Abstract
In this paper, we propose a new clustering method and a new discriminant rule valid on the basic spaced ℜ2. These procedures make use of a new concept in clustering: the concept of closed and connex forms. This hypothesis generalizes the convex hypothesis and is very useful to find non convex natural clusters. Finally, we examine the admissibility of our procedure, in the sense of Fisher and Van Ness [4].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Beaufays, P. and Rasson, J.-P. (1985), A new geometric discriminant rule, in: Computational Statistics Quarterly, 2, 15–30, Elsevier Science B.V.
Bock, H. H. (1997), Probability Models for Convex Clusters, in: Classification and Knowledge Organization, Proceedings of the 20th Annual Conference of the Gesellschaft für Klassifikation e.V., University of Freiburg, March 6–8,1996, Klar-Opitz editors, Springer.
Cressie, N. A.C. (1991), Statistics for spatial data, John Wiley & Sons, New York.
Fisher, L., and Van Ness, J.W. (1971), Admissible clustering procedures, in: Biometrika, 58, 91–104.
Hardy, A., and Rasson, J.-P. (1982), Une nouvelle approche des problèmes de classification automatique, in: Statistiques et Analyse des Données, 7, 41–56.
Karr, A.F. (1991), Point processes and their statistical inference, Marcel Dekker, New-York.
Krickeberg, K. (1982), Processus ponctuels en statistique, in: Ecole d’été de Probabilités de Saint-FlourX-1980, 205–313, Springer-verlag, Berlin.
Matheron, G. (1975), Random Sets and Integral Geometry, John Wiley & sons, New-York.
Rasson, J.-P., Hardy, A., Szary, L. and Schindler, P. (1982), An optimal clustering method based on the Rassoris criterion and resulting from a new approach, in: Pattern Recognition Theory and Applications, 63–71, Kitter, Fu and Pau editions.
Schmitt, M. and Mattioli, J. (1993), Morphologie mathématique, Logiques Mathématiques Informatiques, Masson, Paris.
Serra, J.P. (1982), Image Analysis and Mathematical Morphology, Academic Press, London.
Spath, H. (1980), Cluster analysis algorithms for data reduction and classification of objects, Ellis Horwood Limited, Chichester.
Stoyan, D., and Stoyan, H. (1994), Fractals, Random Shapes and Point Fields, Methods of Geometrical Statistics, John Wiley & Sons, Chichester.
Van Ness, J.W. (1973), Admissible clustering procedures, in: Biometrika, 60, 422–424.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Rasson, JP., Jacquemin, D., Bertholet, V. (1998). A new geometrical hypothesis for clustering and discriminant analysis. In: Rizzi, A., Vichi, M., Bock, HH. (eds) Advances in Data Science and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72253-0_36
Download citation
DOI: https://doi.org/10.1007/978-3-642-72253-0_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64641-9
Online ISBN: 978-3-642-72253-0
eBook Packages: Springer Book Archive