Trace Lasso Regularization for Adaptive Sparse Canonical Correlation Analysis via Manifold Optimization Approach

Canonical correlation analysis(CCA)describes the relationship between two sets of variables by finding a linear combination that maximizes the correlation coefficient.However,in high-dimensional settings where the number of variables exceeds sample size,or in the case that the variables are highly correlated,the traditional CCA is no longer appropriate.In this paper,a new matrix regularization is introduced,which is an extension of the trace Lasso in the vector case.Then we propose an adaptive sparse version of CCA(ASCCA)to overcome these disadvantages by utilizing the trace Lasso regularization.The adaptability of ASCCA is that the sparsity regularization of canonical vectors depends on the sample data,which is more realistic in practical applications.The ASCCA model is further reformulated to an optimization problem on the Riemannian manifold.Then we adopt a manifold inexact augmented Lagrangian method to solve the resulting optimization problem.The performance of the ASCCA model is compared with some existing sparse CCA techniques in different simulation settings and real datasets.