Abstract
The Authors consider the general problem of similarity and dissimilarity measures in Symbolic Data Analysis. First they examine the classical definitions of elementary event, assertion object, hierarchical dependences and logical dependences, then they consider some well-known measures resemblance measures between two objects (Sokal-Michener, Roger-Tanimoto, Sokal-Sneath, Dice-Czekanowski-Sorenson, Russel-Rao). For resemblance measures based on aggregation functions, the authors consider the proposals of Gowda-Diday, De Baets et al., Malerba et al., Vladutu et al., and Ichino-Yaguchi.
This paper is common job of both the Authors. Paragraphs 1 and 4 are referred to A. Rizzi, while paragraphs 2 and 3 to L. Nieddu
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References
BOCCI L., RIZZI A.,(2000): Misure di prossimità nell'analisi dei dati simbolici, Società Italiana di Statistica, Atti della XL riunione scientifica, Firenze,2000
DE BAETS B., DE MEYER H., NAESSENS H.,(2001): A class of rational cardinality-based similarity measures, Journal of Computational and Applied Mathematics, 132, 51–69
DE CARVALHO F.A.T.,(1994): Proximity Coefficients between Boolean Symbolic Objects in: New Approaches in classification and Data Analysis, Diday, E. & Lechevallier, Y. & Schader, M. and
ESPOSITO F., MALERBA D., TAMMA V., BOCK H. H.,(2000): Classical Resemblance Measures, in Analysis of Symbolic Data. Exploratory Methods for extracting statistical information from complex data, Bock, H.H., and Diday E., (Eds.), Series: studies in classification, data analysis and Knowledge Organization, Vol. 15, Springer-Verlag, Berlin, ISBN 3-540-66619-2
GOWDA K. C, DIDAY E.,(1992): Symbolic Clustering using a new similarity measure. IEEE Transaction on Systems, Man and Cybernetics 22(2), 368–378
ICHINO M., YAGUCHI H., (1994): General Minkowski metrics for mixed type data analysis, IEEE Transaction on System, Man and Cybernetics, 24,4, pp. 698–708
LAURO N.C., VERDE R., PALUMBO F.,(2000): Factorial Discriminant Analysis on Symbolic Objects, in Analysis of Symbolic Data. Exploratory Methods for extracting statistical information from complex data, Bock, H.H., and Diday E., (Eds.), Vol. 15, Springer-Verlag, Berlin, ISBN 3-540-66619-2
MALERBA D, ESPOSITO F., GIOVIALE V. & TAMMA V.,(2001): Comparing dissimilarity measures in Symbolic Data Analysis. Proceedings of the Joint Conferences on New Techniques and Technologies for Statistics and Exchange of Technology and Know-how (ETK-NTTS'01), 473–481
MALI K., MITRA S.,(2003): Clustering and its validation in a symbolic framework, Pattern Recognition Letters 24, 2367–2376
NAGABHUSHAN P., GOWDA K.C., DIDAY E.,(1995): Dimensionality reduction of symbolic data, Pattern Recognition Letters, 16, 219–223
PÉRINEL E., LECHEVALLIER Y.,(2000): Symbolic Discrimination Rules, in Analysis of Symbolic Data. Exploratory Methods for extracting statistical information from complex data, Bock, H.H., and Diday E., (Eds.), Vol. 15, Springer-Verlag, Berlin, ISBN 3-540-66619-2
RAVI T.V., GOWDA K.,(1999): An ISODATA clustering procedure for symbolic objects using a distributed genetic algorithm, Pattern Recognition Letters 20, 659–666.
RIZZI, A.,(1998): Metriche nell'analisi dei dati simbolici, Statistica, 4, 577–588
VLADUTU L., PAPADIMITRIOU S., MAVROUDI S., BEZERIANOS A.,(2001): Generalised RBF Networks Trained Using and IBL Algorithm for Mining Symbolic Data, in Advances in Knowledge Discovery and Data Mining, 5th Pacific-Asia Conference, 2001, Hong Kong, China, Cheung D., G. J. Williams and Q. Li (Eds.) Series, Lecture Notes in Artificial Intelligence Volume 2035, pp. 587–593, Springer-Verlag Heidelberg.
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Nieddu, L., Rizzi, A. (2005). Metrics in Symbolic Data Analysis. In: Bock, HH., et al. New Developments in Classification and Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27373-5_9
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DOI: https://doi.org/10.1007/3-540-27373-5_9
Publisher Name: Springer, Berlin, Heidelberg
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