Topology-Based Clustering Using Polar Self-Organizing Map

IEEE Transactions on Neural Networks and Learning Systems

Volumn 26, Issue 4, 2015, Pages 798-808

  Xu, Lu ^a   Chow, Tommy W S ^a   Ma, Eden W M ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Clustering; polar self organizing map (PolSOM); unsupervised learning; visualization

Indexed keywords

CLUSTER ANALYSIS; CONFORMAL MAPPING; FLOW VISUALIZATION; SELF ORGANIZING MAPS; TOPOLOGY; UNSUPERVISED LEARNING;

CLUSTERING; CLUSTERING ACCURACY; COMPUTATIONAL COSTS; CONVENTIONAL METHODS; NUMBER OF CLUSTERS; POLAR SELF-ORGANIZING MAP (POLSOM); SYNTHETIC AND REAL DATA; VISUAL REPRESENTATIONS;

CLUSTERING ALGORITHMS;

EID: 85027928003     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2014.2326427     Document Type: Article

References (56)

1. R. Duda, P. Hart, and D. Stork, Pattern Classification. New York, NY, USA: Wiley, 2001.
2. R. Xu and D. Wunsch, II, "Survey of clustering algorithms," IEEE Trans. Neural Netw., vol. 16, no. 3, pp. 645-678, May 2005.
3. R. Xu and D. Wunsch, II, "Clustering algorithm in biomedical research: A review," IEEE Rev. Biomed. Eng., vol. 3, pp. 120-154, 2010.
4. P. Hansen and B. Jaumard, "Cluster analysis and mathematical programming,"Math. Program., vol. 79, nos. 1-3, pp. 191-215, 1997.
5. G. Lance and W. Williams, "A general theory of classificatory sorting strategies 1. Hierarchical systems," J. Comput., vol. 9, no. 4, pp. 373-380, 1967.
6. F. Murtagh, "A survey of recent advances in hierarchical clustering algorithms," J. Comput., vol. 26, no. 4, pp. 354-359, 1983.
7. A. Jain and R. Dubes, Algorithms for Clustering Data. Englewood Cliffs, NJ, USA: Prentice-Hall, 1988.
8. R. Zass and A. Shashua, "A unifying approach to hard and probabilistic clustering," in Proc. 10th IEEE ICCV, vol. 1. Oct. 2005, pp. 294-301.
9. Z. S. He, S. L. Xie, R. Zdunek, G. X. Zhou, and A. Cichocki, "Symmetric nonnegative matrix factorization: Algorithms and applications to probabilistic clustering," IEEE Trans. Neural Netw., vol. 22, no. 12, pp. 2117-2131, Dec. 2011.
10. Z. S. He, A. Cichocki, S. L. Xie, and K. Choi, "Detecting the number of clusters in n-way probabilistic clustering," IEEE Trans. Pattern Anal. Mach. Intell., vol. 32, no. 11, pp. 2006-2021, Nov. 2010.
11. G. Karypis, E. Han, and V. Kumar, "Chameleon: Hierarchical clustering using dynamic modeling," IEEE Trans. Comput., vol. 32, no. 8, pp. 68-75, Aug. 1999.
12. A. L. N. Fred and J. M. N. Leitão, "A new cluster isolation criterion based on dissimilarity increments," IEEE Trans. Pattern Anal. Mach. Intell., vol. 25, no. 8, pp. 944-958, Aug. 2003.
13. K. A. Heller and Z. Ghahramani, "Bayesian hierarchical clustering," in Proc. 22nd ICML, Bonn, Germany, 2005, pp. 1-8.
14. Y. W. Teh, H. Daumé, III, and D. Roy, "Bayesian agglomerative clustering with coalescents," in Advances in Neural Information Processing Systems, vol. 20. Cambridge, MA, USA: MIT Press, 2007, pp. 1-8.
15. B. Everitt, S. Landau, and M. Leese, Cluster Analysis. London, U.K.: Taylor & Francis, 2001.
16. J. MacQueen, "Some methods for classification and analysis of multivariate observations," in Proc. 5th Berkeley Symp. Math. Statist. Probab., 1967, pp. 281-297.
17. K. Stoffel and A. Belkoniene, "Parallel K-means clustering for large data sets," in Proc. 5th Int. Euro Parallel Process., 1999, pp. 1451-1454.
18. V. Estivill-Castro and J. Yang, "A fast and robust general purpose clustering algorithm," in Proc. 6th Pacific Rim Int. Conf. Artif. Intell., Melbourne, Australia, 2000, pp. 208-218.
19. Z. Huang, "Extensions to the K-means algorithm for clustering large data sets with categorical values," Data Mining Knowl. Discovery, vol. 2, no. 3, pp. 283-304, 1998.
20. S. Das, A. Abraham, and A. Konar, "Automatic clustering using an improved differential evolution algorithm," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 38, no. 1, pp. 218-236, Jan. 2008.
21. J. Dunn, "A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters," J. Cybern. Syst., vol. 3, no. 3, pp. 32-57, 1974.
22. P. K. Simpson, "Fuzzy min-max neural networks. I. Classification,"IEEE Trans. Neural Netw., vol. 3, no. 5, pp. 776-786, Sep. 1992.
23. P. K. Simpson, "Fuzzy min-max neural networks-Part 2: Clustering,"IEEE Trans. Neural Netw., vol. 1, no. 1, pp. 32-45, Feb. 1993.
24. J. C. Bezdek and R. J. Hathaway, "Numerical convergence and interpretation of the fuzzy c-shells clustering algorithm," IEEE Trans. Neural Netw., vol. 3, no. 5, pp. 787-793, Sep. 1992.
25. M. Ester, H. Kriegel, J. Sander, and X. Xu, "A density-based algorithm for discovering clusters in large spatial databases with noise," in Proc. 2nd Int. Conf. Knowl. Discovery Data Mining, 1996, pp. 226-231.
26. A. Hinneburg and D. A. Keim, "An efficient approach to clustering in large multimedia data bases with noise," in Proc. Int. Conf. Knowl. Discovery Data Mining, 1998, pp. 58-65.
27. M. Ankerst, M. M. Breunig, H. Kriegel, and J. Sander, "OPTICS: Ordering points to identify the clustering structure," in Proc. Int. Conf. Manag. Data, 1999, pp. 49-60.
28. E. W. M. Ma and T. W. S. Chow, "A new shifting grid clustering algorithm," Pattern Recognit., vol. 37, no. 3, pp. 503-514, 2004.
29. G. Gupta, A. Liu, and J. Ghosh, "Automated hierarchical density shaving: A robust automated clustering and visualization framework for large biological data sets," IEEE Trans. Comput. Biol. Bioinformat., vol. 7, no. 2, pp. 223-237, Apr./Jun. 2010.
30. X. Wang and D. Huang, "A novel density-based clustering framework by using level set method," IEEE Trans. Knowl. Data Eng., vol. 21, no. 11, pp. 1515-1531, Nov. 2009.
31. G. A. Carpenter and S. Grossberg, "The ART of adaptive pattern recognition by a self-organizing neural network," IEEE Trans. Comput., vol. 21, no. 3, pp. 77-88, Mar. 1988.
32. A. Ultsch and H. P. Siemon, "Kohonen's self organizing feature maps for exploratory data analysis," in Proc. Int. Conf. Neural Netw., 1990, pp. 305-308.
33. S. Wu and T. W. S. Chow, "Clustering of the self-organizing map using a clustering validity index based on inter-cluster and intra-cluster density,"Pattern Recognit., vol. 37, no. 2, pp. 175-188, 2004.
34. K. Tasdemir, P. Milenov, and B. Tapsall, "Topology-based hierarchical clustering of self-organizing maps," IEEE Trans. Neural Netw., vol. 22, no. 3, pp. 474-485, Mar. 2011.
35. M. Halkidi and M. Vazirgiannis, "A density-based cluster validity approach using multi-representatives," Pattern Recognit. Lett., vol. 29, no. 6, pp. 773-786, 2008.
36. K. Tasdemir and E. Merényi, "Exploiting data topology in visualization and clustering of self-organizing maps," IEEE Trans. Neural Netw., vol. 20, no. 4, pp. 549-562, Apr. 2009.
37. J. Vesanto and E. Alhonierni, "Clustering of the self-organizing map,"IEEE Trans. Neural Netw., vol. 11, no. 3, pp. 586-600, May 2000.
38. M. Y. Kiang, "Extending the Kohonen self-organizing map networks for clustering analysis," Comput. Statist. Data Anal., vol. 38, no. 2, pp. 161-180, 2001.
39. D. Brugger, M. Bogdan, and W. Rosenstiel, "Automatic cluster detection in Kohonen's SOM," IEEE Trans. Neural Netw., vol. 19, no. 3, pp. 474-485, Mar. 2008.
40. C.-C. Hsu and S.-H. Lin, "Visualized analysis of mixed numeric and categorical data via extended self-organizing map," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 1, pp. 72-86, Jan. 2012.
41. N. Manukyan, M. J. Eppstein, and D. M. Rizzo, "Data-driven cluster reinforcement and visualization in sparsely-matched self-organizing maps," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 5, pp. 846-852, May 2012.
42. Y. Cao, H. He, and H. Man, "SOMKE: Kernel density estimation over data streams by sequences of self-organizing maps," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 8, pp. 1254-1268, Aug. 2012.
43. T. Kohonen, "Self-organized formation of topologically correct feature maps," Biol. Cybern., vol. 43, no. 1, pp. 59-69, 1982.
44. T. Kohonen, Self-Organizing Maps. Berlin, Germany: Springer-Verlag, 1997.
45. L. Xu, Y. Xu, and T. W. S. Chow, "PolSOM: A new method for multidimensional data visualization," Pattern Recognit., vol. 43, no. 4, pp. 1668-1675, Apr. 2010.
46. K. Bunte, B. Hammer, T. Villmann, M. Biehl, and A. Wismüller, "Exploratory observation machine (XOM) with Kullback-Leibler divergence for dimensionality reduction and visualization," in Proc. Eur. Symp. Artif. Neural Netw., Bruges, Belgium, Apr. 2010, pp. 87-92.
47. G. Hinton and S. Roweis, "Stochastic neighbor embedding," in Advances in Neural Information Processing Systems, vol. 15. Cambridge, MA, USA: MIT Press, 2003, pp. 833-840.
48. L. V. D. Maaten and G. Hinton, "Visualizing data using t-SNE," J. Mach. Learn. Res., vol. 9, pp. 2579-2605, Nov. 2008.
49. T. M. Martinetz, S. G. Berkovich, and K. J. Schulten, "'Neuralgas' network for vector quantization and its application to time-series prediction," IEEE Trans. Neural Netw., vol. 4, no. 4, pp. 558-569, Jul. 1993.
50. J. Si, S. Lin, and M. A. Vuong, "Dynamic topology representing networks," Neural Netw., vol. 13, no. 6, pp. 617-627, Jul. 2000.
51. (2008, Jan. 9). UCI Machine Learning Repository [Online]. Available: http://www.ics.uci.edu/~mlearn/MLRepository.html
52. (2009, Jan. 9). Matlab Codes and Datasets for Feature Learning [Online]. Available: http://www.zjucadcg.cn/dengcai/Data/data.html
53. K. Tasdemir and E. Merenyi, "A validity index for prototype based clustering of data sets with complex cluster structures," IEEE Trans. Syst. Man, Cybern. B, Cybern., vol. 41, no. 4, pp. 1039-1053, Aug. 2011.
54. R. Yager, "Intelligent control of the hierarchical agglomerative clustering process," IEEE Trans. Syst. Man, Cybern. B, Cybern., vol. 30, no. 6, pp. 835-845, Dec. 2000.
55. T. Zhang, R. Ramakrishnan, and M. Livny, "BIRCH: An efficient data clustering method for very large databases," in Proc. ACM SIGMOD Int. Conf. Manag. Data, 1996, pp. 103-114.
56. S. Guha, R. Rastogi, and K. Shim, "CURE: An efficient clustering algorithm for large databases," in Proc. ACM SIGMOD Int. Conf. Manag. Data, 1998, pp. 73-84.