  We in this paper consider Fr\'echet sufficient dimension reduction with
responses being complex random objects in a metric space and high dimension
Euclidean predictors. We propose a novel approach called weighted inverse
regression ensemble method for linear Fr\'echet sufficient dimension reduction.
The method is further generalized as a new operator defined on reproducing
kernel Hilbert spaces for nonlinear Fr\'echet sufficient dimension reduction.
We provide theoretical guarantees for the new method via asymptotic analysis.
Intensive simulation studies verify the performance of our proposals. And we
apply our methods to analyze the handwritten digits data to demonstrate its use
in real applications.
