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Variable Selection in Cluster Analysis: An Approach Based on a New Index

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Classification and Data Mining

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Abstract

In cluster analysis, the inclusion of unnecessary variables may mask the true group structure. For the selection of the best subset of variables, we suggest the use of two overall indices. The first index is a distance between two hierarchical clusterings and the second one is a similarity index obtained as the complement to one of the previous distance. Both criteria can be used for measuring the similarity between clusterings obtained with different subsets of variables. An application with a real data set regarding the economic welfare of the Italian Regions shows the benefits gained with the suggested procedure.

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References

  • Albatineh, A. N., Niewiadomska-Bugaj, M., & Mihalko, D. (2006). On similarity indices and correction for chance agreement. Journal of Classification, 23, 301–313.

    Article  MathSciNet  Google Scholar 

  • Fowlkes, E. B., & Mallows, C. L. (1983). A method for comparing two hierarchical clusterings. JASA, 78, 553–569.

    MATH  Google Scholar 

  • Fowlkes, E. B., Gnanadesikan, R., & Kettenring, J. R. (1988). Variable selection in clustering. Journal of Classification, 5, 205–228.

    Article  MathSciNet  Google Scholar 

  • Fraiman, R., Justel, A., & Svarc, M. (2008). Selection of variables for cluster analysis and classification rules. JASA, 103, 1294–1303.

    MathSciNet  MATH  Google Scholar 

  • Friedman, J. H., & Meulman, J. J. (2004). Clustering objects on subset of attributes. Journal of the Royal Statistical Society B, 66, 815–849.

    Article  MathSciNet  MATH  Google Scholar 

  • Gnanadesikan, R., Kettering, J. R., & Tsao, S. L. (1995). Weighting and selection of variables for cluster analysis. Journal of Classification, 12, 113–136.

    Article  MATH  Google Scholar 

  • Hubert, L. J., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2, 193–218.

    Article  Google Scholar 

  • Montanari, A., & Lizzani, L. (2001). A projection pursuit approach to variable selection. Computational Statistics and Data Analysis, 35, 463–473.

    Article  MathSciNet  MATH  Google Scholar 

  • Raftery, A. E., & Dean, N. (2006). Variable selection for model based clustering. JASA, 101, 168–178.

    MathSciNet  MATH  Google Scholar 

  • Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. JASA, 66, 846–850.

    Google Scholar 

  • Steinley, D., & Brusco, M. J. (2008). Selection of variables in cluster analysis: An empirical comparison of eight procedures. Psychometrika, 73, 125–144.

    Article  MathSciNet  MATH  Google Scholar 

  • Tadesse, M. G., Sha, N., & Vannucci, M. (2005). Bayesian variable selection in clustering high-dimensional data. JASA, 100, 602–617.

    MathSciNet  MATH  Google Scholar 

  • Warrens, M. J. (2008). On the equivalence of Cohen’s Kappa and the Hubert-Arabie adjusted Rand index. Journal of Classification, 25, 177–183.

    Article  MathSciNet  MATH  Google Scholar 

  • Zani, S. (1986). Some measures for the comparison of data matrices. In Proceedings of the XXXIII Meeting of the Italian Statistical Society (pp. 157–169), Bari, Italy.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Economics, University of Modena and Reggio Emilia, Via Berengario 51, 41100, Modena, Italy

    Isabella Morlini

  2. Department of Economics, University of Parma, Via Kennedy 6, 43100, Parma, Italy

    Sergio Zani

Authors
  1. Isabella Morlini
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  2. Sergio Zani
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Corresponding author

Correspondence to Isabella Morlini .

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Editors and Affiliations

  1. Department of Statistics, Università degli Studi di Firenze, Viale G.B. Morgagni 59, Firenze, 50134, Italy

    Antonio Giusti

  2. Fakultät für Informatik, und Mathematik, Universität Passau, Innstr. 33, Passau, 94030, Germany

    Gunter Ritter

  3. Sapienza", Department of Statistics, University of Rome "La, Piazzale Aldo Moro 5, Rome, 00185, Italy

    Maurizio Vichi

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Morlini, I., Zani, S. (2013). Variable Selection in Cluster Analysis: An Approach Based on a New Index. In: Giusti, A., Ritter, G., Vichi, M. (eds) Classification and Data Mining. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28894-4_9

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