  Classical multidimensional scaling is a widely used method in dimensionality
reduction and manifold learning. The method takes in a dissimilarity matrix and
outputs a low-dimensional configuration matrix based on a spectral
decomposition. In this paper, we present three noise models and analyze the
resulting configuration matrices, or embeddings. In particular, we show that
under each of the three noise models the resulting embedding gives rise to a
central limit theorem. We also provide compelling simulations and real data
illustrations of these central limit theorems. This perturbation analysis
represents a significant advancement over previous results regarding classical
multidimensional scaling behavior under randomness.
