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Robust Nonparametric Data Approximation of Point Sets via Data Reduction

  • Stephane Durocher
  • Alexandre Leblanc
  • Jason Morrison
  • Matthew Skala
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7676)

Abstract

In this paper we present a novel nonparametric method for 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 P of n points in the plane that determine a simple polygonal chain consisting of n − 1 segments, we describe algorithms for selecting a subsequence Q ⊂ P (including the first and last points of P) that determines a second polygonal chain to approximate P, such that the number of crossings between the two polygonal chains is maximized, and the cardinality of Q is minimized among all such maximizing subsets of P. Our algorithms have respective running times \(O(n^2\sqrt{\log n})\) when P is monotonic and O(n 2log4/3 n) when P is any simple polyline.

Keywords

Blue Point Consecutive Segment Polygonal Chain Chebyshev Distance Angular Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Stephane Durocher
    • 1
  • Alexandre Leblanc
    • 1
  • Jason Morrison
    • 1
  • Matthew Skala
    • 1
  1. 1.University of ManitobaWinnipegCanada

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