Nearly homogeneous multi-partitioning with a deterministic generator
The need for homogeneous partitions, where all parts have the same distribution, is ubiquitous in machine learning and in other fields of scientific studies. Especially when only few partitions can be generated. In that case, validation sets need to be distributed the same way as training sets to get good estimates of models complexities. And when standard data analysis tools cannot deal with too large data sets, the analysis could be performed onto a smaller subset, as far as its homogeneity to the larger one is good enough to get relevant results. However, pseudo-random generators may generate partitions whose parts have very different distributions because the geometry of the data is ignored. In this work, we propose an algorithm which deterministically generates partitions whose parts have empirically greater homogeneity on average than parts arising from pseudo-random partitions. The data to partition are seriated based on a nearest neighbor rule, and assigned to a part of the partition according to their rank in this seriation. We demonstrate the efficiency of this algorithm on toys and real data sets. Since this algorithm is deterministic, it also provides a way to make reproducible machine learning experiments usually based on pseudo-random partitions.
multi-partition homogeneous partition distribution seriation nearest neighbor reproducibility divergence deterministic sampling random sampling homogeneity measure