Abstract
The paper presents difficulties of measuring clustering quality for symbolic data (such as lack of a “traditional” data matrix). Some hints concerning the usage of known indexes for such kind of data are given and indexes designed exclusively for symbolic data are described. Finally, after the presentation of simulation results, some proposals for choosing the most adequate indexes for popular classification algorithms are given.
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References
BAKER, F.B. and HUBERT, L.J. (1975): Measuring the Power of Hierarchical Cluster Analysis. Journal of the American Statistical Association, 70,349, 31–38.
BALL, F.B. and HALL, D.J. (1965): ISODATA, A Novel Method of Data Analysis and Pattern Classification. Tech. Rep. NTIS No.AD 699616, Stanford Research Institute, Menlo Park.
BOCK, H.-H. and DIDAY, E. (2000): Analysis of Symbolic Data. Explanatory Methods for Extracting Statistical Information from Complex Data. Springer, Berlin.
CALIŃSKI, R.B. and HARABASZ, J. (1974): A Dendrite Method for Cluster Analysis. Communications in Statistics, 3, 1–27.
CHAVENT, M., DE CARVALHO, F.A.T., VERDE, R. and LECHEVALLIER, Y. (2003): Trois Nouvelle Méthodes de Classification Automatique de Données Symboliques de Type Intervalle. Revue de Statistique Appliquée, LI 4, 5–29.
DIDAY, E. (2002): An Introduction to Symbolic Data Analysis and the SODAS Software. J.S.D.A., International EJournal.
FRIEDMAN, H.P. and RUBIN, J. (1967): On Some Invariant Criteria for Grouping Data. Journal of the American Statistical Association, 62, 1159–1178.
GORDON, A.D. (1999): Classification, Chapman & Hall/CRC, London.
HARDY, A. (2005): Validation of Unsupervised Symbolic Classification. Proceedings of ASMDA 2005 Conference. Available at URL: http://asmda2005.enst-bretagne.fr/IMG/pdf/proceedings/379.pdf.
HARTIGAN, J.A. (1975): Clustering Algorithms. New York, Wiley.
HUBERT, L.J. (1974): Approximate Evaluation Technique for the Single-link and Complete-link Hierarchical Clustering Procedures. Journal of the American Statistical Association, 69,347, 698–704.
HUBERT, L.J. and LEVINE, J.R. (1976): Evaluating Object Set Partitions: Free Sort Analysis and Some Generalizations. Journal of Verbal Learning and Verbal Behaviour, 15, 549–570.
KAUFMAN, L. and ROUSSEEUW, P.J. (1990): Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.
KRZANOWSKI, W.J. and LAI, Y.T. (1988): A Criterion for Determining the Number of Groups in a Data Set Using Sum of Squares Clustering. Biometrics, 44, 23–34.
MARRIOT, F.H. (1971). Practical Problems in a Method of Cluster Analysis. Biometrics, 27, 501–514.
MCQUITTY, L.L. (1966): Similarity Analysis by Reciprocal Pairs for Discrete and Continuous Data. Educational and Psychological Measurement, 26, 825–831.
MILLIGAN, G.W. and COOPER, M.C. (1985): An Examination of Procedures for Determining the Number of Clusters in a Data Set. Psychometrika, 2, 159–179.
RATKOVSKI, D.A. and LANCE, G.N. (1978) A Criterion for Determining a Number of Groups in a Classification. Australian Computer Journal, 10, 115–117.
ROUSSEEUW, P.J. (1987): Silhouettes: A Graphical Aid to the Interpretation and Validation of Cluster Analysis. Journal of Computational and Applied Mathematics, 20, 53–65.
SCOTT, A.J. and SYMONS, M.J. (1971) Clustering Methods Based on Likelihood Ratio Criteria. Biometrics, 27, 387–397.
VERDE, R. (2004): Clustering Methods in Symbolic Data Analysis. In: D. Banks et al. (Eds.): Classification, Clustering and Data Mining Applications, Springer, Berlin, 299–318.
WEINGESSEL, A., DIMITRIADOU, A. and DOLNICAR, S. (1999): An Examination Of Indexes For Determining The Number Of Clusters In Binary Data Sets. Available at URL: http://www.wu-wien.ac.at/am/wp99.htm#29.
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Dudek, A. (2007). Cluster Quality Indexes for Symbolic Classification — An Examination. In: Decker, R., Lenz, H.J. (eds) Advances in Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70981-7_4
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DOI: https://doi.org/10.1007/978-3-540-70981-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70980-0
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