An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation

TL;DR

This paper introduces an optimal linear time algorithm for segmenting sequences into monotonic parts with sign alternation, using a new quality metric and precomputation, outperforming existing heuristics in speed and accuracy.

Contribution

The paper presents a novel linear time algorithm for quasi-monotonic segmentation with a new quality metric and a precomputation step enabling constant-time segmentation queries.

Findings

Algorithm is faster than heuristics.

Algorithm achieves higher accuracy.

Precomputation enables instant segmentation retrieval.

Abstract

Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence 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 using the l_inf norm, and we present an optimal linear time algorithm based on novel formalism. Moreover, given a precomputation in time O(n log n) consisting of a labeling of all extrema, we compute any optimal segmentation in constant time. We compare experimentally its performance to two piecewise linear segmentation heuristics (top-down and bottom-up). We show that our algorithm is faster and more accurate. Applications include pattern recognition and qualitative modeling.