Self-organizing maps by difference of convex functions optimization

Data Mining and Knowledge Discovery

Volumn 28, Issue 5-6, 2014, Pages 1336-1365

  Le Thi, Hoai An ^a   Nguyen, Manh Cuong ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

Author keywords

DC programming; DCA; Self organizing maps

Indexed keywords

CONFORMAL MAPPING; MAPS; OPTIMIZATION; SELF ORGANIZING MAPS;

D-C PROGRAMMING; DCA; DIFFERENCE OF CONVEX FUNCTIONS; INNOVATIVE APPROACHES; NONCONVEX OPTIMIZATION; OPTIMIZATION PROBLEMS; QUALITY OF SOLUTION; REAL-WORLD DATASETS;

FUNCTIONS;

EID: 84906779671     PISSN: 13845810     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10618-014-0369-7     Document Type: Article

References (75)

1. Amerijckx C, Legaty JD, Verleysen M (2003) Image compression using self-organizing maps. Syst Anal Modell Simul 43(11):1529-1543
2. Argyrou A (2009) Clustering hierarchical data using self-organizing map: a graph-theoretical approach. Advances in self-organizing maps. Lecture Notes in Computer Science, vol 5629. Springer, Heidelberg, pp 19-27
3. Astudillo CA, Oommen BJ (2014) Topology-oriented self-organizing maps: a survey. Pattern Anal Appl 17:223-248
4. Barreto GA, Araúo AFR, Ritter HJ (2003) Self-organizing feature maps for modeling and control of robotic manipulators. J Intell Robot Syst 36(4):407-450
5. Bradley BS, Mangasarian OL (1998) Feature selection via concave minimization and support vector machines. In: Machine learning proceedings of the fifteenth international conferences (ICML'98), San Francisco, California, MorganKaufmann, pp 82-90
6. Burger M, Graepel T, Obermayer K (1997) Phase transitions in stochastic self-organizing maps. Phys Rev E 56:3876-3890
7. ChandraShekar BH, Shoba G (2009) Classification of documents using Kohonens self-organizing map. Int J Comput Theory Eng 1(5):610-613
8. Chang L, Jun-min L, Chong-xiu Y (2013) Skin detection using a modified self-organizing mixture network. In: Automatic face and gesture recognition (FG), 2013 10th IEEE international conference and workshops, vol 1, no 6, pp 22-26
9. Collobert R, Sinz F, Weston J, Bottou L (2006) Trading convexity for scalability. IN: International conference on machine learning ICML
10. de Carvalho FDA, Bertrand P, De Melo FM (2012) Batch self-organizing maps based on city-block distances for interval variables. Hal-00706519, version 1
11. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc B 39:1-38
12. Dickerson KB, Ventura D (2009) Music recommendation and query-by-content using self-organizing maps. In: Proceedings of the international joint conference on neural networks, pp 705-710
13. Doan NQ, Azzag H, Lebbah M (2012) Self-organizing map and tree topology for graph summarization. Artificial neural networks and machine learning ICANN 2012. Lecture Notes in Computer Science, vol 7553. Springer, Heidelberg, pp 363-370
14. Dozono H, Tokushima H, Hara S, Noguchi Y (2005) An algorithm of SOM using simulated annealing in the batch update phase for sequence analysis. In: International workshop on self-organizing maps (WSOM), pp 171-178
15. Fiannaca A, Fatta GD, Gaglio S, Rizzo R, Urso AM (2007) Improved SOM learning using simulated annealing. Lecture Notes in Computer Science,vol 4668. Springer, Heidelberg, pp 279-288
16. Fort JC, Letremy P, Cottrell M (2002) Advantages and drawbacks of the Batch Kohonen algorithm. IN: The European symposium on artificial neural networks conference - ESANN, pp 223-230
17. Graef G, Schaefer C (2002) Application of ART2 networks and self-organizing maps to collaborative filtering. Hypermedia: openness, structural awareness, and adaptivity. Lecture Notes in Computer Science, vol 2266. Springer, Heidelberg, pp 296-309
18. Graepel T, Burger M, Obermayer K (1998) Self-organizing maps: generalizations and new optimization techniques. Neurocomputing 21(13):173-190
19. Günter S, Bunke H (2002) Self-organizing map for clustering in the graph domain. Pattern Recognit Lett 23(4):405-417
20. Guo X, Wang H, Glass DH (2013) Bayesian self-organizing map for data classification and clustering. Int J Wavelets Multiresolut Inf Process 11(5):91-102
21. Hagenbuchner M, Sperduti A, Tsoi AC (2009) Graph self-organizing maps for cyclic and unbounded graphs. Neurocomputing 72(79):1419-1430
22. Hagenauer J, Helbich M (2013) Hierarchical self-organizing maps for clustering spatiotemporal data. Int J Geograph Inform Sci 27(10):2026-2042
23. Heskes T (1999) Energy functions for self organizingmaps. In Oya S, Kaski E (eds) KohonenMaps. Elsevier, Amsterdam pp 303-316
24. Heskes T (2001) Self-organization maps, vector quantization, and mixture modeling. IEEE Trans Neural Netw 12(6):1299-1305
25. Hiriart Urruty JB, Lemarechal C (1993) Convex analysis and minimization algorithms. Springer Verlag, Berlin Heidelberg
26. Ismail S, Shabri A, Samsudin R (2012) A hybrid model of self organizing maps and least square support vector machine for river flow forecasting. Hydrol Earth Syst Sci 16:4417-4433
27. Kaski S, Lagus K (1996) Comparing self-organizing maps. Lecture Notes in Computer Science, vol 1112. Springer, Heidelberg, pp 809-814
28. Khalilia M, Popescu M (2014) Topology preservation in fuzzy self-organizing maps. Advance trends in soft computing Studies in Fuzziness and Soft Computing, vol 312. Springer, Heidelberg, pp 105-114
29. Kiviluoto K (1996) Topology preservation in self-organizing maps. In: Proceedings of ICNN 96, IEEE international conference on neural networks, vol 1, pp 294-299
30. Kohonen T (1982) Analysis of a simple self-organizing process. Biol Cybern 44:135-140
31. Kohonen T (1997) Self-organization maps. Springer, Heidelberg
32. Krause N, Singer Y (2004) Leveraging the margin more carefully. In: International conference on machine learning ICML
33. Le Thi HA (2005) DC programming and DCA. http://lita.sciences.univ-metz. fr/~lethi
34. Le Thi HA, Pham Dinh T (1997) Solving a class of linearly constrained indefinite quadratic problems by D.C. algorithms. J Glob Optim 11:253-285
35. Le Thi HA, Pham Dinh T (2005) DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann Oper Res 133:23-46
36. Le Thi HA, Le Hoai M, Pham Dinh T (2007) Fuzzy clustering based on nonconvex optimization approaches using difference of convex (DC) functions algorithms. J Adv Data Anal Classif 2:1-20
37. Le Thi HA, Le Hoai M, Nguyen VV, Pham Dinh T (2008) A DC programming approach for feature selection in support vector machines learning. J Adv Data Anal Classif 2(3):259-278
38. Le Thi HA, Le Hoai M, Pham Dinh T, Huynh VN (2012) Binary classification via spherical separator by DC programming and DCA. J Glob Optim 1-15. doi: 10.1007/s10898-012-9859-6
39. Le Thi HA, Le Hoai M, Huynh VN (2013) Block clustering based on DC programming and DCA. NECO Neural Comput 25(10):2776-2807
40. Le Thi HA, Pham Dinh T, Nguyen CN, Le Hoai M DC programming and DCA for diversity data mining. Optimization (to appear)
41. Le Thi HA, Le Hoai M, Pham Dinh T (2014) New and efficient DCA based algorithms for minimum sum-of-squares clustering. Patter Recognit 47:388-401
42. Lee M, Choi P, Woo Y (2002) A hybrid recommender system combining collaborative filtering with neural network. Adaptive hypermedia and adaptive web-based systems. Lecture Notes in Computer Science, vol 2347. Springer-Verlag, Berlin Heidelberg, pp 531-534
43. Lefebvre G, Zheng H, Laurent C (2006) Objectionable image detection by ASSOM competition. Image and video retrieval. Lecture Notes in Computer Science, vol 4071. Springer, Heidelberg, pp 201-210
44. Liu Y, Shen X, Doss H (2005) Multicategory Ψ -learning and support vector machine, computational tools. J Comput Graph Stat 14:219-236
45. Liu Y, Shen X (2006) Multicategory Ψ -learning. J Am Stat Assoc 101(474):500-509
46. Madalina O, Nathalie VV, Christine CA (2013) Multiple Kernel self-organizing maps. In: ESANN 2013 proceedings, European symposium on artificial neural networks, computational intelligence and machine learning. Bruges, Belgium, pp 83-88
47. Van Hulle Marc M (2012) Self-organizing maps. Handbook of natural computing. Springer-Verlag, Berlin, Heidelberg, pp 585-622
48. Marina R (2012) Graph mining based SOM: a tool to analyze economic stability. In: Johnsson M (ed) Applications of self-organizing maps. InTech Publisher, Vienna, pp 1-25
49. Matharage S, Alahakoon D, Rajapakse J, Huang P (2011) Fast growing self organizing map for text clustering. Neural information processing. Lecture Notes in Computer Science, vol 7063. Springer, Heidelberg, pp 406-415
50. Matsushita H, Nishio Y (2010) Batch-learning self-organizing map with weighted connections avoiding false-neighbor effects. In: The 2010 international joint conference on neural networks (IJCNN), pp 1-6
51. Manning CD, Raghavan P, Schtze H (2008) Introduction to information retrieval. Cambridge University Press, Cambridge
52. Neme A, Miramontes P (2014) Self-organizing map formation with a selectively refractory neighborhood. Neural Process Lett 39(1):1-24
53. Ogihara M, Matsumoto H, Marumo T, Kuroda C (2009) Clustering of pressure fluctuation data using self-organizing map. Engineering applications of neural networks. Communications in Computer and Information Science, vol 43. Springer, Heidelberg, pp 45-54
54. Olteanu M, Villa-Vialaneix N, Cierco-Ayrolles C (2013) Multiple Kernel self-organizing maps. Hal-00817920, version 1
55. O'Connell C, Kutics A, Nakagawa A (2013) Layered self-organizing map for image classification in unrestricted domains. Image analysis and processing - ICIAP 2013. Lecture Notes in Computer Science, vol 8156. Springer, Heidelberg, pp 310-319
56. Paul S, Gupta M (2013) Image segmentation by self organizing map with mahalanobis distance. Int J Emerg Technol Adv Eng 3(2):288-291
57. Pham Dinh T, Le Thi HA (1997) Convex analysis approach to D.C. programming: theory, algorithms and applications (dedicated to Professor Hoang Tuy on the occasion of his 70th birthday). Acta Math Vietnam 22:289-355
58. Pham Dinh T, Le Thi HA (1998) DC optimization algorithms for solving the trust region sub-problem. SIAM J Optim 8:476-505
59. Pratiwi D (2012) The use of self organizing map method and feature selection in image database classification system. Int J Comput Sci 9(3):377-381
60. Roh TH, Oh KJ, Han I (2003) The collaborative filtering recommendation based on SOM cluster-indexing CBR. Expert Syst Appl 25(3):413-423, ISSN 0957-4174, doi: 10.1016/S0957-4174(03)00067-8
61. Raskutti B, Leckie C (1999) An evaluation of criteria for measuring the quality of clusters. In: Proceedings of the sixteenth international joint conference on artificial intelligence IJCAI '99, pp 905-910
62. Ruan X, Gao Y, Song H, Chen J (2011) A new dynamic self-organizing method for mobile robot environment mapping. J Intell Learn Syst Appl 3:249-256
63. Saarikoski J, Laurikkala J, Järvelin K, Juhola M (2011) Self-organising maps in document classification: a comparison with six machine learning methods. Adaptive and natural computing algorithms. Lecture Notes in Computer Science, vol 6593. Springer, Heidelberg, pp 260-269
64. Sarlin P, Eklund T (2011) Fuzzy clustering of the self-organizing map: some applications on financial time series. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps. Lecture Notes in Computer Science, vol 6731. Springer, Berlin Heidelberg, pp 40-50
65. Shen X, Tseng GC, Zhang X, Wong WH (2003) ψ -Learning. J Am Stat Assoc 98:724-734
66. Smith T, Alahakoon D (2009) Growing self-organizing map for online continuous clustering. Foundations of Computational Intelligence, vol 4. Stud Comput Intell 204:49-83
67. Szymanski J, Duch W (2012) Self organizing maps for visualization of categories. Neural information processing, Lecture Notes in Computer Science, vol 7663. Springer, Heidelberg, pp 160-167
68. Tsoi AC, Hagenbuchner M, Sperduti A (2006) Self-organising map techniques for graph data applications to clustering of XML documents. Advanced data mining and applications. Lecture Notes in Computer Science, vol 4093. Springer, Heidelberg, pp 19-30
69. Van Laerhoven K (2001) Combining the self-organizing map and K-means clustering for on-line classification of sensor data. Artificial neural networks ICANN 2001. Lecture Notes in Computer Science, vol 2130. Springer, Heidelberg, pp 464-469
70. Vembu S, Baumann S (2004) A self-organizing map based knowledge discovery for music recommendation systems. Computer music modeling and retrieval. Lecture Notes in Computer Science, vol 3310. Springer-Verlag, Berlin Heidelberg, pp 119-129
71. Villa N, Boulet R (2007) Clustering a medieval social network by SOM using a kernel based distance measure. In: ESANN'2007 proceedings - European symposium on artificial neural networks Bruges (Belgium), d-side publi., ISBN 2-930307-07-2
72. Wang J, Shen Z, Pan W (2007) On transductive support vector machines. In: Proceeding of the international conference on machine learning ICML
73. Wehrens R (2010) Self-organising maps for image segmentation. In: Advances in data analysis, data handling and business intelligence studies in classification, Data Analysis, and Knowledge Organization, pp 373-383
74. Yin H (2008) The self-organizing maps: background, theories, extensions and applications. Stud Comput Intell (SCI) 115:715-762
75. Yuille AL, Rangarajan A (2002) The convex concave procedure (CCCP). Advances in neural information processing system, vol 14. MIT Press, Cambrige MA