K-Plane Regression

TL;DR

This paper introduces a novel piecewise linear regression algorithm that partitions data iteratively, learning linear models in each segment, and demonstrates its effectiveness through empirical comparisons with existing methods.

Contribution

It presents a new algorithm for piecewise linear regression that can handle both continuous and discontinuous functions, inspired by k-means and EM algorithms.

Findings

Effective in modeling both continuous and discontinuous functions

Performs favorably compared to state-of-the-art regression algorithms

Applicable to real-world datasets

Abstract

In this paper, we present a novel algorithm for piecewise linear regression which can learn continuous as well as discontinuous piecewise linear functions. The main idea is to repeatedly partition the data and learn a liner model in in each partition. While a simple algorithm incorporating this idea does not work well, an interesting modification results in a good algorithm. The proposed algorithm is similar in spirit to $k$-means clustering algorithm. We show that our algorithm can also be viewed as an EM algorithm for maximum likelihood estimation of parameters under a reasonable probability model. We empirically demonstrate the effectiveness of our approach by comparing its performance with the state of art regression learning algorithms on some real world datasets.