A new similarity measure and its use in determining the number of clusters in a multivariate data set

Communications in Statistics - Theory and Methods

Volumn 33, Issue 7, 2004, Pages 1643-1666

  Vassiliou, A ^a   Tambouratzis, D G ^b   Koutras, M V ^c   Bersimis, S ^c  

^a INSTITUTE OF NANOSCIENCE AND NANOTECHNOLOGY   (Greece)

^b AGRICULTURAL UNIVERSITY OF ATHENS   (Greece)

^c UNIVERSITY OF PIRAEUS   (Greece)

Author keywords

Andrews' plots; Distance measures; Number of clusters; Similarity measure; Success runs

Indexed keywords

ALGORITHMS; DATA ACQUISITION; GRAPH THEORY; HIERARCHICAL SYSTEMS; NUMBER THEORY; SET THEORY;

ANDREWS' PLOTS; DISTANCE MEASURES; NUMBER OF CLUSTERS; SIMILARITY MEASURE; SUCCESS RUNS;

STATISTICS;

EID: 3042550626     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1081/STA-120037266     Document Type: Article

References (34)

1. Aho, A. V., Hopcroft, J. E., Ullman, J. D. (1983). Data Structures and Algorithms. Reading, MA: Addison-Wesley.
2. Andrews, D. F. (1972). Plots of high dimensional data. Biometrics 28:125-136.
3. Balakrishnan, N., Koutras, M.V. (2002). Runs and Scans with Applications. John Wiley & Sons.
4. Bollobas, B. (1978). Extremal Graph Theory. Academic Press.
5. Bollobas, B. (1998). Modern Graph Theory. Springer-Verlag.
6. Brito, M. R., Chavez, E. L., Quiroz, A. J., Yukich, J. E. (1997). Connectivity of the mutual k-nearest-neighbors graph in outlier detection and clustering. Statist. Probab. Lett. 35:33-42.
7. Chernoff, H. (1973). Using faces to represent points in k-dimensional space graphically. J. Amer. Statist. Assoc. 68:361-368.
8. Cormen, T. H., Leiserson, C. E., Rivest, R. L. (1997). An Introduction to Algorithms. MIT Press.
9. Embrechts, P., Herzberg, A. M. (1991). Variations of Andrews plots. Int. Statist. Rev. 59:175-194.
10. Embrechts, P., Herzberg, A. M., Kalbfleisch, H. K., Traves, W. N., Whitla, J. R. (1995). An introduction to wavelets with applications to Andrews' plots. J. Comput. Appl. Math. 64:41-56.
11. Everitt, B. (1978). Graphical Techniques for Multivariate Data. London: Heinemann Educational Books.
12. Everitt, B. S. (1981). Cluster Analysis. Heineman Educational Books.
13. Feller, W. (1968). An Introduction to Probability Theory and Its Applications. Vol. I. 3rd ed. Wiley.
14. Fu, J.C., Koutras, M.V. (1994). Distribution theory of runs: A Markov chain approach. J. Amer. Statist. Assoc. 89:1050-1058.
15. Glasbey, C. A. (1987). Complete linkage as a multiple stopping rule for single linkage clustering. J. Classification 4:103-109.
16. Glaz, J., Balakrishnan, K. (1999). Scan Statistics and Applications. Boston: Birkhauser.
17. Gonzalez-Barrios, J. M., Quiroz, A. J. (2003). A clustering procedure based on the comparison between the k nearest neighbors graph and the minimal spanning tree. Statist. Probab. Lett. 62:23-34.
18. Gower, J. C., Ross, G. J. S. (1969). Minimum spanning trees and single linkage cluster analysis. J. Royal Statist. Soc. (Series C) 18:54-64.
19. Graham, R. L., Hell, P. (1985). On the history of the minimum spanning tree problem. Ann. Hist. Comput. 7:43-57.
20. Harary, F. (1969). Graph Theory. Addison-Wesley.
21. Hardy, A. (1996). On the number of clusters. Comput. Statist. Data Anal. 23:83-96.
22. Jardine, N., Sibson, R. (1971). Mathematical Taxonomy. New York: Wiley.
23. Khattree, R., Naik, D. N. (2002). Andrews plots for multivariate data: Some new suggestions and applications. J. Statist. Plann. Inf. 100:411-425.
24. Koutras, M. V., Alexandrou, V. A. (1995). Runs, scans and urn model distributions; A unified Markov chain approach. Ann. Inst. Statist. Math. 47(4):743-766.
25. Krolak-Schwerdt, S., Eckes, T. (1992). A graph theoretic criterion for determining the number of cluster in a data set. Multivariate Behav. Res. 27(4):541-565.
26. Kruskal, J. B. (1956). On the shortest spanning sub tree of a graph and a traveling salesman problem. Proc. Amer. Math. Soc. 7:48-50.
27. Ling, K. D. (1988). On binomial distributions of order k. Statist. Probab. Lett. 6:247-250.
28. Milligan, G. W. (1985). An algorithm for generating artificial test clusters. Psychometrika 50:123-127.
29. Milligan, G. W., Cooper, M. C. (1985). An examination of procedures for determining the number of clusters in a data set. Psychometrika 50(2): 159-179.
30. Mood, A. M. (1940). The distribution theory of runs. Ann. Math. Statist. 11:367-392.
31. Prim, R. C. (1957). Shortest connection networks and some generalizations. Bell Syst. Tech. J. 36:1389-1401.
32. Tarjan, R. E. (1983). Data Structures and Network Algorithms. SIAM Publications.
33. Wald, A., Wolfowitz, J. (1940). On a test whether two samples are from the same population. Ann. Math. Statist. 11:147-162.
34. West, D. (1998). Introduction to Graph Theory. Prentice Hall.