Abstract
In this paper we present a detailed investigation of the statistical and convergence properties of the Kohonen's Self-Organising Mapping (SOM) in any dimension. Using an extend Central Limit Theorem, we prove that the feature space in SOM learning is an approximation to multiple Gausssian distributed stochastic processes, which will eventually converge in the meansquare sense to the density centres of the input probabilistic sub-spaces. We also demonstrate that combining the SOM with a Kalman filter can smooth and accelerate the learning and convergence of the SOM. In our applications, we show that such a modified SOM achieves a much better performance, namely a lower distortion than the original algorithm, especially in early training stages, and at low extra computational cost. This modification will be particular useful when the available training set is small.
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References
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© 1993 Springer-Verlag Berlin Heidelberg
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Yin, H., Allinson, N.M. (1993). On the distribution of feature space in Self-Organising mapping and convergence accelerating by a Kalman algorithm. In: Mira, J., Cabestany, J., Prieto, A. (eds) New Trends in Neural Computation. IWANN 1993. Lecture Notes in Computer Science, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56798-4_162
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DOI: https://doi.org/10.1007/3-540-56798-4_162
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