  Partial least squares regression (PLSR) has been a popular technique to
explore the linear relationship between two datasets. However, most of
algorithm implementations of PLSR may only achieve a suboptimal solution
through an optimization on the Euclidean space. In this paper, we propose
several novel PLSR models on Riemannian manifolds and develop optimization
algorithms based on Riemannian geometry of manifolds. This algorithm can
calculate all the factors of PLSR globally to avoid suboptimal solutions. In a
number of experiments, we have demonstrated the benefits of applying the
proposed model and algorithm to a variety of learning tasks in pattern
recognition and object classification.
