A MODIFIED CANONICAL CORRELATION ANALYSIS BASED ON LASSO TECHNIQUE

ABSTRACT

Canonical Correlation Analysis (CCA) which is used to model the correlations between two sets or more of variables has undergone various model-based formulations as an optimization problem with objective functions and constraints that is useful in modeling and prediction. These formulations adopt various constraints with the hope of removing non-informative variables in order to produce meaningful results that are interpretable. However, when formulations that are equivalent to multiple regression model are faced with mild condition which tend to hold for multicollinearity, overfitting and high dimensional data setting, they often fail to select pairwise variables that will mutually maximize the correlations between the common subspaces, thereby leading to increase in model complexity with unstable parameter estimates which often produce uninterpretable correlation estimates. Hence, we seek a formulation that will enhance the prediction accuracy and interpretability of the obtained model results. A modification of the conventional model-based CCA that will estimate the association between multiple dependent variables and multiple independent variables by employing the Least Absolute Shrinkage and Selection Operator (LASSO) as an additional restriction on the loglikelihood function in order to maximize the correlations between two sets of variables or canonical variates (CVs) is proposed. This was be done via the modified Optim code in R package for the least squares algorithm where the canonical weights vector is estimated with interactive process that begins by first calculating an initial pair of CVs or canonical root based on an initial starting point and thereafter obtain a new set of the estimated canonical weights and canonical correlations (ρ).