title: Significance analysis and statistical mechanics: an application to clustering.
abstract: This Letter addresses the statistical significance of structures in random data: given a set of vectors and a measure of mutual similarity, how likely is it that a subset of these vectors forms a cluster with enhanced similarity among its elements? The computation of this cluster p value for randomly distributed vectors is mapped onto a well-defined problem of statistical mechanics. We solve this problem analytically, establishing a connection between the physics of quenched disorder and multiple-testing statistics in clustering and related problems. In an application to gene expression data, we find a remarkable link between the statistical significance of a cluster and the functional relationships between its genes.
authors.affiliation: Max Planck Institute for Molecular Genetics, Ihnestraße 63-73, 14195 Berlin, Germany.
authors.forename: Marta
authors.initials: M
authors.lastname: Łuksza
authors.forename: Michael
authors.initials: M
authors.lastname: Lässig
authors.forename: Johannes
authors.initials: J
authors.lastname: Berg