Significance analysis and statistical mechanics: An application to clustering

Marta Łuksza, Michael Lässig, Johannes Berg

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Article number220601
JournalPhysical Review Letters
Issue number22
StatePublished - 23 Nov 2010
Externally publishedYes


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