A Riemannian Model to Orthonormalized Partial Least Squares

One of the most common ways used to ensure the smooth operation of projects in multivariate analysis (MVA) is the use of developed metrics in Euclidean spaces, which are approximations, generally coarse, in non-Euclidean spaces. Metrics in non-Euclidean spaces implies the need to make calculations on curved surfaces studied in differential geometry. In thus paper it is proposed a Riemannian model to orthonormalized partial least squares (OPLS). Results using generalized Stiefel manifold as well a nonlinear search algorithm are developed.