This is a non-Euclidean method for generating geometrically-regular partitions: Ideas based on random-metric partitions of Naor Assaf (https://web.math.princeton.edu/~naor/)'s paper: https://web.math.princeton.edu/~naor/homepage%20files/EXTdiff.pdf
Given a positive integer N and a real-number, this codes partitions the space into N random subsets such that:
- Minimum probability that two nearby data-points are in different partitions,
- Each has the same number of datapoints on average.
Can be used in Architopes (see: https://arxiv.org/abs/2006.14378) to make the regression algorithm semi-supervised.
Dataset used is the California Housing Market found here: https://github.com/bzamanlooy/Architopes/tree/master/data
Additional/Related Literature:
- Related blog-post on probabilistic properties of similar randomly generated metric (
$\Delta$ -bounded) partitions.
https://tcsmath.wordpress.com/2010/06/19/random-partitions-of-metric-spaces/
I'll probably write a paper on this shortly, if anyone is interested email me :)