6 is given by: Differentiating the Lagrangian with respect to the parameters a, b and setting them to zero yields the solution for the parameters in terms of the Lagrangian multipliers α ij as follows: where C α xy = X 1−λ λ Y T + R T and R is a matrix of size d 2 × n with i th column as given by We use superscript α on the crosscovariance matrix to indicate that it is dependent on the Lagrangian multipliers α ij .
the solution is similar to that of the previous formulation except that the residual vectors are weighted by the Lagrangian multipliers instead of the loss function.