Before revision:  Thus, in case of extremely large ambient space dimension, we are able to avoid the curse of dimensionality without having to perform non-linear dimension reduction, which  introduces distortions to the manifold data.
After revision:  Thus, in case of extremely large ambient space dimension, we are able to avoid the computational complexity, commonly encountered in high dimensional approximations, without having to perform non-linear dimension reduction, which introduces distortions to the manifold data.