Modified Fuzzy Gap statistic for estimating preferable number of clusters in Fuzzy k-means clustering

Journal of Bioscience and Bioengineering

Volumn 105, Issue 3, 2008, Pages 273-281

  Arima, Chinatsu ^a   Hakamada, Kazumi ^a   Okamoto, Masahiro ^a   Hanai, Taizo ^a  

^a KYUSHU UNIVERSITY   (Japan)

Author keywords

clustering; estimation of number of clusters; fuzzy k means; microarray data analysis; validity index

Indexed keywords

ACOUSTIC VARIABLES CONTROL; FUZZY CLUSTERING; GENE EXPRESSION; MICROARRAYS; ROBUSTNESS (CONTROL SYSTEMS);

FUZZY K-MEANS; MICROARRAY DATA ANALYSIS; VALIDITY INDEXS;

CLUSTER ANALYSIS;

ARTICLE; CLUSTER ANALYSIS; FUZZY SYSTEM; GENE EXPRESSION; GENETICS; MICROARRAY ANALYSIS; NOISE; STATISTICS;

ALGORITHMS; CLUSTER ANALYSIS; FUZZY LOGIC; GENE EXPRESSION PROFILING; HUMANS; LEUKEMIA, MYELOID, ACUTE; OLIGONUCLEOTIDE ARRAY SEQUENCE ANALYSIS; SACCHAROMYCES CEREVISIAE;

EID: 41549165103     PISSN: 13891723     EISSN: None     Source Type: Journal    
DOI: 10.1263/jbb.105.273     Document Type: Article

References (36)

1. Cho R.J., Campbell M.J., Winzeler E.A., Steinmetz L., Conway A., Wodicka L., Wolfsberg T.G., Gabrielian A.E., Landsman D., Lockhart D.J., and Davis R.W. A genome-wide transcriptional analysis of the mitotic cell cycle. Mol. Cell 2 (1998) 65-73
2. Chu S., DeRisi J., Eisen M., Mulholland J., Botstein D., Brown P.O., and Herskowitz I. The transcriptional program of sporulation in budding yeast. Science 282 (1998) 699-705
3. Spellman P.T., Sherlock G., Zhang M.Q., Iyer V.R., Anders K., Eisen M.B., Brown P.O., Botstein D., and Futcher B. Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Mol. Biol. Cell 9 (1998) 3273-3297
4. Hakamada K., Hanai T., Honda H., and Kobayashi T. A preprocessing method for inferring genetic interaction from gene expression data using Boolean algorithm. J. Biosci. Bioeng. 98 (2004) 457-463
5. Maki Y., Takahashi Y., Arikawa Y., Watanabe S., Aoshima K., Eguchi Y., Ueda T., Aburatani S., Kuhara S., and Okamoto M. An integrated comprehensive workbench for inferring genetic networks: voyagene. J. Bioinform. Comput. Biol. 2 (2004) 533-550
6. Eisen M.B., Spellman P.T., Brown P.O., and Botstein D. Cluster analysis and display of genome-wide expression patterns. Proc. Natl. Acad. Sci. USA 95 (1998) 14863-14868
7. Tavazoie S., Hughes J.D., Campbell M.J., Cho R.J., and Church G.M. Systematic determination of genetic network architecture. Nat. Genet. 22 (1999) 281-285
8. Tamayo P., Slonim D., Mesirov J., Zhu Q., Kitareewan S., Dmitrovsky E., Lander E.S., and Golub T.R. Interpreting patterns of gene expression with self-organizing maps: Methods and application to hematopoietic differentiation. Proc. Natl. Acad. Sci. USA 96 (1999) 2907-2912
9. Tomida S., Hanai T., Honda H., and Kobayashi T. Analysis of expression profile using fuzzy adaptive resonance theory. Bioinformatics 18 (2002) 1073-1083
10. Dembele D., and Kastner P. Fuzzy C-means method for clustering microarray data. Bioinformatics 19 (2003) 973-980
11. Hanai T., Hamada H., and Okamoto M. Application of bioinformatics for DNA microarray data to bioscience, bioengineering and medical field. J. Biosci. Bioeng. 101 (2006) 377-384
12. Gasch A.P., and Eisen M.B. Exploring the conditional coregulation of yeast gene expression through fuzzy k-means clustering. Genome Biol. 3 (2002) 0059.1-005922
13. Cho R.J., Huang M., Campbell M.J., Dong H., Steinmetz L., Sapinoso L., Hampton G., Elledge S.J., Davis R.W., and Lockhart D.J. Transcriptional regulation and function during the human cell cycle. Nat. Genet. 27 (2001) 48-54
14. Dunn J.C. Well separated clusters and optimal fuzzy partitions. J. Cybernet. 4 (1974) 95-104
15. Davies D.L., and Bouldin W. A cluster separation measure. IEEE Trans. Pattern. Anal. Mach. Intell. 1 (1979) 224-227
16. Rousseeuw P.J. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20 (1987) 53-65
17. Kim Y.-I., Kim D.-W., Lee D., and Lee K.H. A cluster validation index for GK cluster analysis based on relative degree of sharing. Inf. Sci. 168 (2004) 225-242
18. Feher M., and Schmidt J.M. Fuzzy clustering as a means of selecting representative conformers and molecular alignments. J. Chem. Inf. Comput. Sci. 43 (2003) 810-818
19. Okada Y., Sahara T., Mitsubayashi H., Ohgiya S., and Nagashima T. Knowledge-assisted recognition of cluster boundaries in gene expression data. Artif. Intell. Med. 35 (2005) 171-183
20. Theodoridis S., and Koutroumbas K. Pattern. Recognition (1999), Academic Press, San Diego
21. Bezdek J.C. Cluster validity with fuzzy sets. J. Cybernet. 3 (1974) 58-72
22. Bezdek, J. C.: Mathematical models for systematics and taxonomy, p. 143-166. In Estabrook, G. F. (ed.), Proceedings of the 8th International Conference on Numerical Taxonomy. Freeman, San Francisco (1975)
23. Gath I., and Geva A.B. Unsupervised optimal fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. 11 (1989) 773-781
24. Xie X.L., and Beni G. A validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. 13 (1991) 841-847
25. Pakhira M.K., Bandyopadhyay S., and Maulik U. Validity index for crisp and fuzzy clusters. Pattern Recognit. 37 (2004) 487-501
26. Tibshirani R., Walther G., and Hastie T. Estimating the number of clusters in a data set via the gap statistic. J. R. Stat. Soc. Ser. B 63 (2001) 411-423
27. Sentelle, C., Hong, S. L., Georgiopoulos, M., and Anagnostopoulos, G. C.: A fuzzy gap statistic for fuzzy c-means, p. 68-73. In del Pobil, A. P. (ed.), Proceeding of the 11th IASTED International Conference Artificial Intelligence and Soft Computing. ACTA Press, Calgary (2007).
28. Golub T.R., Slonim D.K., Tamayo P., Huard C., Gaasenbeek M., Mesirov J.P., Coller H., Loh M.L., Downing J.R., Caligiuri M.A., Bloomfield C.D., and Lander E.S. Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science 286 (1999) 531-537
29. Hakamada K., Okamoto M., and Hanai T. Novel technique for preprocessing high dimensional time-course data from DNA microarray: mathematical model-based clustering. Bioinformatics 22 (2006) 843-848
30. Hubert L., and Arabie P. Comparing partitions. J. Classif. 2 (1985) 193-218
31. Rand W. Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. 66 (1971) 846-850
32. Pal N.R., and Bezdek C. On cluster validity for the fuzzy c-means model. IEEE Trans. Fuzzy Syst. 3 (1995) 370-379
33. Rezaee M.R., Lelieveldt B.P.F., and Reiber J.H.C. A new cluster validity index for the fuzzy c-means. Pattern Recogn. Lett. 19 (1998) 237-246
34. Bertoni A., and Valentini G. Model order selection for bio-molecular data clustering. BMC Bioinformatics 8 suppl. 2 (2007) S7
35. Denoeud L., Garreta H., and Guenoche A. Comparison of distance indices between partitions. In: Batagelj V., Bock H.-H., Ferligoj A., and Ziberna A. (Eds). Proceeding of IFCS '2006 Conference Data Science and Classification (2006), Springer, Berlin 21-28
36. Campello R.J.G.B. A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Pattern Recogn. Lett. 28 (2007) 833-841