TY  - JOUR
A1  - Feher, Kristen
A1  - Whelan, James
A1  - Müller, Samuel
T1  - Assessing modularity using a random matrix theory approach
JF  - Statistical applications in genetics and molecular biology
N2  - 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.
KW  - random matrix theory
KW  - clustering
KW  - modularity
Y1  - 2011
U6  - https://doi.org/10.2202/1544-6115.1667
SN  - 2194-6302
SN  - 1544-6115
VL  - 10
IS  - 1
PB  - De Gruyter
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Feher, Kristen
A1  - Whelan, James
A1  - Müller, Samuel
T1  - Exploring multicollinearity using a random matrix theory approach
JF  - Statistical applications in genetics and molecular biology
N2  - 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.
KW  - random matrix theory
KW  - clustering
KW  - dimension reduction
KW  - inverse correlation estimation
Y1  - 2012
U6  - https://doi.org/10.1515/1544-6115.1668
SN  - 1544-6115
VL  - 11
IS  - 3
PB  - De Gruyter
CY  - Berlin
ER  -