H. Bauer, M. Herrman, and T. Villman. Neural maps and topographic vector quantization. Neural Networks, 12(4-5):659--676, 1999. Home/Search Document Details and Download
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Mobile Robot Local Navigation with a Polar Neural Map - Lagoudakis (1998) (Correct)
....F is composed by a finite number of neurons, in which case a one to one mapping is ruled out. However, with a very large number of neurons, F can be treated as a neural computational continuum. The most interesting case is the many to one mapping where, in fact, categorizes the input signals [BaHV97] The restricted inverse mapping (i) will assign a single prototype signal x i to neuron i, known as the receptive field center (or reference prototype vector,oroptimal stimulus) The true inverse mapping 9 will return the whole subarea X i of the signal space that corresponds to neuron ....
....classical (e.g. feed forward) neural network models and other techniques, like vector quantization, is perhaps the neighborhood preservation property. Neighborhood relationships that exist between similar signals in X are reproduced by neighborhood relationships between similar neurons in F [BaHV97] Finally, the interconnections between neurons in F, which express the similarity between the reference vectors of connected neurons [WiSe98] define a dynamic behavior of the neural field F. An important aspect in this context is the stability related to the dynamic evolution of the state of ....
Bauer, Hans-Ulrich, Michael Herrmann, and Thomas Vilmann, "Neural Maps and Topographic Vector Quantization," submitted to Neural Networks.
Mathematical Aspects of Neural Networks - Hammer, Villmann (2003) (Correct)
....Thereby, the topographic function follows the exact definition [141] However, the topographic function takes much computational effort. Although not based on the mathematical exact definition, the topographic product [10] and its derivatives [139] seem to be the best tools for practical use [9]. Violations of topology preservation do not only arise because of convergence problems: if the lattice dimension DA differs from the effective data dimension Def t E)v topological mismatches occur. The respective theory of meta and instable states is initially based on Fokker Planck ....
H.-U. Bauer, M. Herrmann, and T. Viiimann. Neural maps and topographic vector quantization. Neural Networks, 12(4 5):659 676, 1999.
Second-Order Learning in Self-Organizing Maps - Der, Herrmann (1999) (1 citation) Self-citation (Herrmann) (Correct)
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H.-U. Bauer, M. Herrmann, and T. Villmann. Neural maps and topographic vector quantization. To appear in Neural Networks, 1999.
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H.-U. Bauer, M. Herrmann, and T. Villmann. Neural Maps and Topographic Vector Quantization. Neural Networks 12(4-5):659-676, 1999.
Anastassia Angelopoulou - And (Correct)
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H. Bauer, M. Herrman, and T. Villman. Neural maps and topographic vector quantization. Neural Networks, 12(4-5):659--676, 1999.
Topological Correlation - And (Correct)
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H. U. Bauer, M. Herrmann, and T. Villmann. Neural maps and topographic vector quantization. Neural Networks, 12:659--676, 1999.
Bibliography of Self-Organizing Map (SOM) Papers.. - Merja Oja, Samuel.. (2002) (Correct)
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Bauer, H. U., Herrmann, M., and Villmann, T. (1999). Neural maps and topographic vector quantization. Neural Networks, 12(4--5):659--676.
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H. U. Bauer, M. Herrmann, and T. Villmann. Neural maps and topographic vector quantization. Neural Networks, 12:659--676, 1999.
A Self-Organizing Map with Expanding Force for Data.. - Shum, Jin, Leung, Wong (Correct)
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H. U. Bauer, M. Herrmann, and T. Villmann. Neural maps and topographic vector quantization. Neural Networks, 12:659--676, 1999.
Mathematical Aspects of Neural Networks - Hammer (2003) (Correct)
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H.-U. Bauer, M. Herrmann, and T. Villmann. Neural maps and topographic vector quantization. Neural Networks, 12(4-5):659--676, 1999.
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