An exact test for significance of clusters in binary data

TL;DR

This paper introduces an exact statistical test for evaluating the significance of clusters in binary data, providing a rigorous method for objective cluster validation in exploratory data analysis.

Contribution

It presents a novel exact test for cluster significance in binary data, along with software implementation and supplementary tools for cluster discovery.

Findings

Derived a formula for the distribution of sample sets with a given signature

Developed an exact test applicable to binary data clusters

Provided software and verification tools for the test

Abstract

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.