Using low-discrepancy points for data compression in machine learning: an experimental comparison


Göttlich, Simone ; Heieck, Jacob ; Neuenkirch, Andreas


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DOI: https://doi.org/10.1186/s13362-024-00166-5
URL: https://mathematicsinindustry.springeropen.com/art...
Additional URL: https://www.researchgate.net/publication/387719812...
URN: urn:nbn:de:bsz:180-madoc-686621
Document Type: Article
Year of publication: 2025
The title of a journal, publication series: Journal of Mathematics in Industry
Volume: 15
Issue number: 1
Page range: 1-25
Place of publication: Berlin ; Heidelberg
Publishing house: Springer
ISSN: 2190-5983
Publication language: English
Institution: School of Business Informatics and Mathematics > Wirtschaftsmathematik II: Stochastische Numerik (Neuenkirch 2013-)
School of Business Informatics and Mathematics > Scientific Computing (Göttlich 2011-)
Pre-existing license: Creative Commons Attribution 4.0 International (CC BY 4.0)
Subject: 510 Mathematics
Classification: MSC: 41A99 , 65C05 , 65D15 , 68T07,
Keywords (English): data reduction , low-discrepancy points , quasi-Monte Carlo , digital nets , k-means algorithm , neural networks
Abstract: Low-discrepancy points (also called Quasi-Monte Carlo points) are deterministically and cleverly chosen point sets in the unit cube, which provide an approximation of the uniform distribution. We explore two methods based on such low-discrepancy points to reduce large data sets in order to train neural networks. The first one is the method of Dick and Feischl (J Complex 67:101587, 2021), which relies on digital nets and an averaging procedure. Motivated by our experimental findings, we construct a second method, which again uses digital nets, but Voronoi clustering instead of averaging. Both methods are compared to the supercompress approach of (Stat Anal Data Min ASA Data Sci J 14:217–229, 2021), which is a variant of the K-means clustering algorithm. The comparison is done in terms of the compression error for different objective functions and the accuracy of the training of a neural network.




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