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Maximum Likelihood Estimation ofGEVD: Applications in Bioinformatics
July-Aug. 2014 (vol. 11 no. 4)
pp. 673-680
Minta Thomas, ESAT, STADIUS Center for Dynamical Systems, Signal Processing and Data Analytics/iMinds Future Health Department, KU Leuven, Kasteelpark Arenberg 10, B-3001 Leuven,
Anneleen Daemen, Department of Bioinformatics and Computational Biology, Genentech Inc., South San Francisco,
Bart De Moor, ESAT, STADIUS Center for Dynamical Systems, Signal Processing and Data Analytics/iMinds Future Health Department, KU Leuven, Kasteelpark Arenberg 10, B-3001 Leuven,
We propose a method, maximum likelihood estimation of generalized eigenvalue decomposition (MLGEVD) that employs a well known technique relying on the generalization of singular value decomposition (SVD). The main aim of the work is to show the tight equivalence between MLGEVD and generalized ridge regression. This relationship reveals an important mathematical property of GEVD in which the second argument act as prior information in the model. Thus we show that MLGEVD allows the incorporation of external knowledge about the quantities of interest into the estimation problem. We illustrate the importance of prior knowledge in clinical decision making/identifying differentially expressed genes with case studies for which microarray data sets with corresponding clinical/literature information are available. On all of these three case studies, MLGEVD outperformed GEVD on prediction in terms of test area under the ROC curve (test AUC). MLGEVD results in significantly improved diagnosis, prognosis and prediction of therapy response.
Index Terms:
Eigenvalues and eigenfunctions,Matrix decomposition,Bioinformatics,Maximum likelihood estimation,Principal component analysis,Breast cancer,generalized singular value decomposition,Eigenvalue decomposition,generalized eigenvalue decomposition,maximum likelihood generalized eigenvalue decomposition
Citation:
Minta Thomas, Anneleen Daemen, Bart De Moor, "Maximum Likelihood Estimation ofGEVD: Applications in Bioinformatics," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 11, no. 4, pp. 673-680, July-Aug. 2014, doi:10.1109/TCBB.2014.2304292
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