  We consider one of the classical manifold learning problems, that of
reconstructing up to an almost isometry an embedding of a compact connected
Riemannian manifold in a Euclidean space given the information on intrinsic
distances between points from its almost dense subset. It will be shown that
the most popular methods in data science to deal with such a problem, the
classical Multidimensional scaling (MDS) and the Maximum variance unfolding
(MVU) actually miss the point and may provide results very far from an isometry
(and even may give no biLipshitz embedding). We will then provide an easy
variational formulation of this problem which leads to an algorithm always
providing an almost isometric imbedding with given controlled small distortion
of original distances.
