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Assessing Modularity Using a Random Matrix Theory Approach

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  • Feher Kristen
  • Whelan James
  • Müller Samuel

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.

Suggested Citation

  • Feher Kristen & Whelan James & Müller Samuel, 2011. "Assessing Modularity Using a Random Matrix Theory Approach," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-34, September.
    • Handle: RePEc:bpj:sagmbi:v:10:y:2011:i:1:n:44
    DOI: 10.2202/1544-6115.1667
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    References listed on IDEAS

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    3. Tom C Freeman & Leon Goldovsky & Markus Brosch & Stijn van Dongen & Pierre Mazière & Russell J Grocock & Shiri Freilich & Janet Thornton & Anton J Enright, 2007. "Construction, Visualisation, and Clustering of Transcription Networks from Microarray Expression Data," PLOS Computational Biology, Public Library of Science, vol. 3(10), pages 1-11, October.
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    5. Efron, Bradley, 2007. "Correlation and Large-Scale Simultaneous Significance Testing," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 93-103, March.
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    Cited by:

    1. Feher Kristen & Whelan James & Müller Samuel, 2012. "Exploring Multicollinearity Using a Random Matrix Theory Approach," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(3), pages 1-35, May.
    2. Ruijin Du & Gaogao Dong & Lixin Tian & Minggang Wang & Guochang Fang & Shuai Shao, 2016. "Spatiotemporal Dynamics and Fitness Analysis of Global Oil Market: Based on Complex Network," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-17, October.

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