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Cluster Analysis for Asymmetry

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Methods for the Analysis of Asymmetric Proximity Data

Abstract

Models and methods of cluster analysis for asymmetric data are presented by considering two main classes: hierarchical and non-hierarchical methods. They are presented and applied to the same small illustrative data set which allows to highlight their different features and capabilities by using, when appropriate, graphical representations of the results. Attention is also paid to the issues of model selection and evaluation which are critical in applications.

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References

  1. European Commission. (2006). Eurobarometer: Europeans and their languages. Special Eurobarometer 243, Public Opinion Analysis sector of the European Commission, Brussels.

    Google Scholar 

  2. McQuitty, L. L. (1967). Expansion of similarity analysis by reciprocal pairs for discrete and continuous data. Educational and Psychological Measurement, 27, 253–255.

    Article  Google Scholar 

  3. Hartigan, J. A. (1975). Clustering algorithms. Wiley.

    MATH  Google Scholar 

  4. Landau, S., & Chis Ster, I. (2010). Cluster analysis: Overview. In P. Peterson, E. Baker, & B. McGaw (Eds.), International Encyclopedia of Education (3rd ed., pp. 72–83). Elsevier.

    Chapter  Google Scholar 

  5. Everitt, B., Landau, S., Leese, M., & Stahl, D. (2011). Cluster analysis (5th ed.). Wiley.

    Book  Google Scholar 

  6. Hubert, L. J. (1973). Min and max hierarchical clustering using asymmetric similarity measures. Psychometrika, 38, 63–72.

    Article  Google Scholar 

  7. Fujiwara, H. (1980). Hitaisho sokudo to toshitsusei keisuu o mochiita kurasuta bunsekiho [Methods for cluster analysis using asymmetric measures and homogeneity coefficient]. Kodo Keiryogaku [Japanese Journal of Behaviormetrics], 7(2), 12–21. (in Japanese).

    Article  Google Scholar 

  8. Okada, A., & Iwamoto, T. (1995). Hitaisho kurasuta bunnsekihou niyoru daigakushinngaku niokeru todoufukennkann no kanren no bunseki [An asymmetric cluster analysis study on university enrolment flow among Japanese prefectures]. Riron to Houhou [Sociological Theory and Methods, 10, 1–13 (in Japanese).

    Google Scholar 

  9. Lance, G. N., & Williams, W. T. (1966). A generalized sorting strategy for computer classifications. Nature, 212, 218.

    Article  Google Scholar 

  10. Lance, G. N., & Williams, W. T. (1967). A general theory of classificatory sorting strategies: 1 Hierarchical systems. The Computer Journal, 9, 373–380.

    Article  Google Scholar 

  11. Yadohisa, H. (2002). Formulation of asymmetric agglomerative hierarchical clustering and graphical representation of its result. Bulletin of the Computational Statistics Society of Japan, 15, 309–316. (in Japanese).

    Google Scholar 

  12. Takeuchi, A., Saito, T., & Yadohisa, H. (2007). Asymmetric agglomerative hierarchical clustering algorithms and their evaluations. Journal of Classification, 24, 123–143.

    Article  MathSciNet  Google Scholar 

  13. Okada, A., & Iwamoto, T. (1996). University enrollment flow among the Japanese prefectures: a comparison before and after the joint first stage achievement test by asymmetric cluster analysis. Behaviormetrika, 23, 169–185.

    Google Scholar 

  14. Saito, T., & Yadohisa, H. (2005). Data analysis of asymmetric structures. Advanced approaches in computational statistics. Marcel Dekker.

    Google Scholar 

  15. Brossier, G. (1982). Classification hiérarchique à partir de matrices carrées non symétriques. Statistique et Analyse des Données, 7, 22–40.

    MathSciNet  MATH  Google Scholar 

  16. Vicari, D. (2014). Classification of asymmetric proximity data. Journal of Classification, 31, 386–420.

    Article  MathSciNet  Google Scholar 

  17. Vichi, M. (2008). Fitting semiparametric clustering models to dissimilarity data. Advances in Data Analysis and Classification, 2, 121–161.

    Article  MathSciNet  Google Scholar 

  18. Vicari, D., & Vichi, M. (2000). Non-hierarchical classification structures. In W. Gaul et al. (Eds.), Data analysis. Studies in classification data analysis and knowledge organization (pp. 51–66). Springer.

    Google Scholar 

  19. Vicari, D. (2018). CLUSKEXT: CLUstering model for SKew-symmetric data including EXTernal information. Advances in Data Analysis and Classification, 12, 43–64.

    Article  MathSciNet  Google Scholar 

  20. Vicari, D. (2020). Modelling asymmetric exchanges between clusters. In T. Imaizumi, A. Nakayama, & S. Yokoyama (Eds.), Advanced studies in behaviormetrics and data science. Behaviormetrics: Quantitative approaches to human behavior (pp. 297–313). Springer Nature.

    Google Scholar 

  21. Okada, A., & Yokoyama, S. (2015) Asymmetric CLUster analysis based on SKEW-Symmetry: ACLUSKEW. In I. Morlini, T. Minerva, & M. Vichi (Eds.), Advances in statistical models for data analysis. Studies in classification, data analysis, and knowledge organization (pp. 191–199). Springer.

    Google Scholar 

  22. Tversky, A. (1977). Features of similarity. Psychological Review, 84, 327–352.

    Article  Google Scholar 

  23. MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In L. M. Le Cam & J. Neyman (Eds.), Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 1, pp. 281–297). University of California Press.

    Google Scholar 

  24. Kaufman, L., & Rousseeuw, P. J. (2009). Finding groups in data: An introduction to cluster analysis. Wiley.

    MATH  Google Scholar 

  25. Bove, G., & Okada, A. (2018). Methods for the analysis of asymmetric pairwise relationships. Advances in Data Analysis and Classification, 12, 5–31.

    Article  MathSciNet  Google Scholar 

  26. Madeira, S. C., & Oliveira, A. L. (2004). Biclustering algorithms for biological data analysis: A survey. IEEE Transactions in Computational Biology and Bioinformatics, 1, 24–45.

    Article  Google Scholar 

  27. Prelić, A., Blueler, S., Zimmermann, P., Wille, A., Bühlmann, P., Gruissem, W., & Zitzler, E. (2006). A systematic comparison and evaluation of biclustering methods for gene expression data. Bioinformatics, 22, 1122–1129.

    Article  Google Scholar 

  28. Wilderjans, T. F., Depril, D., & Van Mechelen, I. (2013). Additive biclustering: A comparison of one new and two existing ALS algorithms. Journal of Classification, 30, 56–74.

    Article  MathSciNet  Google Scholar 

  29. Brusco, M. J., Doreian, P., & Steinley, D. (2016). Biclustering methods for one-mode asymmetric matrices. Behavior Research Methods, 48, 487–502.

    Article  Google Scholar 

  30. Muñoz, A., & Martín-Merino, M. (2002). New asymmetric iterative scaling models for the generation of textual word maps. In Proceedings of the International Conference on Textual Data Statistical Analysis JADT 2002 (pp. 593–603).

    Google Scholar 

  31. Olszewski, D. (2011). Asymmetric k-means algorithm. In A. Dovnikar, U. Lotrič, & B. Ster (Eds.), International conference on adaptive and natural computing algorithms (ICANNGA 2011) part II, Lecture notes in computer science (Vol. 6594, pp. 1–10). Springer.

    Google Scholar 

  32. Olszewski, D. (2012). K-means clustering of asymmetric data. In E. Corchado et al. (Eds.), Hybrid artificial intelligent systems 2012, part I, Lecture notes in computer science (Vol. 7208, pp. 243–254). Springer.

    Google Scholar 

  33. Olszewski, D., & Šter, B. (2014). Asymmetric clustering using the alpha-beta divergence. Pattern Recognition, 47, 2031–2041.

    Article  Google Scholar 

  34. Krackhardt, D. (1987). Cognitive social structures. Social Networks, 9, 109–134.

    Article  MathSciNet  Google Scholar 

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Correspondence to Giuseppe Bove .

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Bove, G., Okada, A., Vicari, D. (2021). Cluster Analysis for Asymmetry. In: Methods for the Analysis of Asymmetric Proximity Data. Behaviormetrics: Quantitative Approaches to Human Behavior, vol 7. Springer, Singapore. https://doi.org/10.1007/978-981-16-3172-6_4

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