  The recently introduced basis adaptation method for Homogeneous (Wiener)
Chaos expansions is explored in a new context where the rotation/projection
matrices are computed by discovering the active subspace where the random input
exhibits most of its variability. In the case where a 1-dimensional active
subspace exists, the methodology can be applicable to generalized Polynomial
Chaos expansions, thus enabling the projection of a high dimensional input to a
single input variable and the efficient estimation of a univariate chaos
expansion. Attractive features of this approach, such as the significant
computational savings and the high accuracy in computing statistics of interest
are investigated.
