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The Art of Maximizing Covariance
William S. Rayens
Abstract:
The objective function for partial least squares (PLS) analysis is typically optimized subject to orthogonality constraints on the PLS directions. The form of this solution can be easily derived using Lagrangian multipliers and is well-known. However, when the successive PLS scores are constrained to be $\QTR{bf}{\Gamma }-$uncorrelated, for general positive definite $\QTR{bf}{\Gamma },$ the Lagrangian approach is cumbersome at best. In this short note, a simple method of proof is suggested that allows one to circumvent Lagrange multipliers entirely.
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