Sparse Canonical Correlation Analysis with General Covariance Structure via Convex Optimization

• Activity Number: 39
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Irina Gaynanova*+ and James Booth and Martin Wells
• Companies: Cornell University and Cornell University and Cornell University
• Keywords: Canonical Correlation Analysis ; Convex Optimization ; Sparsity

Abstract

Canonical Correlation Analysis (CCA) is a standard multivariate analysis tool that is used to find linear combinations of two sets of features with the maximum correlation. Its use for the modern high-dimensional data sets is challenging as it is usually of interest to select only a small subset of variables. Consequently, several methods for sparse CCA have been proposed in the literature. Although these methods have performed well in many applications, their main drawbacks are disregard of the covariance structure and lack of theoretical justification. Moreover, most of them require solving non-convex optimization problem and so convergence to the global solution is not guaranteed. In this paper we propose a novel sparse CCA method that overcomes these drawbacks by simultaneously estimating sparse linear combinations of features of both data sets. In addition, we put no assumptions on the underlying covariance structure. The convexity of the resulting optimization problem allows us to use computationally efficient algorithms to find the global solution. We compare our method with previous sparse CCA proposals via simulations and real data applications.