Reduced-Rank Singular Value Decomposition for Dimension Reduction with High-Dimensional Data

Recent technical advances in genomics have led to an abundance of high-dimensional and correlated data. Dimension reduction methods typically rely on matrix decompositions (e.g. SVD and EVD) to compute the quantities needed for further analysis. However, in a high-dimensional setting, these decompositions must be adapted to cope with the singularity of the matrices involved. We illustrate how this can be done in the context of a particular dimension reduction method, Principal Component of Explained Variance (PCEV). PCEV seeks a linear combination of outcomes by maximising the proportion of variance explained by the covariates of interest. Using random matrix theory, we propose a heuristic that provides a fast way to compute valid p-values to test the significance of the decomposition. We compare the power of this approach with that of other common approaches to high-dimensional data. Finally, we illustrate our method using methylation data collected on a small number of individuals.

Date and Time: 

Monday, June 12, 2017 - 14:45 to 15:00

Co-authors (not including you): 

Stepan Grinek
BC Cancer Agency
Celia Greenwood
McGill University
Aurélie Labbe
HEC Montréal

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First Name Middle Name Last Name Primary Affiliation
edit Maxime Turgeon McGill University