  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 [4],
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 [14], 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.
