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.

翻译：未经监督的地物矩阵数据组合是探索性数据分析和实验数据质量控制的一种不可或缺的技术,然而,集群很难客观地评估其统计意义。我们证明一个公式,用以分配一组样品的大小,这些样品来自一个固定大小的人群,这些人群显示一个特定特征,以签字构成的每个特征的边际(频率)为条件。由此产生的“巧合精确测试”广泛适用于任何二进制数据中对集群的客观评估。我们还提供了一个实施测试的软件包、一套主要定理的计算核查,以及一个利用形式概念分析进行集群发现的补充工具。