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arXiv · 0709.1166

An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation

Daniel Lemire·Martin Brooks·Yuhong Yan
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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.

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Daniel Lemire, Martin Brooks, Yuhong Yan. 2007-09-07. An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation. https://doi.org/10.1080/00207160701694153

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