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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

Abstract

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.

Citation

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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. https://doi.org/10.1214/20-EJS1720

Information

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

Subjects:
Primary: 62H12
Secondary: 62B10, 62H30

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Vol.14 • No. 1 • 2020
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