37258
2011
2011
eng
36
1
10
article
De Gruyter
Berlin
1
--
--
--
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.
Statistical applications in genetics and molecular biology
10.2202/1544-6115.1667
2194-6302 (print)
1544-6115 (online)
wos:2011-2013
44
WOS:000295515800003
Feher, K (reprint author), Univ Potsdam, Dept Biol & Biochem, Potsdam, Germany.
Marie Curie Early Stage Training Fellowship Programme
[MEST-CT-2004-513973 BIOSTAR]
Kristen Feher
James Whelan
Samuel Müller
eng
uncontrolled
random matrix theory
eng
uncontrolled
clustering
eng
uncontrolled
modularity
Institut für Biochemie und Biologie
Referiert
36299
2012
2012
eng
35
3
11
article
De Gruyter
Berlin
1
--
--
--
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 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.
Statistical applications in genetics and molecular biology
10.1515/1544-6115.1668
1544-6115 (print)
wos:2011-2013
15
WOS:000305606400015
Feher, K (reprint author), Univ Potsdam, Dept Biol & Biochem, Potsdam, Germany.
ARC [DP110101998]
Kristen Feher
James Whelan
Samuel Müller
eng
uncontrolled
random matrix theory
eng
uncontrolled
clustering
eng
uncontrolled
dimension reduction
eng
uncontrolled
inverse correlation estimation
Institut für Mathematik
Referiert