Issue No. 04 - July-Aug. (2014 vol. 11)
Minta Thomas , Signal Process. & Data Analytics/iMinds Future Health Dept., KU Leuven, Leuven, Belgium
Anneleen Daemen , Dept. of Bioinf. & Comput. Biol., Genentech Inc., San Francisco, CA, USA
Bart De Moor , Signal Process. & Data Analytics/iMinds Future Health Dept., KU Leuven, Leuven, Belgium
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.
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
Minta Thomas, Anneleen Daemen, Bart De Moor, "Maximum Likelihood Estimation of GEVD: Applications in Bioinformatics", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 11, no. , pp. 673-680, July-Aug. 2014, doi:10.1109/TCBB.2014.2304292