## Self-organizing mapsThe Self-Organizing Map (SOM), with its variants, is the most popular artificial neural network algorithm in the unsupervised learning category. Many fields of science have adopted the SOM as a standard analytical tool: in statistics, signal processing, control theory, financial analyses, experimental physics, chemistry and medicine. A new area is organization of very large document collections. The SOM is also one of the most realistic models of the biological brain functions.This new edition includes a survey of over 2000 contemporary studies to cover the newest results; the case examples were provided with detailed formulae, illustrations and tables; a new chapter on software tools for SOM was written, other chapters were extended or reorganized. |

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### Contents

Mathematical Preliminaries | 1 |

Justification of Neural Modeling | 59 |

The Basic SOM | 85 |

Copyright | |

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accuracy adaptive algorithm analysis applications approximation array Artificial Neural Networks ASSOM assumed asymptotic basic basis vectors brain cell classification clustering codebook vectors components computing context convergence corresponding cortex defined denoted described dimensionality distance dot product dynamic elements equation error Euclidean feature filters IEEE Service Center input signals input vector Joint Conf Kangas Kohonen lattice learning learning-rate factor linear linear subspace mathematical matrix method neighborhood function Networks IEEE Service Neural Networks IEEE neuron nodes nonlinear operation optimal orthogonal output parameters pattern recognition phonemes Piscataway probability density function problem Proc reference vectors relating respectively rrii samples scalar self-organizing Self-Organizing Map sequence signal space simulation speech recognition statistical step stochastic stochastic approximation subset subspace supervised learning symbols synaptic tion topology transformation two-dimensional unit values vector quantization Voronoi Voronoi tessellation wavelets weight vectors whereby winner zero