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Discriminant Analysis Tools for Non Convex Pattern Recognition

  • Marcel Rémon
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

Estimation of non convex domains when inside and outside observations are available is often needed in current research applications. The key idea of this paper is to propose a solution based on convex and discriminant analysis tools, even when non convex domains are considered. Simulations are done and comparisons are made with a natural candidate, based on the Voronoï tessellation, for estimation of non convex bodies. However, this solution has irregularity problems.

The question of how to get smooth estimate of the unknown non convex domain is the core of this research. Our solution gives a smooth estimate of the domain and a gain of around 40 percent with respect to the symmetric difference criterion.

Keywords

Inside Point Convex Body Convex Domain Poisson Point Process Smooth Estimate 
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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References

  1. BAUFAYS, P. and RASSON, J.-P. (1985): A new geometric discriminant rule. Computational Statistics Quarterly, 2, 15–30.Google Scholar
  2. GRENANDER, U. (1976): Pattern Synthesis: Lectures in Pattern Theory, vol.1, Springer Verlag, New York.Google Scholar
  3. HACHTEL, G.D., MEILIJSON, I. and NADAS, A. (1981): The estimation of a convex subset of IR k and its probability content, IBM research report, Yorktown Heights N.Y.Google Scholar
  4. REMON, M. (1994): The estimation of a convex domain when inside and outside observations are available, Supplemento ai Rendiconti del Circolo Matematico di Palermo, 35, 227–235.Google Scholar
  5. REMON, M. (1996): A discriminant analysis algorithm for the inside/outside problem, Computational Statistics and Data Analysis, 23, 125–133CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 2000

Authors and Affiliations

  • Marcel Rémon
    • 1
  1. 1.Département de MathématiqueFacultés Universitaires Notre-Dame de la PaixNamurBelgium

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