Information criteria for reduced rank canonical correlation analysis

Canonical correlation analysis is an essential technique in the field of multivariate statistical analysis. In this paper, a framework involving unconstrained optimization criteria is proposed for extracting multiple canonical variates and canonical correlations serially and in parallel. These criteria are derived from optimizing three information based functions. Based on the gradient-ascent or descent methods, we derive many algorithms for performing the true CCA recursively. The main feature of this approach is that orthogonal basis for canonical variates is automatically obtained. The first few singular values and vectors can also be obtained using this framework. The performances of the proposed algorithms is demonstated through simulations.