  We present a new dimension reduction method called the global active subspace
method. The method uses expected values of finite differences of the underlying
function to identify the important directions, and builds a surrogate model
using the important directions on a lower dimensional subspace. The method is a
generalization of the active subspace method which uses the gradient
information of the function to construct a reduced model. We develop the error
analysis for the global active subspace method, and present examples to compare
it with the active subspace method numerically. The results show that the
global active subspace method is accurate, efficient, and robust with respect
to noise or lack of smoothness in the underlying function.
