Estimating the number of clusters using a windowing technique

Pattern Recognition and Image Analysis

Volumn 16, Issue 2, 2006, Pages 143-154

  Boutsinas, B ^a   Tasoulis, D K ^a   Vrahatis, M N ^a  

^a UNIVERSITY OF PATRAS   (Greece)

Author keywords

Automatic cluster detection; Clustering algorithms; Data mining; Range search; Unsupervised learning

Indexed keywords

EID: 33746087056     PISSN: 10546618     EISSN: 15556212     Source Type: Journal    
DOI: 10.1134/S1054661806020015     Document Type: Article

References (50)

1. H. Akaike, "A New Look at the Statistical Model Identification, " IEEE Trans. Automat. Contr. AC-19, 1974, pp. 716-723.
2. D. Alahakoon, S. K. Halgamuge, and B. Srinivasan, "Dynamic Self-Organizing Maps with Controlled Growth for Knowledge Discovery," IEEE Trans. Neural Networks 11 (3), 601-614 (2000).
3. M. S. Aldenderfer and R. K. Blashfield, "Cluster Analysis," in Ser. Quantitative Applications in the Social Sciences (SAGE Publications, London, 1984).
4. P. Alevizos, "An Algorithm for Orthogonal Range Search in d ≥ 3 Dimensions," Proc. of the 14th European Workshop on Computational Geometry, Barcelona, 1998.
5. P. Alevizos, B. Boutsinas, D. K. Tasoulis, and M. N. Vrahatis, "Improving the Orthogonal Range Search k-Windows Clustering Algorithm," Proc. of the 14th IEEE Int. Conf. on Tools with Artificial Intelligence, Washington, D.C., 2002, pp. 239-245.
6. P. Alevizos, D. K. Tasoulis, and M. N. Vrahatis, "Parallelizing the Unsupervised k-Windows Clustering Algorithm," Lecture Notes Comp. Sci. 3019, 225-232 (2004).
7. M. Anderberg, Cluster Analysis for Applications (Academic Press, New York, 1973).
8. G. H. Ball and D. J. Hall, "A Clustering Technique for Summarizing Multivariate Data," Behav. Sci. 12, 153-155 (1967).
9. J. L. Bentley and H. A. Maurer, "Efficient Worst-Case Data Structures for Range Searching," Acta Inform. 13, 1551-1568 (1980).
10. J. Blackmore and R. Miikkulainen, "Visualizing High-Dimensional Structure with the Incremental Grid Growing Neural Network," Proc. of the 12th Int. Conf. on Machine Learning, 1995, pp. 153-155.
11. C. A. Bouman and M. Shapiro, "A Multiscale Random Field Model for Bayesian Image Segmentation," IEEE Trans. Image Processing 3 (2), 162-177 (1994).
12. B. Boutsinas and T. Gnardellis, "On Distributing the Clustering Process," Pattern Recognit. Lett. 23 (8), 999-1008 (2002).
13. G. A. Carpenter and S. Grossberg, "A Massively Parallel Architecture for a Self-Organizing Neural Pattern Rec ognition Machine," Comp. Vis. Graph. Image Processing 37, 54-115 (1987).
14. G. A. Carpenter and S. Grossberg, "A ART-2: Self-Organization of Stable Category Recognition Codes for Analog Input Patterns," Appl. Opt. 26 (23), 4919-4930 (1987).
15. B. Chazelle, "Filtering Search: A New Approach to Query-Answering," SIAM J. Comput. 15 (3), 703-724 (1986).
16. D. Comaniciu and P. Meer, "Robust Analysis of Feature Spaces: Color Image Segmentation," IEEE Conf. Computer Vision and Pattern Recognition (CVPR'97), San Juan, Puerto Rico, 1997, pp. 0-755.
17. R. C. Dubes and A. K. Jain, "Clustering Methodologies in Exploratory Data Analysis," Adv. Comput. 19, 113-228 (1980).
18. M. Ester, H. P. Kriegel, J. Sander, and X. Xu, "A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise," Proc. of 2nd Int. Conf. on Knowledge Discovery and Data Mining, 1996, pp. 226-231.
19. U. M. Fayyad, G. Piatetsky-Shapiro, and P. Smyth, Advances in Knowledge Discovery and Data Mining (MIT Press, 1996).
20. B. Fritzke, "Growing Cell Structure: A Self-Organizing Network for Supervised and Unsupervised Learning," Neural Networks 7 (9), 1441-1460 (1994).
21. A. Gersho and R. M. Gray, Vector Quantization and Signal Compression (Kluwer Academic Publishers, Boston, MA, 1992).
22. S. Guha, R. Rastogi, and K. Shim, "CURE: An Efficient Algorithm for Clustering Large Databases," Proc. of ACM-SIGMOD 1998 Int. Conf. on Management of Data, Seattle, 1998, pp. 73-84.
23. B. Chazelle and L. J. Guibas, "Fractional Cascading: II. Applications," Algorithmica 1, 163-191 (1986).
24. Z. Huang, "Extensions to the k-Means Algorithm for Clustering Large Data Sets with Categorical Values," Data Mining Knowledge Discovery 2, 283-304 (1998).
25. A. K. Jain and R. C. Dubes, Algorithms for Clustering Data (Prentice-Hall, Englewood Cliffs, NJ, 1988).
26. S. Johnson, "Hierarchical Clustering Schemes," Phychometrika (1967), pp. 241-254.
27. G. Karyapis, E. H. Han, and V. Kumar, "CHAMELEON: A Hierarchical Clustering Algorithm Using Dynamic Modeling," IEEE Computer Special Issue on Data Analysis and Mining 32 (8), 68-75 (1999).
28. T. Kohonen, Self-Organizing Map (Springer, Heidelberg, 1995).
29. R. Kothari and D. Pitts, "On Finding the Number of Clusters," Pattern Recognit. Lett. 20, 405-416 (1999).
30. S. Lin and J. Si, "Weight Value Convergence of the SOM Algorithm for Discrete Input," Neural Comput. 10 (4), 807-814 (1998).
31. T. Martinetz, S. Berkovich, and K. Schulten, "Neural-Gas Network for Vector Quantization and Its Application to Time-Series Prediction," IEEE Trans. Neural Networks 4 (4), 558-569 (1993).
32. A. Osareh, M. Mirmehdi, B. Thomas, and R. Markham, "Automatic Recognition of Exudative Maculopathy Using Fuzzy c-Means Clustering and Neural Networks," Proc. Medical Image Understanding and Analysis Conference (BMVA Press, 2001), pp. 49-52.
33. D. Pelleg and A. Moore, "X-Means: Extending k-Means with Efficient Estimation of the Number of Clusters," Proc. of the 17th Int. Conf. on Machine Learning, 2000, pp. 727-734.
34. F. Preparata and M. Shamos, Computational Geometry (Springer Verlag, 1985).
35. J. B. MacQueen, "Some Methods for Classification and Analysis of Multivariate Observations," Proc. of the 5th Berkeley Symposium on Mathematics Statistics and Probability, 1967, pp. 281-297.
36. V. Ramasubramanian and K. Paliwal, "Fast k-Dimensional Tree Algorithms for Nearest-Neighbor Search with Application to Vector Quantization Encoding," IEEE Trans. Signal Processing 40 (3), 518-531 (1992).
37. J. Rissanen, "A Universal Prior for Integers and Estimation by Minimum Description Length," Ann. Stat. 11 (2), 417-431 (1983).
38. E. H. Ruspini, "A New Approach to Clustering," Inf. Control 15, 22-32 (1969).
39. J. Sander, M. Ester, H. P. Kriegel, and X. Xu, "Density-Based Clustering in Spatial Databases: The Algorithm GDBSCAN and Its Applications," Data Mining Knowledge Discovery 2 (2), 169-194 (1998).
40. J. Si, S. Lin, and M. A. Vuong, "Dynamic Topology Representing Networks," Neural Networks 13, 617-627 (2000).
41. R. Sokal and C. D. Michener, "A Statistical Method for Evaluating Systematic Relationships," Univ. Kansas Sci. Bull. 38, 1409-1438 (1958).
42. M. Sollenborn and P. Funk, "Category-Based Filtering and User Stereotype Cases to Reduce the Latency Problem in Recommender Systems," Proc. of the 6th Europ. Conf. on Case Based Reasoning, ECCBR2002, Springer Verlag Lecture Notes Series (2002), pp. 395-405.
43. D. K. Tasoulis, P. Alevizos, B. Boutsinas, and M. N. Vrahatis, "Parallel Unsupervised k-Windows: an Efficient Parallel Clustering Algorithm," Lecture Notes Comp. Sci. 2763, 336-344 (2003).
44. D. K. Tasoulis and M. N. Vrahatis, "Unsupervised Distributed Clustering," IASTED Int. Conf. on Parallel and Distributed Computing and Networks, 2004, pp. 347-351.
45. D. K. Tasoulis and M. N. Vrahatis, "Unsupervised Clustering on Dynamic Databases," Pattern Recognit. Lett. 26, 2116-2127 (2005).
46. D. K. Tasoulis and M. N. Vrahatis, "Generalizing the k-Windows Clustering Algorithm in Metric Spaces," Math. Comput. Modeling (2006) (in press).
47. M. N. Vrahatis, B. Boutsinas, P. Alevizos, and G. Pavlides, "The New k-Windows Algorithm for Improving the k-Means Clustering Algorithm," J. Complexity 18, 375-391 (2002).
48. T. Villmann, R. Der, M. Hermann, and M. Martinetz, "Topology Preservation in Self-Organizing Feature Maps: Exact Definition and Measurement," IEEE Trans. Neural Networks 8, 256-266 (1997).
49. L. Xu, "Bayesian Ying-Yang Machine, Clustering and Number of Clusters," Pattern Recognit. Lett. 18, 1167-1178 (1997).
50. T. Zhang, R. Ramakrisnnan, and M. Livny, "BIRCH: An Efficient Data Clustering Method for Very Large Databases," Proc. of ACM SIGMOD Int. Conf. on Management of Data, 1996, pp. 103-114.