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Locally fitting hyperplanes to high-dimensional data

Hou, M.; Kambhampati, C.

Authors

M. Hou



Abstract

Problems such as data compression, pattern recognition and artificial intelligence often deal with a large data sample as observations of an unknown object. An effective method is proposed to fit hyperplanes to data points in each hypercubic subregion of the original data sample. Corresponding to a set of affine linear manifolds, the locally fitted hyperplanes optimally approximate the object in the sense of least squares of their perpendicular distances to the sample points. Its effectiveness and versatility are illustrated through approximation of nonlinear manifolds Möbius strip and Swiss roll, handwritten digit recognition, dimensionality reduction in a cosmological application, inter/extrapolation for a social and economic data set, and prediction of recidivism of criminal defendants. Based on two essential concepts of hyperplane fitting and spatial data segmentation, this general method for unsupervised learning is rigorously derived. The proposed method requires no assumptions on the underlying object and its data sample. Also, it has only two parameters, namely the size of segmenting hypercubes and the number of fitted hyperplanes for user to choose. These make the proposed method considerably accessible when applied to solving various problems in real applications.

Citation

Hou, M., & Kambhampati, C. (2022). Locally fitting hyperplanes to high-dimensional data. Neural Computing and Applications, 34(11), 8885-8896. https://doi.org/10.1007/s00521-022-06909-y

Journal Article Type Article
Acceptance Date Jan 4, 2022
Online Publication Date Apr 27, 2022
Publication Date Jun 1, 2022
Deposit Date Jul 31, 2023
Publicly Available Date Jul 31, 2023
Journal Neural Computing and Applications
Print ISSN 0941-0643
Electronic ISSN 1433-3058
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 34
Issue 11
Pages 8885-8896
DOI https://doi.org/10.1007/s00521-022-06909-y
Public URL https://hull-repository.worktribe.com/output/4004569

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http://creativecommons.org/licenses/by/4.0

Copyright Statement
©The Author(s) 2022.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.





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