English

Robust Non-Parametric Data Approximation of Pointsets via Data Reduction

Computational Geometry 2012-05-31 v1

Abstract

In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing the average length of sequences of consecutive input points that lie on any one side of the simplified curve. Specifically, given a sequence PP of nn points in the plane that determine a simple polygonal chain consisting of n1n-1 segments, we describe algorithms for selecting an ordered subset QPQ \subset P (including the first and last points of PP) that determines a second polygonal chain to approximate PP, such that the number of crossings between the two polygonal chains is maximized, and the cardinality of QQ is minimized among all such maximizing subsets of PP. Our algorithms have respective running times O(n2logn)O(n^2\log n) when PP is monotonic and O(n2log2n)O(n^2\log^2 n) when PP is an arbitrary simple polyline. Finally, we examine the application of our algorithms iteratively in a bootstrapping technique to define a smooth robust non-parametric approximation of the original sequence.

Keywords

Cite

@article{arxiv.1205.6717,
  title  = {Robust Non-Parametric Data Approximation of Pointsets via Data Reduction},
  author = {Stephane Durocher and Alexandre Leblanc and Jason Morrison and Matthew Skala},
  journal= {arXiv preprint arXiv:1205.6717},
  year   = {2012}
}

Comments

13 pages, 6 figures

R2 v1 2026-06-21T21:11:45.507Z