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Community detection for correlation matrices

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  • Mel MacMahon
  • Diego Garlaschelli
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    Abstract

    A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, the attempts made so far have merely replaced network data with correlation matrices, a procedure that we show to be intrinsically biased due to its inconsistency with the null hypotheses underlying the existing algorithms. Here we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anti-correlated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested sub-communities with `hard' cores and `soft' peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard sectorial taxonomy, detect `soft stocks' that alternate between communities, and discuss implications for portfolio optimization and risk management.

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    File URL: http://arxiv.org/pdf/1311.1924
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1311.1924.

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    Date of creation: Nov 2013
    Date of revision: Apr 2014
    Handle: RePEc:arx:papers:1311.1924

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    Web page: http://arxiv.org/

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