Assessing modularity using a random matrix theory approach

Kristen Feher, James Whelan, Samuel Müller

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Random matrix theory (RMT) is well suited to describing the emergent properties of systems with complex interactions amongst their constituents through their eigenvalue spectrums. Some RMT results are applied to the problem of clustering high dimensional biological data with complex dependence structure amongst the variables. It will be shown that a gene relevance or correlation network can be constructed by choosing a correlation threshold in a principled way, such that it corresponds to a block diagonal structure in the correlation matrix, if such a structure exists. The structure is then found using community detection algorithms, but with parameter choice guided by RMT predictions. The resulting clustering is compared to a variety of hierarchical clustering outputs and is found to the most generalised result, in that it captures all the features found by the other considered methods.

Original languageEnglish
Article number44
Pages (from-to)1-34
Number of pages35
JournalStatistical Applications in Genetics and Molecular Biology
Volume10
Issue number1
DOIs
Publication statusPublished - Jan 2011
Externally publishedYes

Keywords

  • random matrix theory
  • clustering
  • modularity

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