Summary
In this paper, we present a method which can be viewed as a generalization of discriminant analysis to more than one qualitative variable. This method is applied to a pair of data matrices where the variables of the first one are quantitative and those of the second one are qualitative. The intersection of the classes associated to the categories of all the qualitative variables are not strictly empty. They can therefore be compared to the spatial neighbourhoods defined in the contiguity analysis.
We propose a new version of Huyghens formula extended to overlapping classes and generalize the variances within and between classes to the case where the classes are not disjoint. Some tools are proposed for interpreting the results of a such analysis.
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.
References
BURTCHY B., LEBART L. (1991). Contiguity analysis and Projection Pursuit, 5th International Symposium on Applied Stochastic Models and Data Analysis, Granada, April 23–26, 1991.
CAZES B., MOREAU J. (1991), Analysis of a contingency table in which the rows and columns have a graph structure, Journèes Internationales de Versailles, 18–20 septembre 1991, p. 271–280.
ESCOFIER B. (1989), Multiple coresponding analysis and neighboring relation, Actes des Journèes Internationales, Antibes 11–14 septembre 1989, p.55–62.
FARAJ A. (1993). Analyse de la contiguítè: une analyse discriminante généralisé à plusieurs variables qualitatives, Revue de Statistique Appliquée.
LEBART L., (1969), Analyse statistique de la contiguïté, Publication de l’ISUP, XVIII, pp. 81–112.
LEBART L. (1974), Description statistique de certaines relations binaires, Actes du 3ème colloque sur l’analyse des données en Géographie, Besançon, pp. 75–101.
LE FOLL Y. (1982), Pondération des distances en analyse factorielle, Statistique et Analyse des données, pp. 13–31.
MATHERON G. (1970), La théorie des variables régionalisées et ses applications, Pub. Les Cahiers du Centre de Morphologie Mathématique de Fontainebleau, Fascicule 5.
MOM A. (1988), Méthodologie statistique de la classification des réseaux de transports, Thèse USTL, Montpellier.
MONESTIEZ P. (1978), Présentation de deux méthodes utilisant la contiguïté pour l’analyse des données géographiques, Thèse de docteur ingénieur, Paris 6.
ROMEDER J.M. (1973), Méthodes et programmes d’analyse discriminante, Dunod, Paris.
ROYER J.J. (1988), Analyse multivariable et filtrage des données régionales, Thèse de Doctorat, CRPG/INPL Nancy.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Faraj, A. (1994). Interpretation Tools For Generalized Discriminant Analysis. In: Diday, E., Lechevallier, Y., Schader, M., Bertrand, P., Burtschy, B. (eds) New Approaches in Classification and Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51175-2_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-51175-2_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58425-4
Online ISBN: 978-3-642-51175-2
eBook Packages: Springer Book Archive