Quality indices for (practical) clustering evaluation

Intelligent Data Analysis

Volumn 13, Issue 5, 2009, Pages 725-740

  Cardoso, Margarida G M S ^a   de Carvalho, André Ponce de Leon F ^b  

^a UNIVERSITY INSTITUTE OF LISBON   (Portugal)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Cluster validation; Clustering; Quality indices; Validation indices

Indexed keywords

EID: 70350780484     PISSN: 1088467X     EISSN: 15714128     Source Type: Journal    
DOI: 10.3233/IDA-2009-0390     Document Type: Article

References (44)

1. H. Akaike, Maximum likelihood identification of Gaussian autorregressive moving average models, Biometrika 60 (1973), 255-265.
2. A. Asuncion and D.J. Newman, UCI Machine Learning Repository [http://www.ics.uci.edu/~mlearn/MLRepository.html]. Irvine, CA:, Technical Report University of California, School of Information and Computer Science., 2007.
3. J.C. Bezdek and N.R. Pal, Some new indexes of cluster validity, IEEE Transactions on Systems, Man & Cybernetics: Part B 28(3) (1998), 301-315.
4. H.H. Bock, On some significance tests in cluster analysis, Journal of Classification 2 (1985), 77-108.
5. H.H. Bock, Significance Tests in Cluster Analysis, in Clustering and Classification. 1996, World Scientific Publishers.
6. N. Bolshakova and F. Azuaje, Cluster validation techniques for genome expression data, Signal Processing 83 (2003), 825-833.
7. M. Bouguessa, S. Wang and H. Sun, An objective approach to cluster validation, Pattern Recognition Letters 27 (2006), 1419-1430.
8. H. Bozdogan, Model Selection and Akaikes's Information Criterion (AIC): The General Theory and its Analytical Extensions, Psycometrika 52 (1987), 345-370.
9. M. Brun et al., Model-based evaluation of clustering validation measures, Pattern Recognition 40 (2007), 807-824.
10. Calinski and Harabasz, A dendrit method for cluster analysis, Communications in Statistics 3 (1974), 1-27.
11. D.L. Davies and D.W. Bouldin, A cluster separation measure, IEEE Transactions on Pattern Analysis and Machine Intelligence 1(2) (1979), 224-227.
12. S. Dudoit and J. Fridlyand, A prediction-based resampling method for estimating the number of clusters in a data set, Genome Biology 3(7) (2002).
13. J.C. Dunn, A fuzzy relative isodata process and its use in detecting compact well separated factore, Journal of Cybernetics 3 (1974), 32-57.
14. J.C. Dunn, Well separated clusters and optimal fuzzy partitions, Journal of Cybernetics 4 (1974), 95-104.
15. A. Famili, G. Liu and Z. Liu, Evaluation and optimization of clustering in gene expression data analysis, Bioinformatics 20(10) (2004), 1535-1545.
16. G. Schwarz, Estimating the Dimension of a Model, The Annals of Statistics 6 (1978), 461-464.
17. H. García and I. González, Self-organizing map and clustering for wastewater treatment monitoring, Engineering Applications of Artificial Intelligence 17(3) (2004), 215-225.
18. A.D. Gordon, Classification, Monographs on Statistics and Applied Probability 82, Chapman & Hall/CRC, 1999.
19. M. Hakididi, Y. Batistakis and M. Vazirgiannis, Cluster validity methods: Part I, SIGMOD Record 31(2) (2002).
20. J. Hartigan, Clustering Algorithms, Wiley, 1975.
21. E.R. Hruschka, R.J.G.B. Campello and L.N.d. Castro, Evolving clusters in gene-expression data, Information Sciences 176(13) (2006), 1898-1927.
22. L. Hubert and J. Schultz, Quadratic assignment as a general data-analysis strategy, British Journal of Mathematical and Statistical Psychologie 29 (1976), 190-241.
23. A.K. Jain and R.C. Dubes, Algorithms for clustering data, Englewood Cliffs, N.J.: Prentice Hall, 1988.
24. L. Kaufman and P.J. Rousseeuw, Finding groups in data: An Introduction to cluster analysis, Wiley, N.Y., 1990.
25. D. Kim, K.H. Lee and D. Lee, Fuzzy cluster validation index based on inter-cluster proximity, Pattern Recogn Lett 24(15) (2003), 2561-2574.
26. N. Laskaris and A. Ioannides, Semantic geodesic maps: A unifying geometrical approach for studying the structure and dynamics of single trial evoked responses, Clin Neurophysiol 113(8) (2002), 1209-1226.
27. M.H. Law and A.K. Jain, Cluster validity by bootstrapping partitions, Technical Report MSU-CSE-03-5, Department of Computer Science and Engineering. Michigan State University, 2003.
28. G.W. Milligan, An examination of the effect of six types of error perturbation on fifteen clustering algorithms, Psychometrka 45 325-342) (1980).
29. G.W. Milligan and M.C. Cooper, An examination of procedures to determine the number of clusters in a data set, Psychometrika 50 (1985), 159-179.
30. B. Mirkin, Mathematical Classification and Clustering, Kluwer Academic Publishers, 1996.
31. U. Möller and D. Radke, Performance of data resampling methods for robust class discovery based on clustering, Intelligent Data Analysis 10(2) (2006), 139-162.
32. C. Möller-Levet and H. Yin, Modelling and analysis of gene expression time-series based on co-expression, International Journal of Neural Systems, Special Issue on Bioinformatics 15(4) (2005), 311-322.
33. M.G.H. Omran, A.P. Engelbrecht and A. Salman, An overview of clustering methods, Intelligent Data Analysis 11(1-23) (2007).
34. M.K. Pakhira, S. Bandyopadhyay and U. Maulik, Validity index for crisp and fuzzy clusters, Pattern Recognition 37(3) (2004), 487-501.
35. N.R. Pal and J.C. Bezdek, On cluster validity for the fuzzy c-means model, IEEE Transactions on Fuzzy Systems 3(3) (1995), 370-379.
36. W.M. Rand, Objective criteria for the evaluation of clustering methods, Journal of the American Statistical Association 66 (1971), 846-850.
37. L. Rokach, O. Maimon and Lavi, Space Decomposition in Data Mining: A Clustering Approach. Foundations of Intelligent Systems, Lecture Notes in Computer Science 2871 (2003), 24-31.
38. Rousseeuw, Silhouettes: A graphical aid to the interpretation and validation of cluster analysis, Journal of Computational and Applied Mathematics 20 (1987), 53-65.
39. J. Siemiatycki, Mantel's space-time clustering statistic: Computing higher moments and a comparison of various data transforms, Journal of Statistical Computation and Simulation 7 (1978), 13-31.
40. H. Sun, S. Wang and J. Qingshan, A new validation index for determining the number of clusters in a data set. in: IJCNN'01 International Joint Conference on Neural Networks, IEEE ed. (2001), 1852-1857.
41. R. Tibshirani et al., Cluster validation by prediction strength, Technical Report Department of Statistics, Stanford University, 2001.
42. R. Tibshirani, G.Walther and T. Hastie, Estimating the number of clusters in a dataset via the gap statistic, Journal of the Royal Statistical Society. Series B: Statistical Methodology 32(2) (2001), 411-423.
43. Y. Xu and R.G. Brereton, A comparative study of cluster validation indices applied to genotyping data, Chemometrics and Intelligent Laboratory Systems 78 (2005), 30-40.
44. B.S. Everitt, S. Landau and M. Lesse, Cluster Analysis, Wiley, NY, 4th Edition, 2009.