Abstract
A multilayer hierarchical self-organizing map (HSOM) is discussed as an unsupervised clustering method. The HSOM is shown to form arbitrarily complex clusters, in analogy with multilayer feedforward networks. In addition, the HSOM provides a natural measure for the distance of a point from a cluster that weighs all the points belonging to the cluster appropriately. In experiments with both artificial and real data it is demonstrated that the multilayer SOM forms clusters that match better to the desired classes than do direct SOM’s, classical k-means, or Isodata algorithms.
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References
R. Hecht-Nielsen, “Theory of backpropagation neural network,” in Proc. IEEE Int. Joint Conf. on Neural Networks, vol. I, Washington, DC, 1989, pp. 593–611.
R. Hecht-Nielsen, Neurocomputing, Addison-Wesley: Reading, MA, 1990.
K. Hornik, M. Stinchcombe, and H. White, “Multi-layer feedforward networks are universal approximators,” Neural Net., vol. 2, pp. 359–366, 1989.
M.D. Richard and R.P. Lippmann, “Neural network classifiers estimate Bayesian a posteriori probabilities,” Neural Comput., vol. 3, 1991, pp. 461–483.
T. Kohonen, Self-Organization and Associative Memory, Springer-Verlag: Berlin, 1989.
T. Kohonen, “Self-organized formation of topologically correct feature maps,” Biol. Cybernet., vol. 43, pp. 59–69, 1982.
S. Amari, “Topographic organization of nerve fields,” Bull. Math. BioL, vol. 42, pp. 339–364, 1980.
H. Ritter and K. Schulten, “Kohonen’s self-organizing maps: exploring their computational capabilities,” in Proc. IEEE Int. Joint Conf. on Neural Networks, vol. 1, San Diego, CA, 1988, pp. 109–116.
S.P. Luttrell, “Self-organisation: A derivation from first principles of a class of learning algorithms,” Proc. IEEE Int. Joint Conf. on Neural Networks, vol. 2, Washington, DC, 1989, pp. 495–498.
T. Kohonen, “Self-organizing maps: optimization approaches,” in Artificial Neural Networks, vol. 2, T. Kohonen, K. Mäkisara, J. Kangas, and O. Simula, eds., North-Holland: Amsterdam, 1991, pp. 981–990.
P.A. Devijver and J. Kittler, Pattern Recognition: A Statistical Approach, Prentice Hall: London, 1982.
J.0 Gower and G.J.S Ross, “Minimum spanning trees and single linkage cluster analysis,” Appl. Statist., vol. 18, pp. 54–64, 1969.
S.P. Luttrell, “Image compression using a multilayer neural network,” Pattern Recog. Lett., vol. 10, pp. 1–7, 1989.
J. Lampinen, “Distortion tolerant pattern recognition using invariant transformations and hierarchical SOFM clustering,” in Artificial Neural Networks, vol. 1, T. Kohonen, K. Mäkisara, J. Kangas, and O. Simula, eds., North-Holland: Amsterdam, 1991, pp. 99–104.
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© 1993 Springer Science+Business Media New York
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Lampinen, J., Oja, E. (1993). Clustering Properties of Hierarchical Self-Organizing Maps. In: Dougherty, E.R., Astola, J. (eds) Mathematical Nonlinear Image Processing. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3148-7_12
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DOI: https://doi.org/10.1007/978-1-4615-3148-7_12
Publisher Name: Springer, Boston, MA
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