二进制数据聚类显著性的精确检验
An exact test for significance of clusters in binary data
摘要：
特征矩阵数据的无监督聚类是进行探索性数据分析和实验数据质量控制不可缺少的技术。然而，聚类很难以客观的方式评估统计意义。我们证明了一个公式的样本集的大小的分布，出人口的固定大小，显示一个给定的签名，条件的边缘（频率）的每个单独的功能，包括签名。由此产生的“精确检验的巧合”是广泛适用于任何二进制数据的集群的客观评估。我们还提出了一个软件包实现的测试，一套计算验证的主要定理，和集群发现使用形式概念分析的补充工具。
英文摘要：
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.
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