A greedy approach to sparse canonical correlation analysis

Abstract

We consider the problem of sparse canonical correlation analysis (CCA), i.e., the search for two linear combinations, one for each multivariate, that yield maximum correlation using a specified number of variables. We propose an efficient numerical approximation based on a direct greedy approach which bounds the correlation at each stage. The method is specifically designed to cope with large data sets and its computational complexity depends only on the sparsity levels. We analyze the algorithm's performance through the tradeoff between correlation and parsimony. The results of numerical simulation suggest that a significant portion of the correlation may be captured using a relatively small number of variables. In addition, we examine the use of sparse CCA as a regularization method when the number of available samples is small compared to the dimensions of the multivariates.

5 pages, 3 pages

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• Least Angle Regression
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
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Cited by in corpus (10)

• Sparse CCA: Adaptive Estimation and Computational Barriers
• Sparse CCA via Precision Adjusted Iterative Thresholding
• Minimax estimation in sparse canonical correlation analysis
• An Alternating Manifold Proximal Gradient Method for Sparse PCA and Sparse CCA
• Sparse Canonical Correlation Analysis via Concave Minimization
• Permutation Inference for Canonical Correlation Analysis
• Sparse Kernel Canonical Correlation Analysis via ${\ell }_1$-regularization
• ${\ell }_0$-based Sparse Canonical Correlation Analysis
• Significance testing for canonical correlation analysis in high dimensions
• Feature selection for high-dimensional integrated data