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We in this paper consider Fr\'echet sufficient dimension reduction withresponses being complex random objects in a metric space and high dimensionEuclidean predictors. We propose a novel approach called weighted inverseregression ensemble method for linear Fr\'echet sufficient dimension reduction.The method is further generalized as a new operator defined on reproducingkernel 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 weapply our methods to analyze the handwritten digits data to demonstrate its usein real applications.

Fr\'echet Sufficient Dimension Reduction for Random Objects