A Central Limit Theorem for Classical Multidimensional Scaling

04/02/2018

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by   Gongkai Li, et al.

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Classical multidimensional scaling (CMDS) is a widely used method in manifold learning. It takes in a dissimilarity matrix and outputs a coordinate matrix based on a spectral decomposition. However, there are not yet any statistical results characterizing the performance ofCMDS under randomness, such as perturbation analysis when the objects are sampled from a probabilistic model. In this paper, we present such an analysis given that the objects are sampled from a suitable distribution. In particular, we show that the resulting embedding gives rise to a central limit theorem for noisy dissimilarity measurements, and provide compelling simulation and real data illustration of this CLT for CMDS.