a formula for the distribution of the size of the set
of samples, out of a population of fixed size, which display a given signature,
conditional on the marginals (frequencies) of each individual feature
comprising the signature. The resulting "exact test for coincidence" is widely
applicable to objective assessment of clusters in any binary data. We also
present a software package implementing the test, a suite of computational
verifications of the main theorems, and a supplemental tool for cluster
discovery using Formal Concept Analysis.
