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<p>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, <CitationRef CitationID="CR5">2021</CitationRef>), 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, <CitationRef CitationID="CR14">2021</CitationRef>), which is a variant of the <i>K</i>-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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月3日

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  • S. Göttlich,
  • J. Heieck,
  • A. Neuenkirch

摘要

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.