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2020 Central limit theorems for classical multidimensional scaling
Gongkai Li, Minh Tang, Nicolas Charon, Carey Priebe
Electron. J. Statist. 14(1): 2362-2394 (2020). DOI: 10.1214/20-EJS1720


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.


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Gongkai Li. Minh Tang. Nicolas Charon. Carey Priebe. "Central limit theorems for classical multidimensional scaling." Electron. J. Statist. 14 (1) 2362 - 2394, 2020.


Received: 1 March 2020; Published: 2020
First available in Project Euclid: 1 July 2020

zbMATH: 07235714
MathSciNet: MR4118332
Digital Object Identifier: 10.1214/20-EJS1720

Primary: 62H12
Secondary: 62B10 , 62H30

Keywords: central limit theorem , Classical multidimensional scaling , dissimilarity matrix , Perturbation analysis


Vol.14 • No. 1 • 2020
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