organization in the final version. 2 Reviewer

We thank the reviewers for their valuable feedback. This is the standard definition based on least square interpolation. We shall clarify this appropriately in the final draft. "I can't see many weaknesses, apart from the complexity matters: I would be curious to have some insights on this "This paper proposed to utilize the kernel embedding method to reduce the dimensionality of the statistical optimal This work does not propose to perform dimensionality reduction. "The proposed kernel embedding formulation of OT is based on the cross-covariance operator which ignores higher No, the higher order moments are not ignored. Q5) "The dimensionality of canonical feature maps can be infinity.