Fig. 1: An illustrative comparison between MT-CoReg and CoReg [13].
α*, θ* are the ideal regression and canonical vectors for one dataset (M = 2 here). CoReg produces a single solution β, while MT-CoReg estimation is represented by two components α, θ. In this situation, where coefficients between the predictive and cross-correlated components (e.g. first 3 and last 2 features) are different, CoReg fails by trying to simultaneously represent both with a single component. On the other hand, MT-CoReg is flexible enough to properly estimate both components correctly.