# Cluster, Classify, Regress: A General Method For Learning Discountinous Functions

## TL;DR

This paper introduces a three-stage method combining clustering, classification, and regression to effectively learn highly nonlinear and discontinuous functions, demonstrated on toy and plasma fusion simulation problems.

## Contribution

It proposes a novel integrated approach that combines clustering, classification, and regression for discontinuous function learning, a combination not previously explored in this way.

## Key findings

- Method effectively models discontinuous functions.
- Robustness demonstrated on toy and plasma fusion problems.
- Combines fundamental machine learning components in a novel way.

## Abstract

This paper presents a method for solving the supervised learning problem in which the output is highly nonlinear and discontinuous. It is proposed to solve this problem in three stages: (i) cluster the pairs of input-output data points, resulting in a label for each point; (ii) classify the data, where the corresponding label is the output; and finally (iii) perform one separate regression for each class, where the training data corresponds to the subset of the original input-output pairs which have that label according to the classifier. It has not yet been proposed to combine these 3 fundamental building blocks of machine learning in this simple and powerful fashion. This can be viewed as a form of deep learning, where any of the intermediate layers can itself be deep. The utility and robustness of the methodology is illustrated on some toy problems, including one example problem arising from simulation of plasma fusion in a tokamak.