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Concept
Neural gas
Summary
Neural gas is an artificial neural network, inspired by the self-organizing map and introduced in 1991 by Thomas Martinetz and Klaus Schulten. The neural gas is a simple algorithm for finding optimal data representations based on feature vectors. The algorithm was coined "neural gas" because of the dynamics of the feature vectors during the adaptation process, which distribute themselves like a gas within the data space. It is applied where data compression or vector quantization is an issue, for example speech recognition, or pattern recognition. As a robustly converging alternative to the k-means clustering it is also used for cluster analysis.
Given a probability distribution of data vectors and a finite number of feature vectors .
With each time step , a data vector randomly chosen from is presented. Subsequently, the distance order of the feature vectors to the given data vector is determined. Let denote the index of the closest feature vector, the index of the second closest feature vector, and the index of the feature vector most distant to . Then each feature vector is adapted according to
with as the adaptation step size and as the so-called neighborhood range. and are reduced with increasing . After sufficiently many adaptation steps the feature vectors cover the data space with minimum representation error.
The adaptation step of the neural gas can be interpreted as gradient descent on a cost function. By adapting not only the closest feature vector but all of them with a step size decreasing with increasing distance order, compared to (online) k-means clustering a much more robust convergence of the algorithm can be achieved. The neural gas model does not delete a node and also does not create new nodes.
A number of variants of the neural gas algorithm exists in the literature so as to mitigate some of its shortcomings. More notable is perhaps Bernd Fritzke's growing neural gas, but also one should mention further elaborations such as the Growing When Required network and also the incremental growing neural gas.
Official source
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