Some aspects of nonlinear dimensionality reduction

Liwen Wang, Yongda Wang, Shifeng Xiong () and Jiankui Yang
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Liwen Wang: Ministry of Education, School of Science, Beijing University of Posts and Telecommunications
Yongda Wang: University of Chinese Academy of Sciences
Shifeng Xiong: University of Chinese Academy of Sciences
Jiankui Yang: Ministry of Education, School of Science, Beijing University of Posts and Telecommunications

Computational Statistics, 2025, vol. 40, issue 2, No 12, 883-906

Abstract: Abstract In this paper we discuss nonlinear dimensionality reduction within the framework of principal curves. We formulate dimensionality reduction as problems of estimating principal subspaces for both noiseless and noisy cases, and propose the corresponding iterative algorithms that modify existing principal curve algorithms. An R squared criterion is introduced to estimate the dimension of the principal subspace. In addition, we present new regression and density estimation strategies based on our dimensionality reduction algorithms. Theoretical analyses and numerical experiments show the effectiveness of the proposed methods.

Keywords: Density estimation; Intrinsic dimension; Kernel reconstruction regression; Principal curve; Principal surface (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00180-024-01514-0

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