Automatically determining the number of clusters in unlabeled data sets

IEEE Transactions on Knowledge and Data Engineering

Volumn 21, Issue 3, 2009, Pages 335-350

  Wang, Liang ^a   Leckie, Christopher ^a   Ramamohanarao, Kotagiri ^a   Bezdek, James ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Cluster tendency; Clustering; Reordered dissimilarity image; VAT

Indexed keywords

BLOCK EXTRACTION; CLUSTER TENDENCY; CLUSTERING; DATA SETS; DETERMINING THE NUMBER OF CLUSTERS; DISSIMILARITY MATRIX; DISTANCE TRANSFORMS; FIRST-ORDER DERIVATIVE; MORPHOLOGICAL FILTERING; NUMBER OF CLUSTERS; PIXEL VALUES; REAL-WORLD; REORDERED DISSIMILARITY IMAGE; SIGNAL PROCESSING TECHNIQUE; UNLABELED DATA; VAT; VISUAL ASSESSMENT OF CLUSTER TENDENCY;

BINARY IMAGES; CLUSTERING ALGORITHMS; SET THEORY; SIGNAL PROCESSING;

CLUSTER ANALYSIS;

EID: 67649260243     PISSN: 10414347     EISSN: None     Source Type: Journal    
DOI: 10.1109/TKDE.2008.158     Document Type: Article

References (46)

1. R.C. Gonzalez and R.E. Woods, Digital Image Processing. Prentice Hall, 2002.
2. I. Dhillon, D. Modha, and W. Spangler, "Visualizing Class Structure of Multidimensional Data, " Proc. 30th Symp. Interface: Computing Science and Statistics, 1998.
3. R.F. Ling, "A Computer Generated Aid for Cluster Analysis, " Comm. ACM, vol. 16, pp. 355-361, 1973.
4. T. Tran-Luu, "Mathematical Concepts and Novel Heuristic Methods for Data Clustering and Visualization, " PhD dissertation, Univ. of Maryland, College Park, 1996.
5. J.C. Bezdek and R. Hathaway, "VAT: A Tool for Visual Assessment of (Cluster) Tendency, " Proc. Int'l Joint Conf. Neural Networks (IJCNN '02), pp. 2225-2230, 2002.
6. J. Huband, J.C. Bezdek, and R. Hathaway, "bigVAT: Visual Assessment of Cluster Tendency for Large Data Sets, " Pattern Recognition, vol. 38, no. 11, pp. 1875-1886, 2005.
7. R. Hathaway, J.C. Bezdek, and J. Huband, "Scalable Visual Assessment of Cluster Tendency, " Pattern Recognition, vol. 39, pp. 1315-1324, 2006.
8. W.S. Cleveland, Visualizing Data. Hobart Press, 1993.
9. A.K. Jain and R.C. Dubes, Algorithms for Clustering Data. Prentice Hall, 1998.
10. J.C. Bezdek, R.J. Hathaway, and J. Huband, "Visual Assessment of Clustering Tendency for Rectangular Dissimilarity Matrices, " IEEE Trans. Fuzzy Systems, vol. 15, no. 5, pp. 890-903, 2007.
11. R. Xu and D. Wunsch II, "Survey of Clustering Algorithms, " IEEE Trans. Neural Networks, vol. 16, no. 3, pp. 645-678, 2005.
12. P. Guo, C. Chen, and M. Lyu, "Cluster Number Selection for a Small Set of Samples Using the Bayesian Ying-Yang Model, " IEEE Trans. Neural Networks, vol. 13, no. 3, pp. 757-763, 2002.
13. N. Otsu, "A Threshold Selection Method from Gray-level Histograms, " IEEE Trans. Systems, Man, and Cybernetics, vol. 9, no. 1, pp. 62-66, 1979.
14. P. Soille, Morphological Image Analysis: Principles and Applications. Springer, 1999.
15. X. Hu and L. Xu, "A Comparative Study of Several Cluster Number Selection Criteria, " Proc.
16. P.J. Rousseeuw, "A Graphical Aid to the Interpretations and Validation of Cluster Analysis, " J. Computational and Applied Math., vol. 20, pp. 53-65, 1987.
17. G. Milligan and M. Cooper, "An Examination of Procedures for Determining the Number of Clusters in a Data Set, " Psychometrika, vol. 50, pp. 159-179, 1985.
18. U. Maulik and S. Bandyopadhyay, "Performance Evaluation of Some Clustering Algorithms and Validity Indices, " IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 12, pp. 1650-1654, Dec. 2002.
19. R.B. Calinski and J. Harabasz, "A Dendrite Method for Cluster Analysis, " Comm. in Statistics, vol. 3, pp. 1-27, 1974.
20. M. Windham and A. Cutler, "Information Ratios for Validating Mixture Analysis, " J. Am. Statistical Assoc., vol. 87, pp. 1188-1192, 1992.
21. P. Grünwald, P. Kontkanen, P. Myllymäki, T. Silander, and H. Tirri, "Minimum Encoding Approaches for Predictive Modeling, " Proc. 14th Int'l Conf. Uncertainty in Artificial Intelligence (UAI '98), pp. 183-192, 1998.
22. J.W. Tukey, Exploratory Data Analysis. Addison-Wesley, 1997.
23. R. Tibshirani, G. Walther, and T. Hastie, "Estimating the Number of Clusters in a Dataset via the Gap Statistics, " J. Royal Statistical Soc. B, vol. 63, pp. 411-423, 2001.
24. UCI Repository of Machine Learning Databases, http://www.ics.uci.edu/ ~mlearn/MLRepository.html, 2008.
25. I. Sledge, J. Huband, and J.C. Bezdek, "(Automatic) Cluster Count Extraction from Unlabeled Datasets, " Joint Proc. Fourth Int'l Conf. Natural Computation (ICNC) and Fifth Int'l Conf. Fuzzy Systems and Knowledge Discovery (FSKD), 2008.
26. L. Wang and D. Suter, "Visual Learning and Recognition of Sequential Data Manifolds with Applications to Human Movement Analysis, " Computer Vision and Image Understanding, 2007.
27. J.C. Bezdek, J.M. Keller, R. Krishnapuram, and N.R. Pal, Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Kluwer Academic Publishers, 1999.
28. J.C. Bezdek and N.R. Pal, "Some New Indices of Cluster Validity, " IEEE Trans. System, Man and Cybernetics, vol. 28, no. 3, pp. 301-315, 1998.
29. J.C. Bezdek, W. Li, Y. Attikiouzel, and M.P. Windham, "A Geometric Approach to Cluster Validity for Normal Mixtures, " Soft Computing, vol. 1, pp. 166-179, 1997.
30. W. Wang and Y. Zhang, "On Fuzzy Cluster Validity Indices, " Fuzzy Sets and Systems, vol. 158, pp. 2095-2117, 2007.
31. S. Monti et al., "Molecular Profiling of Diffuse Large B-cell Lymphoma Identifies Robust Subtypes Including One Characterized by Host Inflammatory Response, " Blood, vol. 106, no. 5, pp. 1851-1861, 2005.
32. G.D. Floodgate and P.R. Hayes, "The Adansonian Taxonomy of Some Yellow Pigmented Marine Bacteria, " J. General Microbiology, vol. 30, pp. 237-244, 1963.
33. N. Pal, J. Keller, M. Popescu, J. Bezdek, J. Mitchell, and J. Huband, "Gene Ontology-Based Knowledge Discovery through Fuzzy Cluster Analysis, " J. Neural, Parallel and Scientific Computing, vol. 13, pp. 337-361, 2005.
34. A. Juan and E. Vidal, "Fast K-Means-like Clustering in Metric Space, " Pattern Recognition Letters, vol. 15, no. 1, pp. 19-25, 1994.
35. Decomposition Methodology for Knowledge Discovery and Data Mining, O. Maimon and L. Rokach, eds., pp. 90-94. World Scientific, 2005.
36. W. McCormick, P. Schweitzer, and T. White, "Problem Decomposition and Data Reorganization by a Cluster Technique, " Operations Research, vol. 20, no. 5, pp. 993-1009, 1972.
37. Statistical Pattern Recognition. A. Webb, ed., pp. 345-357. John Wiley & Sons, 2002.
38. A. Gordon, Classification, second ed. Chapman and Hall, CRC, 1999.
39. S. Roweis and L. Saul, "Nonlinear Dimensionality Reduction by Locally Linear Embedding, " Science, vol. 290, no. 5500, pp. 2323-2326, 2000.
40. J.B. Tenenbaum, V. Silva, and J. Langford, "A Global Geometric Framework for Nonlinear Dimensionality Reduction, " Science, vol. 290, no. 5500, pp. 2319-2323, 2000.
41. D. Cai, X. He, and J. Han, "Spectral Regression for Efficient Regularized Subspace Learning, " Proc. 11th Int'l Conf. Computer Vision (ICCV), 2007.
42. M. Belkin and P. Niyogi, "Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering, " Proc. Advances in Neural Information Processing Systems (NIPS), 2002.
43. M. Breitenbach and G. Grudic, "Clustering through Ranking on Manifolds, " Proc. 22nd Int'l Conf. Machine Learning (ICML), 2005.
44. R.B. Cattell, "A Note on Correlation Clusters and Cluster Search Methods, " Psychometrika, vol. 9, no. 3, pp. 169-184, 1944.
45. P. Sneath, "A Computer Approach to Numerical Taxonomy, " J. General Microbiology, vol. 17, pp. 201-226, 1957.
46. T.C. Havens, J.C. Bezdek, J.M. Keller, M. Popescu, and J.M. Huband, "Is VAT Really Single Linkage in Disguise?" Pattern Recognition Letters, 2008, in review.