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
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