The key observation is that the success4 of the proposed method depends solely on the intrinsic property of the data manifold instead of specific sampling5 procedures (Theorem 4.2),whichmakesourextension non-trivial. About the curvature estimation method: we apologize for not including enough details in the description of the15 proposed curvature estimation method. When estimating the curvature at some pointp, our method requires (Sect. What is the dimension of the NRPCA space, is it two? Is the neighborhood patch defined with respect to Xi or Xi?

We thank all the reviewers for their time and effort. We are particularly grateful for the suggestion of the reviewers about Section 5-6. Specifically, we will move Sect. We will also follow Reviewer 1's and Reviewer 2's advice to add the derivation of Eq. (13) and Eq. Due to space limitations, below we only address the major concerns raised by the reviewers. NN in the Dijkstra's algorithm used to compute the geodesic distances (mentioned Does the methodology presented in Section 2 work for non-Gaussian noise too?