The Self-Organizing Map

Proceedings of the IEEE

Volumn 78, Issue 9, 1990, Pages 1464-1480

  Kohonen, Teuvo ^a,b  

^a AALTO UNIVERSITY   (Finland)

^b ACADEMY OF FINLAND   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

LEARNING SYSTEMS;

ARTIFICIAL NEURAL NETWORKS; NEURAL NETWORK MODELS;

NEURAL NETWORKS;

EID: 0025489075     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/5.58325     Document Type: Article

References (116)

1. S.-I. Amari, "Topographic organization of nerve fields," Bull. Math. Biology, vol. 42, pp. 339–364, 1980.
2. B. Angéniol, G. de la Croix Vaubois, and J.-Y. Le Texier, "Self-organizing feature maps and the travelling salesman problem," Neural Networks, vol. 1, pp. 289–293, 1988.
3. N. Ansari and Y. Chen, "Dynamic digital satellite communication network management by self-organization," Proc. Int. Joint Conf. on Neural Networks, IJCNN-90-WASH-DC (Washington, DC, 1990) pp. II-567-II-570.
4. D. S. Bradburn, "Reducing transmission error effects using a self-organizing network," Proc. Int. joint Conf. on Neural Networks, IJCNN 89 (Washington, D.C., 1989) pp. 11531-537.
5. D.J. Burr, "An improved elastic net method for the traveling salesman problem," Proc. IEEE Int. Conf. on Neural Networks, ICNN-88 (San Diego, Cal., 1988) pp. I-69-I-76.
6. A. Caramazza, "Some aspects of language processing revealed through the analysis of acquired aphasia: The lexical system," Ann. Rev. Neurosci., vol. 11, pp. 395–421, 1988.
7. M. Cottrell and J.-C. Fort, "A stochastic model of retinotopy: A self-organizing process," Biol. Cybern., vol. 53, pp. 405–411, 1986.
8. "Etude d’un processus d’auto–organisation," Ann. Inst. Henri Poincaré, vol. 23, pp. 1–20, 1987.
9. A. R. Damasio, H. Damasio, and G. W. Van Hoesen, "Prosopagnosia: Anatomic basis and behavioral mechanisms," Neurology, vol. 24, pp. 89–93, 1975.
10. R. Durbin and D. Willshaw, "An analogue approach to the travelling salesman problem using an elastic net method," Nature, vol. 326, pp. 689–691, 1987.
11. D. Essen, "Functional organization of primate visual cortex," in Cerebral Cortex, vol. 3, A. Peters, E. C. Jones (Eds.). New York: Plenum Press, 1985, pp. 259–329.
12. J. Fuller and A. Farsaie, "Invariant target recognition using feature extraction," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH-DC (Washington, DC, 1990) pp. II-595-II-598.
13. D. Gabor, "Theory of communication," J.I.E.E., vol. 93, pp. 429–459, 1946.
14. A. Gersho, "On the structure of vector quantizers," IEEE Trans. Inform. Theory, vol. IT-25, no. 4, pp. 373–380, July 1979.
15. H. Goodglass, A. Wingfield, M. R. Hyde, and J. C. Theurkauf, "Category specific dissociations in naming and recognition by aphasic patients," Cortex, vol. 22, pp. 87–102, 1986.
16. I. Grabec, "Self-organization based on the second maximum entropy principle," First IEE Int. Conf. on Artificial Neural Networks, Conference Publication No. 313. (London, 1989) pp. 12–16.
17. D. H. Graf and W. R. LaLonde, "A neural controller for collision-free movement of general robot manipulators," Proc. IEEE Int. Conf. on Neural Networks, ICNN-88 (San Diego, Cal., 1988) pp. I-77-I-84.
18. D. H.Graf and W. R. LaLonde, "Neuroplanners for hand/eye coordination," Proc. Int. Joint Conf. on Neural Networks, IJCNN 89 (Washington, DC, 1989) pp. II-543-II–548.
19. R. M. Gray, "Vector quantization," IEEE ASSP Mag., vol. 1, pp. 4–29, 1984.
20. S. Grossberg, "On the development of feature detectors in the visual cortex with applications to learning and reaction-diffusion systems," Biol. Cybern., vol. 21, pp. 145–159,1976.
21. "Adaptive pattern classification and universal recoding: I. Parallel development and coding of neural feature detectors; II. Feedback, expectation, olfaction, illusions," Biol. Cybern., vol. 23, pp. 121–134 and 187–202, 1976.
22. R. Hecht-Nielsen, "Applications of counter propagation network," Neural Networks, vol. 1, pp. 131–139,1988.
23. A. Hemani and A. Postula, "Scheduling by self organisation," Proc. Int. joint. Conf. on Neural Networks, IJCNN-90-WASH-DC (Washington, DC, 1990) pp. II-543-II-546.
24. R. E. Hodges and C.-H. Wu, "A method to establish an autonomous self-organizing feature map," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH-DC (Washington, DC, 1990) pp. 1–517–1–520.
25. R. E. Hodges, C.-H. Wu, and C.-J. Wang, "Parallelizing the self-organizing feature map on multi-processor systems," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH–DC (Washington, DC, 1990) pp. II-141–II-144.
26. R. M. Holdaway, "Enhancing supervised learning algorithms via self-organization," Proc. Int. Joint Conf. on Neural Networks, IJCNN 89 (Washington, D.C., 1989) pp. II-523-II-529.
27. J. J. Hopfield, "Neural networks and physical systems with emergent collective computational abilities," Proc. Nat. Acad. Sci. USA, vol. 79, pp. 2554–2558, 1982.
28. H. Iwamida, S. Katagiri, E. McDermott, and Y. Tohkura, "A hybrid speech recognition system using HMMs with an LVQ-trained codebook," ATR Technical Report TR-A-0061, ATR Auditory and Visual Perception Research Laboratories, 1989.
29. J. H. Kaas, R. J. Nelson, M. Sur, C. S. Lin, and M. M. Merzenich, "Multiple representations of the body within the primary somatosensory cortex of primates," Science, vol. 204, pp. 521–523, 1979.
30. J. H. Kaas, M. M. Merzenich, and H. P. Killackey, "The reorganization of somatosensory cortex following peripheral nerve damage in adult and developing mammals," Annual Rev. Neurosci., vol. 6, pp. 325–356, 1983.
31. J. Kangas, T. Kohonen, and J. Laaksonen, "Variants of self–organizing maps," IEEE Trans. Neural Networks, vol. 1, pp. 93–99, 1990.
32. A. Kertesz, Ed., Localization in Neuropsychology. New York, N.Y.: Academic Press, 1983.
33. E. I. Knudsen, S. du Lac, and S. D. Esterly, "Computational maps in the brain," Ann. Rev. Neurosci., vol. 10, pp. 41–65, 1987.
34. T. Kohonen, "Automatic formation of topological maps of patterns in a self-organizing system," Proc. 2nd Scandinavian Conf. on Image Analysis (Espoo, Finland, 1981) pp. 214–220.
35. "Self-organized formation of topologically correct feature maps," Biol. Cybern., vol. 43, pp. 59–69, 1982.
36. "Clustering, taxonomy, and topological maps of patterns," Proc. Sixth Int. Conf. on Pattern Recognition (Munich, Germany, 1982) pp. 114–128.
37. "Dynamically expanding context, with application to the correction of symbol strings in the recognition of continuous speech," Proc. Eighth Int. Conf. on Pattern Recognition (Paris, France, 1986) pp. 1148–1151.
38. "Learning Vector Quantization," Helsinki University of Technology, Laboratory of Computer and Information Science, Report TKK-F-A-601,1986.
39. Content-Addressable Memories, 2nd ed. Berlin, Heidelberg, Germany: Springer-Verlag, 1987.
40. "Self-learning inference rules by dynamically expanding context," Proc. IEEE First Ann. Int. Conf. on Neural Networks (San Diego, CA, 1987) pp. II-3-II-9.
41. "An introduction to neural networks," Neural Networks, vol. 1, pp. 3–16,1988.
42. "The ‘neural’ phonetic typewriter," Computer, vol. 21, pp. 11–22, March 1988.
43. "Learning vector quantization," Neural Networks, vol. 1, suppl. 1, p. 303, 1988.
44. Self-Organization and Associative Memory, 3rd ed. Berlin, Heidelberg, Germany: Springer-Verlag, 1989.
45. T. Kohonen, G. Barna, and R. Chrisley, "Statistical pattern recognition with neural networks: Benchmarking studies," Proc. IEEE Int. Conf. on Neural Networks, ICNN-88 (San Diego, Cal., 1988) pp. 1-61–1-68.
46. T. Kohonen, K. Makisara, and T. Saramaki, "Phonotopic maps—insightful representation of phonological features for speech recognition," Proc. Seventh Int. Conf. on Pattern Recognition (Montreal, Canada, 1984) pp. 182–185.
47. T. Kohonen, K. Raivio, O. Simula, O. Venta, and J. Hen-riksson, "An adaptive discrete-signal detector based on self-organizing maps," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH-DC (Washington, DC, 1990) pp. II-249-II-252.
48. T. Kohonen, K. Torkkola, M. Shozakai, J. Kangas, and O. Venta, "Microprocessor implementation of a large vocabulary speech recognizer and phonetic typewriter for Finnish and Japanese," Proc. European Conference on Speech Technology (Edinburgh, 1987) pp. 377–380.
49. H. J. Kushner and D. S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems. New York, Berlin: Springer-Verlag, 1978.
50. J. Lampinen and E. Oja, "Fast self-organization by the probing algorithm," Proc. Int. Joint Conf. on Neural Networks, IJCNN 89 (Washington, DC, 1989) pp. II-503-II-507.
51. A. LaVigna, "Nonparametric classification using learning vector quantization," Ph.D. Thesis, University of Maryland, 1989.
52. J. Lazarro, S. Ryckebusch, M. A. Mahowald, and C. A. Mead, "Winner-take-all network of O(N) complexity," in advances in Neural Information Processing Systems I, D. S. Touretzky, Ed. San Mateo, CA: Morgan Kaufmann Publishers, 1989.
53. S. E. Levinson, L. R. Rabiner, and M. M. Sondhi, "An introduction to the application of the theory of probabilistic functions of a Markov process to automatic speech recognition," Bell Syst. Tech. J., pp. 1035–1073, Apr. 1983.
54. Y. Linde, A. Buzo, and R. M. Gray, "An algorithm for vector quantization," IEEE Trans. Communication, vol. COM-28, pp. 84–95, 1980.
55. S. P. Luttrell, "Self-organizing multilayer topographic mappings," Proc. IEEE Int. Conf. on Neural Networks, ICNN–88 (San Diego, CA, 1988) pp. 1-93-1–100.
56. "Hierarchical self-organizing networks," First IEE Int. Conf. on Artificial Neural Networks, Conference Publication No. 313. (London, 1989) pp. 2–6.
57. "Self-organization: A derivation from first principles of a class of learning algorithms," Proc. Int. Joint Conf. on Neural Networks, IJCNN 89 (Washington, DC, 1989) pp. II-495-II-498.
58. J. Makhoul, S. Roucos, and H. Gish, "Vector quantization in speech coding," Proc. IEEE, vol. 73, pp. 1551–1588, 1985.
59. Ch. V. D. Malsburg, "Self-organization of orientation sensitive cells in the striate cortex," Kybernetik, vol. 14, pp. 85–100, 1973.
60. Ch. V. D. Malsburg and D. J. Willshaw, "How to label nerve cells so that they can interconnect in an ordered fashion," Proc. Natl. Acad. Sci. USA, vol. 74, pp. 5176–5178, 1977.
61. R. Mann and S. Haykin, "A parallel implementation of Kohonen feature maps on the Warp systolic computer," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH-DC (Washington, DC, 1990) pp. II-84-II-87.
62. K. M. Marks and K. F. Goser, "Analysis of VLSI process data based on self-organizing feature maps," Proc. Neuro-Nfmes’88 (Nîmes, France, 1988) pp. 337–347.
63. J. Martinetz, H. J. Ritter, and K. J. Schulten, "Three-dimensional neural net for learning visuomotor coordination of a robot arm," IEEE Trans. Neural Networks, vol. 1, pp. 131–136,1990.
64. J. Max, "Quantizing for minimum distortion," IRE Trans. Inform. Theory, vol. IT-6, no. 2, pp. 7–12, Mar. 1960.
65. R. A. McCarthy and E. K. Warrington, "Evidence for modality specific meaning systems in the brain," Nature, vol. 334, pp. 428–430, 1988.
66. E. McDermott and S. Katagiri, "Shift-invariant, multi-category phoneme recognition using Kohonen’s LVQ2," Proc. Int. Conf. on Acoustics, Signals, and Speech, ICASSP 89 (Glasgow, Scotland) pp. 81–84.
67. P. McKenna and E. K. Warrington, "Category-specific naming preservation: A single case study,";. Neurol. Neurosurg. Psychiatry, vol. 41, pp. 571–574, 1978.
68. R. Miikkulainen and M.–G. Dyer, "Forming global representations with extended backpropagation," Proc. IEEE Int. Conf. on Neural Networks, ICNN 88 (San Diego, CA, 1988) pp. 285–292.
69. P. Morasso, "Neural models of cursive script handwriting," Proc. Int. Joint Conf. on Neural Networks, IJCNN 89 (Washington, DC, 1989) pp. II-539-II-542.
70. J. T. Murphy, H. C. Kwan, W. A. MacKay, and Y. C. Wong, "Spatial organization of precentral cortex in awake primates, III, Input-output coupling,";. Neurophysiol., vol.41, pp. 1132–1139, 1977.
71. N. M. Nasrabadi and Y. Feng, "Vector quantization of images based upon the Kohonen Self-Organizing Feature Maps," Proc. IEEE Int. Conf. on Neural Networks, ICNN-88 (San Diego, CA, 1988) pp. 1-101–1-108.
72. M. M. Nass and L. N. Cooper, "Atheoryforthedevelopment of feature detecting cells in visual cortex," Biol. Cybern., vol. 19, pp. 1–18, 1975.
73. E. K. Neumann, D. A. Wheeler, J. W. Burnside, A. S. Bernstein, and J. C. Hall, "A technique for the classification and analysis of insect courtship song," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH-DC, (Washington, DC, 1990) pp. II-257–262.
74. Y. Nishikawa, H. Kita, and A. Kawamura, "NN/I: a neural network which divides and learns environments," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH-DC, (Washington, DC, 1990) pp. I-684-I-687.
75. G. A. Ojemann, "Brain organization for language from the perspective of electrical stimulation mapping," Behav. Brain Sci., vol. 2, pp. 189–230, 1983.
76. J. Orlando, R. Mann, and S. Haykin, "Radar classification of sea-ice using traditional and neural classifiers," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH-DC, (Washington, DC, 1990) pp. II-263-II-266.
77. K. J. Overton and M. A. Arbib, "The branch arrow model of the formation of retinotectal connections," Biol. Cybern., vol. 45, pp. 157–175, 1982.
78. K. J. Pearson, L. H. Finkel, and G. M. Edelman, "Plasticity in the organization of adult cerebral maps: a computer simulation based on neuronal group selection," J. Neurosci., vol. 12, pp. 4209–4223, 1987.
79. R. Perez, L. Glass, and R. J. Shlaer, "Development of specificity in cat visual cortex,"J. Math. Biol., vol. 1, pp. 275–288, 1975.
80. S. E. Petersen, P. T. Fox, M. I. Ponsner, M. Mintun, and M. E. Raichle, "Positron emission tomographic studies of the cortical anatomy of single-word processing," Nature, vol. 331, pp. 585–589, 1988.
81. M. Porat and Y. Y. Zeevi, "The generalized Gabor scheme of image representation in biological and machine vision," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-10, pp. 452–468, 1988.
82. H. Ritter, "Combining self-organizing maps," Proc. Int. Joint Conf. on Neural Networks, IJCNN 89 (Washington, DC, 1989) pp. II-499-II-502.
83. "Asymptotic level density for a class of vector quantization processes," Helsinki University of Technology, Lab. of Computer and Information Science, Report A9, 1989.
84. H. Ritter and T. Kohonen, "Self-organizing semantic maps," Biol. Cybern., vol. 61, pp. 241–254, 1989.
85. H. J. Ritter, T. M. Martinetz, and K. J. Schulten, "Topology conserving maps for learning visuo-motor-coordination," Neural Networks, vol. 2, pp. 159–168, 1989.
86. H. Ritter and K. Schulten, "On the stationary state of Kohonen’s self-organizing sensory mapping," Biol. Cybern., vol. 54, pp. 99–106, 1986.
87. "Topology conserving mappings for learning motor tasks," Proc. Neural Networks for Computing, AIP Conference (Snowbird, Utah, 1986) pp. 376–380.
88. "Extending Kohonen’s self-organizing mapping algorithm to learn ballistic movements," NATO ASI Series, vol. F41, pp. 393–406,1988.
89. "Kohonen’s self–organizing maps: exploring their computational capabilities," Proc. IEEE Int. Conf. on Neural Networks, ICNNN 88 (San Diego, CA, 1988) pp. 1-109–1-116.
90. "Convergency properties of Kohonen’s topology conserving maps: Fluctuations, stability and dimension selection," Biol. Cybern., vol. 60, pp. 59–71, 1989.
91. R. A. Reale and T. J. Imig, "Tonotopic organization in auditory cortex of the cat,"J. Comp. Neurol., vol. 192, pp. 265–291, 1980.
92. H. Robbins and S. Monro, "A stochastic approximation method," Ann. Math. Statist., vol. 22, pp. 400–407, 1951.
93. E. T. Rolls, "Neurons in the cortex of the temporal lobe and in the amygdala of the monkey with responses selective for faces," Hum. Neurobiol., vol. 3, pp. 209–222, 1984.
94. D. E. Rumelhart, G. E. Hinton, and R. J. Williams, "Learning internal representations by error propagation," in Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Vol. 1.: Foundations, D. E. Rumelhart, J. L. McClelland and the PDP research group, Eds. Cambridge, Mass.: MIT Press, 1986, pp. 318–362.
95. J. K. Samarabandu and O. E. Jakubowicz, "Principles of sequential feature maps in multi-level problems," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH-DC (Washington, DC, 1990) pp. II-683-II-686.
96. P. G. Schyns, "Expertise acquisition through concepts refinement in a self-organizing architecture," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH-DC (Washington, DC, 1990) pp. I-236-I-239.
97. D. L. Sparks and J. S. Nelson, "Sensory and motor maps in the mammalian superior colliculus," TINS, vol. 10, pp. 312–317, 1987.
98. N. Suga and W. E. O’Neill, "Neural axis representing target range in the auditory cortex of the mustache bat," Science, vol. 206, pp. 351–353, 1979.
99. N. V. Swindale, "A model for the formation of ocular dominance stripes," Proc. R. Soc, vol. B208, pp. 243–264, 1980.
100. A. Takeuchi and S. Amari, "Formation of topographic maps and columnar microstructures," Biol. Cybern., vol. 35, pp. 63–72, 1979.
101. T. Tanaka, M. Naka, and K. Yoshida, "Improved back-propagation combined with LVQ," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH-DC (Washington, DC, 1990) pp. 1-731–734.
102. V. Tryba, K. M. Marks, U. Rückert, and K. Goser, "Selbstorganisierende Karten als lernende klassifizierende Speicher," ITG Fachbericht, vol. 102, pp. 407–419, 1988.
103. A. R. Tunturi, "Physiological determination of the arrangement of the afferent connections to the middle ectosylvian auditory area in the dog," Am. J. Physiol., vol. 162, pp. 489–502, 1950.
104. "The auditory cortex of the dog," Am. J. Physiol., vol. 168, pp. 712–717, 1952.
105. A.Waibel,T. Hanazawa, G. Hinton, K. Shikano,and K.J. Lang, "Phoneme recognition using time-delay neural networks," IEEE Trans. Acoust. Speech and Signal Processing, vol. ASSP-37, pp. 382–339, 1989.
106. E. K. Warrington, "The selective impairment of semantic memory," Q. J. Exp. Psychol., vol. 27, pp. 635–657, 1975.
107. E. K. Warrington and R. A. McCarthy, "Category specific access dysphasia," Brain, vol. 106, pp. 859–878,1983.
108. "Categories of knowledge," Brain, vol. 110, pp. 1273- 1296, 1987.
109. E. K. Warrington and T. Shallice, "Category-specific impairments," Brain, vol. 107, pp. 829–854, 1984.
110. D.J. Willshaw and Ch. V. D. Malsburg, "How patterned neural connections can be set up by self-organization," Proc. R. Soc. London, vol. B 194, pp. 431–445, 1976.
111. "A marker induction mechanism for the establishment of ordered neural mappings: its application to the retinotectal problem," Proc. R. Soc. London, vol. B 287, pp. 203–243, 1979.
112. L. Xu and E. Oja, "Vector pair correspondence by a simplified counter-propagation model: a twin topographic map," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH–DC (Washington, DC, 1990) pp. II-531–534.
113. "Adding top-down expectation into the learning procedure of self-organizing maps," Proc. Int. Joint. Conf. on Neural Networks, IJCNN-90-WASH-DC (Washington, DC, 1990) pp. I-735–738.
114. A. Yamadori and M. L. Albert, "Word category aphasia," Cortex, vol. 9, pp. 112–125, 1973.
115. P. L. Zador, "Asymptotic quantization error of continuous signals and the quantization dimension," IEEE Trans. Inform. Theory, vol. IT-28, pp. 139–149, March 1982.
116. S. Zeki, "The representation of colours in the cerebral cortex," Nature, vol. 284, pp. 412–418, 1980.