Summary
The aim of this paper is to present an approach to calculate the proximity between Boolean symbolic objects (BSO), that take into account simultaneously the variability, as range of values, and some kinds of logical dependencies between variables. A BSO is described by a logical conjunction of properties, each property being a disjunction of values on a variable. Our approach is based on both a comparison function and an aggregation fuction A comparison function is a proximity index based on a positive measure, called description potential of a Boolean elementary event (cardinal of the disjunction of values on a variable of a BSO), and on the proximity indices related to data matrix of binary variables. An aggregation function is a proximity index, related to Minkowsky distance, that aggregate the p results given by the comparison functions.
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
DE CARVALHO, F.A.T. (1992): Méthodes Descriptives en Analyse de Données Symboliques. Thèse de Doctorat. Université Paris-IX Dauphine, Paris.
DIDAY, E. (1991): Des objets de l’analyse de données à ceux de l’analyse de connaissances. In: Y. Kodratoff and E. Diday (eds.): Induction symbolique et numérique à partir de données Cepadue Editions, Toulouse, 9–75.
GOWDA, K.C. and DIDAY, E. (1991): Symbolic clustering using a new dissimilarity measure. Pattern Recognition, 24 (6), 567–578
GOWER, J.C. (1971): A general coefficient of similarity and some of its properties. Biometrics, 27, 857–871
GOWER, J.C. and LEGENDRE, P. (1986): Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3, 5–48
ICHINO, M. (1988): General metrics for mixed features. The Cartesian space theory for pattern recognition. International Conference on Systems, Man and Cybernetics.
JARDINE, N. and SIBSON, R. (1971): Mathematical taxonomy. John Wiley and Sons Ltd, London.
KENDRICK, W.B. (1965): Complexity and dependence in computer taxonomy. Taxon, 14, 141–154
SNEATH, P.H. and SOKAL, R.R. (1973): Numerical Taxonomy. The principles and practice of numerical classification. W.H. Freeman and Company, San Francisco.
VIGNES, R. (1991): Caractérisation automatique de groupes biologiques. Thèse de Doctorat. Univeristé Paris-VI Pierre et Marie Curie, Paris.
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
de A. T. de Carvalho, F. (1994). Proximity Coefficients between Boolean symbolic objects. 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_44
Download citation
DOI: https://doi.org/10.1007/978-3-642-51175-2_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58425-4
Online ISBN: 978-3-642-51175-2
eBook Packages: Springer Book Archive