W4(n+1)=W(an)+A.;(n)n(n)(x(m)-w(m) (n)=o0(1-n/N)n(n)=no(1-n/() FIGURE 20 18 Kohonen SOFM neighbors using a Gaussian neighborhood function A. The output PEs are arranged in linear or two-dimensional neighborhoods(Fig. 20.18 Kohonen SOFM networks produce a mapping between the continuous input space to the discrete output space preserving topological properties of the input space(i.e, local neighbors in the input space are mapped to neighbors in the output space). During training, both the spatial neighborhoods and the learning constant are decreased slowly by starting with a large neighborhood oo, and decreasing it (No controls the scheduling) The initial step size no also needs to be scheduled(by k) The Kohonen SOFM network is useful to project the input to a subspace as an alternative to PCA networks The topological properties of the output space provide more information about the input than straight C. M. Bishop, Neural Networks for Pattern Recognition, New York: Oxford University Press, 1995 de Vries and J C. Principe, The gamma model -a new neural model for temporal processing, Neural S. Haykin, Neural Networks: A Comprehensive Foundation, New York: Macmillan, 1994 S. Y. Kung, Digital Neural Networks, Englewood Cliffs, N.J. Prentice-Hall, 1993 J. M. Zurada, Artificial Neural Systems, West Publishing, 1992. Further Information The literature in this field is voluminous. we decided to limit the references to text books for an engineering audience, with different levels of sophistication. Zurada is the most accessible text, Haykin the most compre hensive. Kung provides interesting applications of both PCA networks and nonlinear signal processing and system identification. Bishop concentrates on the design of pattern classifiers. Interested readers are directed to the following journals for more information: IEEE Transactions on Signal Processing, IEEE Tranactions on Neural Networks, Neural Networks, Neural Computation, and Proceedings of the Neural Information Processing System Conference(NIPS) c 2000 by CRC Press LLC© 2000 by CRC Press LLC neighbors using a Gaussian neighborhood function L. The output PEs are arranged in linear or two-dimensional neighborhoods (Fig. 20.18) Kohonen SOFM networks produce a mapping between the continuous input space to the discrete output space preserving topological properties of the input space (i.e., local neighbors in the input space are mapped to neighbors in the output space). During training, both the spatial neighborhoods and the learning constant are decreased slowly by starting with a large neighborhood s0, and decreasing it (N0 controls the scheduling). The initial step size h0 also needs to be scheduled (by K). The Kohonen SOFM network is useful to project the input to a subspace as an alternative to PCA networks. The topological properties of the output space provide more information about the input than straight clustering. References C. M. Bishop, Neural Networks for Pattern Recognition, New York: Oxford University Press, 1995. de Vries and J. C. Principe, “The gamma model — a new neural model for temporal processing,” Neural Networks, Vol. 5, pp. 565–576, 1992. S. Haykin, Neural Networks: A Comprehensive Foundation, New York: Macmillan, 1994. S. Y. Kung, Digital Neural Networks, Englewood Cliffs, N.J.: Prentice-Hall, 1993. J. M. Zurada, Artificial Neural Systems, West Publishing, 1992. Further Information The literature in this field is voluminous. We decided to limit the references to text books for an engineering audience, with different levels of sophistication. Zurada is the most accessible text, Haykin the most compre￾hensive. Kung provides interesting applications of both PCA networks and nonlinear signal processing and system identification. Bishop concentrates on the design of pattern classifiers. Interested readers are directed to the following journals for more information: IEEE Transactions on Signal Processing, IEEE Tranactions on Neural Networks, Neural Networks, Neural Computation, and Proceedings of the Neural Information Processing System Conference (NIPS). FIGURE 20.18 Kohonen SOFM