publication . Article . Preprint . Other literature type . 2019

Constructing networks by filtering correlation matrices: a null model approach

Kojaku, Sadamori; Masuda, Naoki;
Open Access
  • Published: 13 Nov 2019 Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, volume 475, page 20,190,578 (issn: 1364-5021, eissn: 1471-2946, Copyright policy)
  • Publisher: The Royal Society
Abstract
Network analysis has been applied to various correlation matrix data. Thresholding on the value of the pairwise correlation is probably the most straightforward and common method to create a network from a correlation matrix. However, there have been criticisms on this thresholding approach such as an inability to filter out spurious correlations, which have led to proposals of alternative methods to overcome some of the problems. We propose a method to create networks from correlation matrices based on optimisation with regularization, where we lay an edge between each pair of nodes if and only if the edge is unexpected from a null model. The proposed algorithm...
Subjects
free text keywords: General Engineering, General Physics and Astronomy, General Mathematics, Physics - Physics and Society
42 references, page 1 of 3

[1] J.-P. Onnela, K. Kaski, and J. Kertész. Clustering and information in correlation based financial networks. Eur. Phys. J. B, 38:353-362, 2004. [OpenAIRE]

[2] C. K. Tse, J. Liu, and F. C. M. Lau. A network perspective of the stock market. J. Emp. Fin., 17:659-667, 2010.

[3] M. E. J. Newman. Networks, 2nd edition. Oxford University Press, Oxford, 2018.

[4] M. Rubinov and O. Sporns. Complex network measures of brain connectivity: Uses and interpretations. NeuroImage, 52:1059-1069, 2010.

[5] B. C. M. van Wijk, C. J. Stam, and A. Daffertshofer. Comparing brain networks of different size and connectivity density using graph theory. PLOS ONE, 5:e13701, 2010.

[6] M. Zanin, P. Sousa, D. Papo, R. Bajo, J. García-Prieto, F. del Pozo, E. Menasalvas, and S. Boccaletti. Optimizing functional network representation of multivariate time series. Sci. Rep., 2:630, 2012.

[7] F. De Vico Fallani, J. Richiardi, M. Chavez, and S. Achard. Graph analysis of functional brain networks: practical issues in translational neuroscience. Phil. Trans. Royal Soc. B: Biological Sciences, 369:20130521, 2014. [OpenAIRE]

[8] F. Kose, W. Weckwerth, T. Linke, and O. Fiehn. Visualizing plant metabolomic correlation networks using clique-metabolite matrices. Bioinformatics, 17:1198-1208, 2001. [OpenAIRE]

[9] R. N. Mantegna. Hierarchical structure in financial markets. Eur. Phys. J. B, 11:193-197, 1999.

[10] M. Tumminello, T. Aste, T. Di Matteo, and R. N. Mantegna. A tool for filtering information in complex systems. Proc. Natl. Acad. Sci. USA, 102:10421-10426, 2005. [OpenAIRE]

[11] V. De Vico Fallani, F.and Latora and M. Chavez. A topological criterion for filtering information in complex brain networks. PLOS Comput. Bio., 13:e1005305, 2017. [OpenAIRE]

[12] D. A. Jackson and K. M. Somers. The spectre of 'spurious' correlations. Oecologia, 86:147-151, 1991. [OpenAIRE]

[13] T. Vigen. Spurious correlations. Hachette books, 2015.

[14] J. P. Bouchaud and M. Potters. Theo. Fin. Risk Derivative Pricing, 2nd edition. Cambridge University Press, Weinheim, 2003.

[15] M. MacMahon and D. Garlaschelli. Community detection for correlation matrices. Phys. Rev. X, 5:021006, 2015.

42 references, page 1 of 3
Abstract
Network analysis has been applied to various correlation matrix data. Thresholding on the value of the pairwise correlation is probably the most straightforward and common method to create a network from a correlation matrix. However, there have been criticisms on this thresholding approach such as an inability to filter out spurious correlations, which have led to proposals of alternative methods to overcome some of the problems. We propose a method to create networks from correlation matrices based on optimisation with regularization, where we lay an edge between each pair of nodes if and only if the edge is unexpected from a null model. The proposed algorithm...
Subjects
free text keywords: General Engineering, General Physics and Astronomy, General Mathematics, Physics - Physics and Society
42 references, page 1 of 3

[1] J.-P. Onnela, K. Kaski, and J. Kertész. Clustering and information in correlation based financial networks. Eur. Phys. J. B, 38:353-362, 2004. [OpenAIRE]

[2] C. K. Tse, J. Liu, and F. C. M. Lau. A network perspective of the stock market. J. Emp. Fin., 17:659-667, 2010.

[3] M. E. J. Newman. Networks, 2nd edition. Oxford University Press, Oxford, 2018.

[4] M. Rubinov and O. Sporns. Complex network measures of brain connectivity: Uses and interpretations. NeuroImage, 52:1059-1069, 2010.

[5] B. C. M. van Wijk, C. J. Stam, and A. Daffertshofer. Comparing brain networks of different size and connectivity density using graph theory. PLOS ONE, 5:e13701, 2010.

[6] M. Zanin, P. Sousa, D. Papo, R. Bajo, J. García-Prieto, F. del Pozo, E. Menasalvas, and S. Boccaletti. Optimizing functional network representation of multivariate time series. Sci. Rep., 2:630, 2012.

[7] F. De Vico Fallani, J. Richiardi, M. Chavez, and S. Achard. Graph analysis of functional brain networks: practical issues in translational neuroscience. Phil. Trans. Royal Soc. B: Biological Sciences, 369:20130521, 2014. [OpenAIRE]

[8] F. Kose, W. Weckwerth, T. Linke, and O. Fiehn. Visualizing plant metabolomic correlation networks using clique-metabolite matrices. Bioinformatics, 17:1198-1208, 2001. [OpenAIRE]

[9] R. N. Mantegna. Hierarchical structure in financial markets. Eur. Phys. J. B, 11:193-197, 1999.

[10] M. Tumminello, T. Aste, T. Di Matteo, and R. N. Mantegna. A tool for filtering information in complex systems. Proc. Natl. Acad. Sci. USA, 102:10421-10426, 2005. [OpenAIRE]

[11] V. De Vico Fallani, F.and Latora and M. Chavez. A topological criterion for filtering information in complex brain networks. PLOS Comput. Bio., 13:e1005305, 2017. [OpenAIRE]

[12] D. A. Jackson and K. M. Somers. The spectre of 'spurious' correlations. Oecologia, 86:147-151, 1991. [OpenAIRE]

[13] T. Vigen. Spurious correlations. Hachette books, 2015.

[14] J. P. Bouchaud and M. Potters. Theo. Fin. Risk Derivative Pricing, 2nd edition. Cambridge University Press, Weinheim, 2003.

[15] M. MacMahon and D. Garlaschelli. Community detection for correlation matrices. Phys. Rev. X, 5:021006, 2015.

42 references, page 1 of 3
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