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Statistical Conditions for a Linear Complexity for an Algorithm of Hierarchical Classification Under Constraint of Contiguity

  • Kaddour Bachar
  • Israël-César Lerman
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

In the best conditions, the time complexity of classical algorithms of hierarchical ascendent classification is for a number n of elements to be classified of order O(n2). In this paper the proposed CAHCVR algorithm is based on the principle of the “reciprocal neighbourhood” algorithm (CAHVR). It takes into account a contiguity constraint defined by a given connected graph. We study the properties of its results (absorbing class, inversion,…) and demonstrate that the average time complexity is in O(n) (linear complexity). The proposed CAHCVR algorithm is applied to image analysis in order to solve the image segmentation problem.

Keywords

hierarchical ascendent classification connected graph of contiguity reciprocal neighbourhood image segmentation 

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References

  1. Bachar, K [1994] Contributions en analyse factorielle et en classification ascendante hiérarchique sous contrainte de contiguïté. Applications à la segmentation d’images. Thèse de doctorat, Université de Rennes 1 (France).Google Scholar
  2. Benzécri, J-P [1982] Sur la proportion des paires de voisins réciproques pour une distribution uniforme dans un espace euclidien. Les cahiers de l’analyse des données, Vol. 7, p. 185–188.Google Scholar
  3. Lebart, L [1978] Programme d’agrégation avec contraintes. Les cahiers de l’analyse des données, Vol. 3, p. 275–287.Google Scholar
  4. Lerman, I-C [1991] Foundations of the Likelihood Linkage Analysis(LLA) Classification method. Applied Stochastic Models and Data Analysis, Vol.7, #1, march 1991, p.63–76, John Wiley.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • Kaddour Bachar
    • 1
    • 2
  • Israël-César Lerman
    • 3
  1. 1.ESSCA- 1, rue LakanalAngersFrance
  2. 2.Campus de BeaulieuLTSI -Université de Rennes 1RennesFrance
  3. 3.Campus de BeaulieuIRISA-Université de Rennes 1RennesFrance

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