  Incorporating prior knowledge into a data-driven modeling problem can
drastically improve performance, reliability, and generalization outside of the
training sample. The stronger the structural properties, the more effective
these improvements become. Manifolds are a powerful nonlinear generalization of
Euclidean space for modeling finite dimensions. Structural impositions in
constrained systems increase when applying group structure, converting them
into Lie manifolds. The range of their applications is very wide and includes
the important case of robotic tasks. Canonical Correlation Analysis (CCA) can
construct a hierarchical sequence of maximal correlations of up to two paired
data sets in these Euclidean spaces. We present a method to generalize this
concept to Lie Manifolds and demonstrate its efficacy through the substantial
improvements it achieves in making structure-consistent predictions about
changes in the state of a robotic hand.
