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The Self-Organizing Maps: Background, Theories, Extensions and Applications

  • Hujun Yin
Part of the Studies in Computational Intelligence book series (SCI, volume 115)

For many years, artificial neural networks (ANNs) have been studied and used to model information processing systems based on or inspired by biological neural structures. They not only can provide solutions with improved performance when compared with traditional problem-solving methods, but also give a deeper understanding of human cognitive abilities. Among various existing neural network architectures and learning algorithms, Kohonen’s selforganizing map (SOM) [46] is one of the most popular neural network models. Developed for an associative memory model, it is an unsupervised learning algorithm with a simple structure and computational form, and is motivated by the retina-cortex mapping. Self-organization in general is a fundamental pattern recognition process, in which intrinsic inter- and intra-pattern relationships among the stimuli and responses are learnt without the presence of a potentially biased or subjective external influence. The SOM can provide topologically preserved mapping from input to output spaces. Although the computational form of the SOM is very simple, numerous researchers have already examined the algorithm and many of its problems, nevertheless research in this area goes deeper and deeper — there are still many aspects to be exploited.

In this Chapter, we review the background, theories and statistical properties of this important learning model and present recent advances from various pattern recognition aspects through a number of case studies and applications. The SOM is optimal for vector quantization. Its topographical ordering provides the mapping with enhanced fault- and noise-tolerant abilities. It is also applicable to many other applications, such as dimensionality reduction, data visualization, clustering and classification. Various extensions of the SOM have been devised since its introduction to extend the mapping as effective solutions for a wide range of applications. Its connections with other learning paradigms and application aspects are also exploited. The Chapter is intended to serve as an updated, extended tutorial, a review, as well as a reference for advanced topics in the subject.

Keywords

Neural Network Local Linear Embed Kernel Principal Component Analysis Neighbourhood Function Nonlinear Principal Component Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Allinson NM, Obermayer K, Yin H 2002 Neural Networks (Special Issue on New Developments in Self-Organising Maps), 15: 937-1155.Google Scholar
  2. 2.
    Allinson NM, Yin H 1999 Self-organising maps for pattern recognition. In: Oja E, Kaski S (eds.) Kohonen Maps, Elsevier, Amsterdam, The Netherlands: 111-120.Google Scholar
  3. 3.
    Ameri S-I(1980) Topographic organisation of nerve fields. Bulletin Mathematical Biology, 42: 339-364.Google Scholar
  4. 4.
    Andras P 2002 Kernel-Kohonen networks. Intl. J. Neural Systems, 12: 117-135.Google Scholar
  5. 5.
    Banfield JD, Raftery AE 1992 Ice floe identification in satellite images using mathematical morphology and clustering about principal curves. J. American Statistical Association, 87: 7-16.Google Scholar
  6. 6.
    Barreto GA, Araujo AFR, Ducker C, Ritter H 2002 A distributed robotic con-trol system based on a temporal self-organizing neural network. IEEE Trans. Systems, Man and Cybernetics - C, 32: 347-357.Google Scholar
  7. 7.
    Bauer H-U, Pawelzik KR 1992 Quantifying the neighborhood preservation of self-organizing feature maps. IEEE Trans. Neural Networks, 3: 570-579.Google Scholar
  8. 8.
    Bishop CM, Svensén M, Williams CKI 1998 GTM: the generative topographic mapping. Neural Computation, 10: 215-235.Google Scholar
  9. 9.
    Bruce V, Green PR 1990 Visual Perception: Physiology, Psychology and Ecology (2nd ed.), Lawerence Erlbraum Associates, East Essex, UK.Google Scholar
  10. 10.
    Chang K-Y, Ghosh J 2001 A unified model for probabilistic principal surfaces. IEEE Trans. Pattern Analysis and Machine Intelligence, 23: 22-41.Google Scholar
  11. 11.
    Chappell GJ, Taylor JG 1993 The temporal Kohonen map. Neural Networks, 6: 441-445.Google Scholar
  12. 12.
    Cottrell M, Fort JC 1986 A stochastic model of retinotopy: a self-organising process. Biological Cybernetics, 53: 405-411.zbMATHMathSciNetGoogle Scholar
  13. 13.
    Cottrell M, Verleysen M 2006 Neural Networks (Special Issue on Advances in Self-Organizing Maps), 19: 721-976.Google Scholar
  14. 14.
    Cox TF, Cox MAA 1994 Multidimensional Scaling, Chapman & Hall, London, UK.zbMATHGoogle Scholar
  15. 15.
    de Bolt E, Cottrell M, Verleysen M 2002 Statistical tools to assess the reliability of self-organising maps. Neural Networks, 15: 967-978.Google Scholar
  16. 16.
    De Ridder D, Duin RPW 1997 Sammon mapping using neural networks: a comparison. Pattern Recognition Letters, 18: 1307-1316.Google Scholar
  17. 17.
    Dersch DR, Tavan P 1995 Asymptotic level density in topological feature maps. IEEE Trans. Neural Networks, 6: 230-236.Google Scholar
  18. 18.
    Durbin R, Mitchison G(1990) A dimension reduction framework for understanding cortical maps. Nature, 343: 644-647.Google Scholar
  19. 19.
    Erwin E, Obermayer K, Schulten K 1992 Self-organising maps: ordering, convergence properties and energy functions. Biological Cybernetics, 67: 47-55.zbMATHGoogle Scholar
  20. 20.
    Erwin E, Obermayer K, Schulten K 1992 Self-organising maps: stationary states, metastability and convergence rate. Biological Cybernetics, 67: 35-45.zbMATHGoogle Scholar
  21. 21.
    Estévez PA, Figueroa CJ 2006 Online data visualization using the neural gas network. Neural Networks, 19: 923-934.zbMATHGoogle Scholar
  22. 22.
    Ferguson KL, Allinson NM 2004 Efficient video compression codebooks using SOM-based vector quantisation. Proc. IEE - Vision, Image and Signal Processing, 151: 102-108.Google Scholar
  23. 23.
    Freeman R, Yin H 2004 Adaptive topological tree structure (ATTS) for document organisation and visualisation. Neural Networks, 17: 1255-1271.zbMATHGoogle Scholar
  24. 24.
    Gaze RM 1970 The Information of Nerve Connections, Academic Press, London, UK.Google Scholar
  25. 25.
    Goodhill GJ, Sejnowski T 1997 A unifying objective function for topographic mappings. Neural Computation, 9: 1291-1303.Google Scholar
  26. 26.
    Graepel T, Burger M, Obermayer K 1997 Phase transitions in stochastic self-organizing maps. Physics Reviews E, 56: 3876-3890.Google Scholar
  27. 27.
    Haritopoulos M, Yin H, Allinson NM 2002 Image denoising using self-organising map-based nonlinear independent component analysis. Neural Networks, 15: 1085-1098.Google Scholar
  28. 28.
    Hastie T, Stuetzle W(1989) Principal curves. J. American Statistical Association, 84: 502-516.zbMATHMathSciNetGoogle Scholar
  29. 29.
    Haykin S 1998 Neural Networks: A Comprehensive Foundation (2nd ed.), Prentice Hall, Englewood Cliffs, NJ.Google Scholar
  30. 30.
    Hebb D 1949 Organisation of behavior, Wiley, New York, NY.Google Scholar
  31. 31.
    Herrmann M, Yang H 1996 Perspectives and limitations of self-organising maps in blind separation of source signals. In: Amari S-I, Xu L, Chan L-W, KIng I, Leung K-S (eds.) Proc. Intl. Conf. Neural Information Process-ing (ICONIP’96), 24-27 September, Hong Kong. Springer-Verlag, Singapore: 1211-1216.Google Scholar
  32. 32.
    Heskes T 1999 Energy functions for self-organizing maps, In: Oja E, Kaski S (eds.) Kohonen Maps, Elsevier, Amsterdam: 303-315.Google Scholar
  33. 33.
    Hodge VJ, Austin J 2001 Hierarchical growing cell structures: TreeGCS. IEEE Trans. Knowledge and Data Engineering, 13: 207-218.Google Scholar
  34. 34.
    Honkela T, Kaski S, Lagus K, Kohonen T (1997) WEBSOM-self-organizing maps of document collections. In: Proc. Workshop on Self-Organizing Maps (WSOM’97), 4-6 June, Helsinki, Finland. Helsinkis University of Technology: 310-315.Google Scholar
  35. 35.
    Hsu C-C 2006 Generalising self-organising map for categorical data. IEEE Trans. Neural Networks, 17: 294-304.Google Scholar
  36. 36.
    Hyvärinen A, Karhunen J, Oja E 2001 Independent Component Analysis. Wiley, New York, NY.Google Scholar
  37. 37.
    Hyvärinen A, Pajunen P 1999 Nonlinear independent component analysis: Existence and uniqueness results. Neural Networks, 12: 429-439.Google Scholar
  38. 38.
    Ishikawa M, Miikkulainen R, Ritter H 2004 Neural Networks (Special Issue on New Developments in Self-Organizing Systems), 17: 1037-1389.zbMATHGoogle Scholar
  39. 39.
    Karhunen J, Joutsensalo J 1995 Generalisation of principal component analysis, optimisation problems, and neural networks. Neural Networks, 8: 549-562.Google Scholar
  40. 40.
    Kaski S, Kangas J, Kohonen T 1998 Bibliography of self-organizing map (SOM) papers: 1981-1997. Neural Computing Surveys, 1: 1-176.Google Scholar
  41. 41.
    Kaski S, Kohonen T 1996 Exploratory data analysis by the self-organizing map: Structures of welfare and poverty in the world. In: Refenes A-PN, Abu-Mostafa Y, Moody J, Weigend A (eds.) Neural Networks in Financial Engineering, World Scientific, Singapore: 498-507.Google Scholar
  42. 42.
    Kegl B, Krzyzak A, Linder T, Zeger K 1998 A polygonal line algorithm for constructing principal curves. Neural Information Processing Systems (NIPS’98), 11: 501-507.Google Scholar
  43. 43.
    Kohonen T 1972 Correlation matrix memory. IEEE Trans. Computers, 21: 353-359.zbMATHGoogle Scholar
  44. 44.
    Kohonen T 1973 A new model for randomly organised associative memory. Intl. J. Neuroscience, 5: 27-29.Google Scholar
  45. 45.
    Kohonen T 1974 An adaptive associative memory principle. IEEE Trans. Computers, 23: 444-445.zbMATHGoogle Scholar
  46. 46.
    Kohonen T 1982 Self-organised formation of topologically correct feature map. Biological Cybernetics, 43: 56-69.MathSciNetGoogle Scholar
  47. 47.
    Kohonen T 1984 Self-organization and Associative Memory, Springer-Verlag, Berlin.zbMATHGoogle Scholar
  48. 48.
    Kohonen T 1986 Representation of sensory information in self-organising feature maps, and relation of these maps to distributed memory networks. Proc. SPIE, 634: 248-259.Google Scholar
  49. 49.
    Kohonen T 1987 Adaptive, associative, and self-organizing functions in neural computing, Applied Optics, 26: 4910-4918.Google Scholar
  50. 50.
    Kohonen T 1991 Self-organizing maps: optimization approaches. In: Kohonen T, Makisara K, Simula O, Kangas J (eds.) Artificial Neural Networks 2, North-Holland, Amsterdam, The Netherlands: 981-990.Google Scholar
  51. 51.
    Kohonen T 1995 The adaptive-subspace SOM (ASSOM) and its use for the implementation of invariant feature detection. In: Fogelman-Soulié, Gallinari P (eds.) Proc. Intl. Conf. Artificial Neural Systems (ICANN’95), 9-13 October, Paris, France. EC2 Nanterre, France, 1: 3-10.Google Scholar
  52. 52.
    Kohonen T 1996 Emergence of invariant-feature detectors in the adaptive-subspace self-organizing map. Biological Cybernetics, 75: 281-291.zbMATHGoogle Scholar
  53. 53.
    Kohonen T 1997 Self-Organising Maps (2nd ed.). Springer-Verlag, Berlin.Google Scholar
  54. 54.
    Kohonen T 1999 Comparison of SOM point densities based on different criteria. Neural Computation, 11: 2081-2095.Google Scholar
  55. 55.
    Kohonen T, Somervuo P 2002 How to make a large self-organising maps for nonvectorial data. Neural Networks, 15: 945-952.Google Scholar
  56. 56.
    Kramer MA 1991 Nonlinear principal component analysis using autoassociative neural networks. American Institute Chemical Engineers J.,37: 233-243.Google Scholar
  57. 57.
    Laaksonen J, Koskela M, Laakso S, Oja E 2000 PicSOM - content-based image retrieval with self-organizing maps. Pattern Recognition Letters, 21: 1199-1207.zbMATHGoogle Scholar
  58. 58.
    Lampinen J, Oja E 1992 Clustering properties of hierarchical self-organizing maps. J. Mathematical Imaging and Vision, 2: 261-272.zbMATHGoogle Scholar
  59. 59.
    Lau KW, Yin H, Hubbard S(2006) Kernel self-organising maps for classification. Neurocomputing, 69: 2033-2040.Google Scholar
  60. 60.
    LeBlanc M, Tibshirani RJ 1994 Adaptive principal surfaces. J. American Statistical Association, 89: 53-64.zbMATHGoogle Scholar
  61. 61.
    Lee RCT, Slagle JR, Blum H 1977 A triangulation method for the sequential mapping of points from n-space to two-space. IEEE Trans. Computers, 27: 288-292.Google Scholar
  62. 62.
    Lin S, Si J 1998 Weight-value convergence of the SOM algorithm for discrete input. Neural Computation, 10: 807-814.Google Scholar
  63. 63.
    Linde Y, Buzo A, Gray RM 1980 An algorithm for vector quantizer design. IEEE  Trans. Communications, 28: 84-95.Google Scholar
  64. 64.
    Lo ZP, Bavarian B 1991 On the rate of convergence in topology preserving neural networks. Biological Cybernetics, 65: 55-63.zbMATHMathSciNetGoogle Scholar
  65. 65.
    Lowe D, Tipping ME 1996 Feed-forward neural networks and topographic mappings for exploratory data analysis. Neural Computing and Applications, 4: 83-95.Google Scholar
  66. 66.
    Luttrell SP 1990 Derivation of a class of training algorithms. IEEE Trans. Neural Networks, 1: 229-232.Google Scholar
  67. 67.
    Luttrell SP 1991 Code vector density in topographic mappings: Scalar case, IEEE Trans. Neural Networks, 2: 427-436.Google Scholar
  68. 68.
    Luttrell SP(1994) A Bayesian analysis of self-organising maps. Neural Computation, 6: 767-794.zbMATHGoogle Scholar
  69. 69.
    MacDonald D, Fyfe C (2000) The kernel self organising map. In: Proc. 4th Intl. Conf. Knowledge-based Intelligence Engineering Systems and Applied Tech-nologies, 30 August - 1 September, Brighton, UK, IEEE Press, Piscataway, NJ: 317-320.Google Scholar
  70. 70.
    Malthouse EC 1998 Limitations of nonlinear PCA as performed with generic neural networks. IEEE Trans. Neural Networks, 9: 165-173.Google Scholar
  71. 71.
    Mao J, Jain AK 1995 Artificial Neural Networks for Feature Extraction and Multivariate Data Projection. IEEE Trans. Neural Networks, 6: 296-317.Google Scholar
  72. 72.
    Marr D 1969 A theory of cerebellar cortex. J. Physiology, 202: 437-70.Google Scholar
  73. 73.
    Marsland S, Shapiron J, Nehmzow U 2002 A self-organising network that grows when required. Neural Networks, 15: 1041-1058.Google Scholar
  74. 74.
    Martinetz TM, Schulten KJ 1991 A “neuralgas” network learns topologies. In: Kohonen T, Mäkisara K, Simula O, Kangas J (eds.) Artificial Neural Networks, NorthHolland, Amsterdam, The Netherlands: 397-402.Google Scholar
  75. 75.
    Martinetz TM, Schulten KJ 1994 Topology representing networks. Neural Networks, 7: 507-522.Google Scholar
  76. 76.
    Miikkulainen R 1990 Script recognition with hierarchical feature maps. Connection Science, 2: 83-101.Google Scholar
  77. 77.
    Miikkulainen R 1997 Dyslexic and category-specific aphasic impairments in a self-organizing feature map model of the lexicon. Brain and Language, 59: 334-366.Google Scholar
  78. 78.
    Mitchison G 1995 A type of duality between self-organising maps and minimal wiring. Neural Computation, 7: 25-35.Google Scholar
  79. 79.
    Möller-Levet CS, Yin H 2005 Modeling and analysis of gene expression time-series based on co-expression. Intl. J. Neural Systems, (Special Issue on Bioinformatics), 15: 311-322.Google Scholar
  80. 80.
    Möller-Levet CS, Yin H 2005 Circular SOM for temporal characterisation of modelled gene expressions. In: Gallagher M, Hogan J, Maire F (eds.) Proc. Intl. Conf. Intelligent Engineering Data Engineering and Automated Learning Conf. (IDEAL’05), 6-8 July, Brisbane, Australia. Lecture Notes in Computer Science 3578, Springer-Verlag, Berlin: 319-326.Google Scholar
  81. 81.
    Oja E (1989) Neural networks, principal components, and subspaces. Intl. J. Neural Systems, 1: 61-68.MathSciNetGoogle Scholar
  82. 82.
    Oja E 1995 PCA, ICA, and nonlinear Hebbian learning. In: Fogelman-Soulié F, Gallinari P (eds.) Proc. Intl. Conf. Artificial Neural Networks (ICANN’95), 9-13 October, Paris, France. EC2, Nanterre, France: 89-94.Google Scholar
  83. 83.
    Oja M, Kaski S, Kohonen T (2003) Bibliography of self-organizing map (SOM) papers: 1998-2001 addendum. Neural Computing Surveys, 3: 1-156.Google Scholar
  84. 84.
    Pajunen P, Hyvärinen A, Karhunen J 1996 Nonlinear blind source separation by self-organising maps. In: Amari S-I, Xu L, Chan L-W, King I, Leung K-S (eds.) Proc. Intl. Conf. Neural Information Processing (ICONIP’96), 24-27 September, Hong Kong. Springer-Verlag, Singapore: 1207-1210.Google Scholar
  85. 85.
    Pan ZS, Chen SC, Zhang DQ 2004 A kernel-base SOM classifier in input space. Acta Electronica Sinica, 32: 227-231 (in Chinese).Google Scholar
  86. 86.
    Pearson D, Hanna E, Martinez K 1990 Computer-generated cartoons. In: . Barlow H, Blakemore C, Weston-Smith M (eds.) Images and Understandings, Cambridge University Press, Cambridge, UK.Google Scholar
  87. 87.
    Ratcliff F 1965 Mach Bands: Quantitative Studies on Neural Networks in the Retina. Holden-Day, Inc., San Francisco, CA.Google Scholar
  88. 88.
    Rauber A, Merkl D, Dittenbach M 2002 The growing hierarchical self-organizing map: exploratory analysis of high-dimensional data. IEEE Trans. Neural Networks, 13: 1331-1341.Google Scholar
  89. 89.
    Ritter H 1991 Asymptotical level density for class of vector quantisation processes. IEEE Trans. Neural Networks, 2: 173-175.MathSciNetGoogle Scholar
  90. 90.
    Ritter H, Schulten K 1988 Convergence properties of Kohonen’s topology conserving maps: fluctuations, stability, and dimension selection. Biological Cybernetics, 60: 59-71.zbMATHMathSciNetGoogle Scholar
  91. 91.
    Ritter H, Martinetz T, Schulten K(1992) Neural Computation and Self-organising Maps: An Introduction. Addison-Wesley, Reading, MA.Google Scholar
  92. 92.
    Robbins H, Monro S 1952 A stochastic approximation method. Annals Mathematical Statistics, 22: 400-407.MathSciNetGoogle Scholar
  93. 93.
    Roweis ST, Saul LK 2000 Nonlinear dimensionality reduction by locally linear embedding. Science, 290: 2323-2326.Google Scholar
  94. 94.
    Sakrison DJ 1966 Stochastic approximation: A recursive method for solving regression problems. In: Balakrishnan V (ed.) Advances in Communication Systems: Theory and Applications 2, Academic Press, New York, NY: 51-100.Google Scholar
  95. 95.
    Sammon JW 1969 A nonlinear mapping for data structure analysis. IEEE Trans. Computers, 18: 401-409.Google Scholar
  96. 96.
    Sanger TD 1991 Optimal unsupervised learning in a single-layer linear feedforward network. Neural Networks, 2: 459-473.Google Scholar
  97. 97.
    Schölkopf B, Smola A, Müller KR 1998 Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10: 1299-131.Google Scholar
  98. 98.
    Seiffert U, Michaelis B 2001 Multi-dimensional self-organizing maps on mas-sively parallel hardware. In: Allinson N, Yin H, Allinson L, Slack J (eds.) Advances in Self-Organising Maps, Springer-Verlag, London: 160-166.Google Scholar
  99. 99.
    Shepherd GM 1988 Neurobiology (2nd ed.), Oxford University Press, Oxford, UK.Google Scholar
  100. 100.
    Sum J, Leung C-S, Chan L-W, Xu L 1997 Yet another algorithm which can generate topography map. IEEE Trans. Neural Networks, 8: 1204-1207.Google Scholar
  101. 101.
    Sutton RS, Barto AG, Williams RJ (1991) Reinforcement learning is direct adaptive optimal control. In: Proc. American Control Conf., 26-28 June, Boston, MA. IEEE Press, Piscataway, NJ: 2143-2146.Google Scholar
  102. 102.
    Tenenbaum JB, de Silva V, Langford JC 2000 A global geometric framework for nonlinear dimensionality reduction. Science, 290: 2319-2323.Google Scholar
  103. 103.
    Tibshirani R 1992 Principal curves revisited. Statistics and Computation, 2: 183-190.Google Scholar
  104. 104.
    Törönen P, Kolehmainen K, Wong G, Castrén E 1999 Analysis of gene expression data using self-organising maps. Federation European Biochemical Socities Letters, 451: 142-146.Google Scholar
  105. 105.
    Ultsch A 1993 Self-organising neural networks for visualisation and classification. In: Opitz O, Lausen B, Klar R (eds.) Information and Classification, Springer-Verlag, Berlin: 864-867.Google Scholar
  106. 106.
    Van Hulle MM(1998) Kernel-based equiprobabilitic topographic map formation. Neural Computation, 10: 1847-1871.Google Scholar
  107. 107.
    Van Hulle MM 2002 Kernel-based equiprobabilitic topographic map formation achieved with an information-theoretic approach. Neural Networks, 15: 1029-1040.Google Scholar
  108. 108.
    Varsta M, del Ruiz Millän J, Heikkonen J(1997) A recurrent self-organizing map for temporal sequence processing. Proc. ICANN’97, Lausanne, Switzerland. Springer-Verlag, Berlin: 197-202.Google Scholar
  109. 109.
    Villmann T, Der R, Herrmann M, Martinetz TM 1997 Topology preservation in self-organizing feature maps: exactdefinition and measurement. IEEE Trans. Neural Networks, 8: 256-266.Google Scholar
  110. 110.
    Voegtlin T(2002) Recursive self-organizing maps. Neural Networks,15: 979-992.Google Scholar
  111. 111.
    von der Malsburg C, Willshaw DJ 1973 Self-organization of orientation sensitive cells in the striate cortex. Kybernetik, 4: 85-100.Google Scholar
  112. 112.
    Walter J, Ritter H 1996 Rapid learning with parametrized self-organizing maps. Neurocomputing, 12: 131-153.zbMATHGoogle Scholar
  113. 113.
    Wang Y, Yin H, Zhou L-Z, Liu Z-Q 2006 Real-time synthesis of 3D animations by learning parametric gaussians using self-organizing mixture networks. In: King I, Wang J, Chan L, Wang D (eds.) Proc. Intl. Conf. Neural Information Processing (ICONIP’06), 2-6 October, Hong Kong. Lecture Notes in Computer Science 4233, Springer-Verlag, Berlin, II: 671-678.Google Scholar
  114. 114.
    Willshaw DJ, Buneman OP, Longnet-Higgins HC (1969) Non-holographic associative memory. Nature, 222: 960-962.Google Scholar
  115. 115.
    Willshaw DJ, von der Malsburg C 1976 How patterned neural connections can be set up by self-organization. Proc. Royal Society of London - Series B, 194: 431-445.Google Scholar
  116. 116.
    Wu S, Chow TWS 2005 PRSOM: A new visualization method by hybridizing multidimensional scaling and self-organizing map. IEEE Trans. Neural Networks, 16: 1362-1380.Google Scholar
  117. 117.
    Yin H 1996 Self-Organising Maps: Statistical Analysis, Treatment and Applications, PhD Thesis, Department of Electronics, University of York, UK.Google Scholar
  118. 118.
    Yin H 2001 Visualisation induced SOM (ViSOM). In: Allinson N, Yin H, Allinson L, Slack J (eds.) Advances in Self-Organising Maps, Springer-Verlag, London, UK: 81-88.Google Scholar
  119. 119.
    Yin H 2002 ViSOM-A novel method for multivariate data projection and structure visualisation. IEEE Trans. Neural Networks, 13: 237-243.Google Scholar
  120. 120.
    Yin H 2002 Data visualisation and manifold mapping using the ViSOM. Neural Networks, 15: 1005-1016.Google Scholar
  121. 121.
    Yin H 2003 Nonlinear multidimensional data projection and visualisation. In: Liu J, Cheung Y, Yin H (eds.) Proc. Intl. Conf. Intelligent Data Engineering and Automated Learning (IDEAL’03), 21-23 March, Hong Kong. Lecture Notes in Computer Science 2690, Springer-Verlag, Berlin: 377-388.Google Scholar
  122. 122.
    Yin H (2003) Resolution enhancement for the ViSOM. In: Proc. Workshop on Self-Organizing Maps, 11-14 September, Kitakyushu, Japan. Kyushu Institute of Technology: 208-212.Google Scholar
  123. 123.
    Yin H 2006. On the equivalence between kernel self-organising maps and self-organising mixture density networks. Neural Networks, 19: 780-784.zbMATHGoogle Scholar
  124. 124.
    Yin H (2007) Connection between self-organising maps and metric multidimensional scaling. In: Proc. Intl. Joint Conf. Neural Networks (IJCNN2007), 12-17 August, Orlando, FL. IEEE Press, Piscataway, NJ: (in press).Google Scholar
  125. 125.
    Yin H, Allinson NM 1994 Unsupervised segmentation of textured images using a hierarchical neural structure. Electronics Letters, 30: 1842-1843.Google Scholar
  126. 126.
    Yin H, Allinson NM 1995 On the distribution and convergence of the feature space in self-organising maps. Neural Computation, 7: 1178-1187.Google Scholar
  127. 127.
    Yin H, Allinson NM 1999 Interpolating self-organising map (iSOM). Electronics Letters, 35: 1649-1650.Google Scholar
  128. 128.
    Yin H, Allinson NM 2001 Self-organising mixture networks for probability density estimation. IEEE Trans. Neural Networks, 12: 405-411.Google Scholar
  129. 129.
    Yin H, Allinson NM 2001 Bayesian self-organising map for Gaussian mixtures. Proc. IEE - Vision, Image and Signal Processing, 148: 234-240.Google Scholar

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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hujun Yin
    • 1
  1. 1.School of Electrical and Electronic EngineeringThe University of ManchesterUK

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