  We present a method for individual and integrative analysis of high
dimension, low sample size data that capitalizes on the recurring theme in
multivariate analysis of projecting higher dimensional data onto a few
meaningful directions that are solutions to a generalized eigenvalue problem.
We propose a general framework, called SELP (Sparse Estimation with Linear
Programming), with which one can obtain a sparse estimate for a solution vector
of a generalized eigenvalue problem. We demonstrate the utility of SELP on
canonical correlation analysis for an integrative analysis of methylation and
gene expression profiles from a breast cancer study, and we identify some genes
known to be associated with breast carcinogenesis, which indicates that the
proposed method is capable of generating biologically meaningful insights.
Simulation studies suggest that the proposed method performs competitive in
comparison with some existing methods in identifying true signals in various
underlying covariance structures.
