Abstract
We have a class of statistical units from a population, for which the data table may contain symbolic data; that is rather than having a single value for an observed variable, an observed value for the aggregated statistical units we treat here may be multivalued. Our aim is to describe a partition of this class of statistical units by further partitioning it, where each class of the partition is described by a conjunction of characteristic properties. We use a stepwise top-down binary tree method. At each step we select the best variable and its optimal splitting to optimize simultaneously a discrimination criterion given by a prior partition and a homogeneity criterion; we also aim to insure that the descriptions obtained describe the units in the class to describe and not the rest of the population. We present a real example.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
BOCK, H.H. and DIDAY, E. (2000): Analysis of Symbolic Data. Springer, Heidelberg.
BREIMAN, L., FRIEDMAN, J.H., OLSHEN, R.A., and STONE, C.J. (1984): Classification and Regression Trees. Wadsworth, Belmont, California.
CHAVENT, M. (1997): Analyse de Données Symboliques, Une Méthode Divisive de Classification. Thèse de Doctorat, Universite Paris IX Dauphine.
DIDAY, E. (2000): Symbolic Data Analysis and the SODAS Project: Purpose, History, and Perspective In: H.H. Bock and E. Diday (Eds.): Analysis of Symbolic Data. Springer, Heidelberg, 1–23.
LIMAM, M., DIDAY, E., and WINSBERG, S. (2003): Symbolic class description with interval data. Journal of Symbolic Data Analysis, 1. [available online: http://www.jsda.unina2.it/newjsda/volumes/index.htm.]
PÉRINEL, E. (1999): Construire un arbre de discrimination binaire à partir de données imprécises. Revue de Statistique Appliquée, 47, 5–30.
QUINLAN, J.R. (1986): Induction of decision trees. Machine Learning, 1, 81–106.
VRAC, M., LIMAM, M., DIDAY, E., and WINSBERG, S. (2002): Symbolic class description In: K. Jajuga, A. Sokolowski, and H.H. Bock (Eds.): Classification, Clustering, and Data Analysis. Springer, Heidelberg, 329–337.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin · Heidelberg
About this chapter
Cite this chapter
Diday, E., Limam, M.M., Winsberg, S. (2005). A Tree Structured Classifier for Symbolic Class Description. In: Baier, D., Decker, R., Schmidt-Thieme, L. (eds) Data Analysis and Decision Support. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28397-8_3
Download citation
DOI: https://doi.org/10.1007/3-540-28397-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26007-3
Online ISBN: 978-3-540-28397-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)