  We generalize the classical Multidimensional Scaling procedure to the setting
of general metric measure spaces. We develop a related spectral theory for the
generalized cMDS operator, which provides a more natural and rigorous
mathematical background for cMDS. Also, we show that the sum of all negative
eigenvalues of the cMDS operator is a new invariant measuring non-flatness of a
metric measure space. Furthermore, the cMDS output of several non-finite
exemplar metric measures spaces, in particular the cMDS for spheres S^{d-1} and
subsets of Euclidean space, are studied. Finally, we prove the stability of the
generalized cMDS process with respect to the Gromov-Wasserstein distance.
