Assessing modularity using a random matrix theory approach

  • 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.

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Author:Kristen Feher, James Whelan, Samuel Müller
ISSN:2194-6302 (print)
ISSN:1544-6115 (online)
Parent Title (English):Statistical applications in genetics and molecular biology
Publisher:De Gruyter
Place of publication:Berlin
Document Type:Article
Year of first Publication:2011
Year of Completion:2011
Release Date:2017/03/26
Tag:clustering; modularity; random matrix theory
Funder:Marie Curie Early Stage Training Fellowship Programme [MEST-CT-2004-513973 BIOSTAR]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Biochemie und Biologie
Peer Review:Referiert