An analysis of classical multidimensional scaling with applications to clustering.

Autor: Little A; Department of Mathematics, Utah Center for Data Science, University of Utah, Salt Lake City, UT 84112, USA., Xie Y; Department of Computational Mathematics, Science and Engineering, Department of Statistics, Michigan State University, East Lansing, MI 48824, USA., Sun Q; Department of Statistical Sciences, University of Toronto, Toronto, ON M5G 1Z5, Canada.
Jazyk: angličtina
Zdroj: Information and inference : a journal of the IMA [Inf inference] 2022 Apr 23; Vol. 12 (1), pp. 72-112. Date of Electronic Publication: 2022 Apr 23 (Print Publication: 2023).
DOI: 10.1093/imaiai/iaac004
Abstrakt: Classical multidimensional scaling is a widely used dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of embedded samples produced by classical multidimensional scaling. This lays a foundation for various downstream statistical analyses, and we focus on clustering noisy data. Our results provide scaling conditions on the signal-to-noise ratio under which classical multidimensional scaling followed by a distance-based clustering algorithm can recover the cluster labels of all samples. Simulation studies confirm these scaling conditions are sharp. Applications to the cancer gene-expression data, the single-cell RNA sequencing data and the natural language data lend strong support to the methodology and theory.
(© The Author(s) 2022. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.)
Databáze: MEDLINE
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