Clustering Large Data Sets Described with Discrete Distributions and its Application on TIMSS Data Set

Statistical Analysis and Data Mining

Volumn 4, Issue 2, 2011, Pages 199-215

  Korenjak Černe, Simona ^a   Batagelj, Vladimir ^a   Japelj Pavešić, Barbara ^b  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

^b Research Institute   (Slovenia)

Author keywords

Agglomerative hierarchical clustering method; Clustering; k means method; Large data sets; Leaders method; Mixed units; Symbolic object; TIMSS; Ward's method

Indexed keywords

CLUSTERING ALGORITHMS; TEACHING;

AGGLOMERATIVE HIERARCHICAL CLUSTERING; AGGLOMERATIVE HIERARCHICAL CLUSTERING METHOD; CLUSTERINGS; HIERARCHICAL CLUSTERING METHODS; K-MEANS METHOD; LARGE DATASETS; LEADER METHOD; MIXED UNIT; SCIENCE STUDIES; SYMBOLIC OBJECTS; TREND IN INTERNATIONAL MATHEMATIC AND SCIENCE STUDY; WARD METHOD;

CLUSTER ANALYSIS;

EID: 79953040750     PISSN: 19321872     EISSN: 19321864     Source Type: Journal    
DOI: 10.1002/sam.10105     Document Type: Article

References (26)

1. H. H. Bock and E. Diday, Symbolic objects, In Analysis of Symbolic Data. Exploratory Methods for Extracting Statistical Information from Complex Data, Heidelberg, Springer, 2000.
2. L. Billard and E. Diday, Symbolic Data Analysis. Conceptual Statistics and Data Mining, Wiley Series in Computational Statistics, John Wiley & Sons Ltd, Chichester, UK, 2006.
3. E. Diday and M. Noirhomme-Fraiture, Symbolic Data Analysis and the SODAS Software, JohnWiley & Sons, Ltd., Chichester, UK, 2008.
4. P. H. A. Sneath and R. R. Sokal, Numerical Taxonomy (2nd ed.), San Francisco, Freeman, 1973.
5. M. R. Anderberg, Cluster Analysis for Applications, New York, Academic Press, 1973.
6. J. A. Hartigan, Clustering Algorithms, New York, Wiley, 1975.
7. L. Kaufman and P. J. Rousseeuw, Finding Groups in Data: An Introduction to Cluster Analysis, New York, Wiley, 1990.
8. J. H. Ward, Hierarchical grouping to optimize an objective function, Journal of the American Statistical Association 58 (1963), 236-244.
9. C. Müller, B. Wellman, and A. Marin, How to use SPSS to study ego-centered networks, Bulletin de méthodologies Sociologiques 64 (1999), 63-76.
10. S. Korenjak-Černe, Symbolic Data Analysis Approach to Clustering Large Ego-Centered Networks, Metodološki zvezki 17, Developments in Statistics, FDV Ljubljana, 2002, 45-53.
11. The TIMSS International Database. TIMSS & PIRLS International Study Center. Boston College, Lynch School of Education. USA. Available: [Last accessed November 30, 2010].
12. M. O. Martin, I. V. S. Mullis, and S. J. Chrostowski, eds. "TIMSS 2003 Technical Report", Chestnut Hill, MA, TIMSS & PIRLS International Study Center, Boston College, 2004. Available: [Last accessed November 30, 2010].
13. The Educational Research Institute, Slovenia. Available: [Last accessed November 30, 2010].
14. D. Malerba, F. Esposito, V. Gioviale, and V. Tamma, Comparing Dissimilarity Measures for Symbolic Data Analysis, In Proceedings of Techniques and Technologies for Statistics-Exchange of Technology and Know-How. Crete, 1, 2001, 473-481. Available:
15. L. Nieddu and A. Rizzi, Metrics in symbolic data analysis, In New developments in Classification and Data Analysis. Proceedings of the Meeting of the Classification and Data analysis Group (CLADAG) of the Italian Statistical Society, Universitiy of Bologna. Berlin Heidelberg, Springer, 2003, 71-78.
16. R. Verde, F. A. T. de Carvalho, and Y. Lechevallier, A dynamic clustering algorithm for multi-nominal data, In Data Analysis, Classification, and Related Methods, Springer-Verlag Berlin-Heidelberg, 2000.
17. N. Kejžar, S. Korenjak-Černe and V. Batagelj, Clustering of discrete distributions: a case of patents citations (Submitted).
18. E. Diday, Optimisation en classification automatique, Tome 1., 2. INRIA, Rocquencourt (in French), 1979.
19. T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, The analysis of a simple k-means clustering algorithm, In Proceedings of the Symposium on Computational Geometry, 2000, 100-109.
20. A. Ferligoj and V. Batagelj, Clustering with Relational Constraint, Psychometrika 47(4), (1982), 413-425.
21. V. Batagelj, Agglomerative Methods in clustering with Constraints, Presented at the Joint European Meeting of the Psychometric and Clasification Societies, Jouy-en-Josas, France, July, 6-8, 1983.
22. V. Batagelj, Generalized Ward and related clustering problems, In Classification and Related Methods of Data Analysis, Amsterdam, North-Holland, 1988, 67-74.
23. G. N. Lance and W. T. Williams, A general theory of classificatory sorting startegies, 1. Hierarchical systems, The Computer Journal 9, (1967), 373-380.
24. V. Batagelj, Note on ultrametric hierarchical clustering algorithms, Psychometrika 46(3) (1981), 351-352.
25. B. Japelj Pavešić and S. Korenjak-Černe, Differences in teaching and learning mathematics in classes over the world: the application of adapted leaders clustering method, In Proceedings of the IRC-2004: IEA International Research Conference, Nicosia, University of Cyprus, Department of Education, 2004, 85-101.
26. B. Japelj Pavešić, Comparison of teaching mathematics: An application of Adapted Leaders Clustering Method, Presented on the International Conference IFCS 2006 in Ljubljana.