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

Abstract

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.

Keywords

• Data reduction
• Low-discrepancy points
• Quasi-Monte Carlo
• Digital nets
• K-means algorithm
• Neural networks