An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation

TL;DR

This paper introduces an optimal linear time algorithm for segmenting arrays into monotonic segments with alternating signs, improving speed and accuracy over existing methods, with applications in pattern recognition and modeling.

Contribution

The paper presents a novel formalism and an optimal linear time algorithm for quasi-monotonic segmentation, outperforming previous top-down regression approaches.

Findings

The proposed algorithm is faster than existing methods.

It achieves higher accuracy in segmenting arrays.

Experimental results validate the efficiency and effectiveness.

Abstract

Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting an array in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for this problem, present an optimal linear time algorithm based on novel formalism, and compare experimentally its performance to a linear time top-down regression algorithm. We show that our algorithm is faster and more accurate. Applications include pattern recognition and qualitative modeling.