I sample a 2D surface in $\mathbb{R}^3$ with $N$ points, and compute an isomap using pairwise weighted geodesic distances. I am thus able to embed this surface into a $M$ dimensional space in which pairwise euclidean distances closely match their respective weighted geodesic distances on the original manifold. In brief, I just perform a standard isomap, solved with the SMACOF procedure.

However, I am wondering if this approach can lead to a self-intersecting manifold. If so, does increasing the dimensionality $M$ of the target space guarantee that at some point their won't be any intersection remaining ? Otherwise, how can I prevent self intersections from happening ?