A Penalized Matrix Decomposition, with Applications to Sparse Principal Components and Canonical Correlation Analysis

• Activity Number: 603
• Type: Invited
• Date/Time: Thursday, August 5, 2010 : 8:30 AM to 10:20 AM
• Sponsor: WNAR
• Author(s): Daniela Witten*+ and Rob Tibshirani and Trevor Hastie
• Companies: Stanford University and Stanford University and Stanford University
• Keywords: genomics ; sparsity ; lasso ; canonical correlation ; penalization ; SVD

Abstract

We present a penalized matrix decomposition, a new framework for computing a low-rank approximation for a matrix. Our low-rank approximation is a generalization of the singular value decomposition. While the singular value decomposition results in singular vectors that have no elements that are exactly equal to zero, our new decomposition results in sparse singular vectors. When this decomposition is applied to a data matrix, it can yield interpretable results. If applied to a variance-covariance matrix, it yields a new method for sparse principal components analysis, and if it is applied to a matrix of cross-products, it results in a new method for sparse canonical correlation analysis (CCA). We show that sparse CCA can be used to perform an integrative analysis of two or more genomic data sets with measurements taken on a single set of samples.