Exploring multicollinearity using a random matrix theory approach

  • Clustering of gene expression data is often done with the latent aim of dimension reduction, by finding groups of genes that have a common response to potentially unknown stimuli. However, what is poorly understood to date is the behaviour of a low dimensional signal embedded in high dimensions. This paper introduces a multicollinear model which is based on random matrix theory results, and shows potential for the characterisation of a gene cluster's correlation matrix. This model projects a one dimensional signal into many dimensions and is based on the spiked covariance model, but rather characterises the behaviour of the corresponding correlation matrix. The eigenspectrum of the correlation matrix is empirically examined by simulation, under the addition of noise to the original signal. The simulation results are then used to propose a dimension estimation procedure of clusters from data. Moreover, the simulation results warn against considering pairwise correlations in isolation, as the model provides a mechanism whereby a pair ofClustering of gene expression data is often done with the latent aim of dimension reduction, by finding groups of genes that have a common response to potentially unknown stimuli. However, what is poorly understood to date is the behaviour of a low dimensional signal embedded in high dimensions. This paper introduces a multicollinear model which is based on random matrix theory results, and shows potential for the characterisation of a gene cluster's correlation matrix. This model projects a one dimensional signal into many dimensions and is based on the spiked covariance model, but rather characterises the behaviour of the corresponding correlation matrix. The eigenspectrum of the correlation matrix is empirically examined by simulation, under the addition of noise to the original signal. The simulation results are then used to propose a dimension estimation procedure of clusters from data. Moreover, the simulation results warn against considering pairwise correlations in isolation, as the model provides a mechanism whereby a pair of genes with 'low' correlation may simply be due to the interaction of high dimension and noise. Instead, collective information about all the variables is given by the eigenspectrum.show moreshow less

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Metadaten
Author:Kristen Feher, James Whelan, Samuel Müller
DOI:https://doi.org/10.1515/1544-6115.1668
ISSN:1544-6115 (print)
Parent Title (English):Statistical applications in genetics and molecular biology
Publisher:De Gruyter
Place of publication:Berlin
Document Type:Article
Language:English
Year of first Publication:2012
Year of Completion:2012
Release Date:2017/03/26
Tag:clustering; dimension reduction; inverse correlation estimation; random matrix theory
Volume:11
Issue:3
Pagenumber:35
Funder:ARC [DP110101998]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer Review:Referiert