Self-organization and associative memory: 3rd edition
Self-organization and associative memory: 3rd edition
Topology representing networks
Neural Networks
Dynamic cell structure learns perfectly topology preserving map
Neural Computation
On the distribution and convergence of feature space in self-organizing maps
Neural Computation
GTM: the generative topographic mapping
Neural Computation
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
Kalman filter implementation of self-organizing feature maps
Neural Computation
Neural maps and topographic vector quantization
Neural Networks
Self-Organizing Maps
Controlling the magnification factor of self-organizing feature maps
Neural Computation
Growing a hypercubical output space in a self-organizing feature map
IEEE Transactions on Neural Networks
Topology preservation in self-organizing feature maps: exact definition and measurement
IEEE Transactions on Neural Networks
Self-organizing feature maps with self-adjusting learning parameters
IEEE Transactions on Neural Networks
Self organized mapping of data clusters to neuron groups
Neural Networks
Applied Intelligence
Improved SOM learning using simulated annealing
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
AI'04 Proceedings of the 17th Australian joint conference on Advances in Artificial Intelligence
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An important technique for exploratory data analysis is to form a mapping from the high-dimensional data space to a low-dimensional representation space such that neighborhoods are preserved. A popular method for achieving this is Kohonen's self-organizing map (SOM) algorithm. However, in its original form, this requires the user to choose the values of several parameters heuristically to achieve good performance. Here we present the Auto-SOM, an algorithm that estimates the learning parameters during the training of SOMs automatically. The application of Auto-SOM provides the facility to avoid neighborhood violations up to a user-defined degree in either mapping direction. Auto-SOM consists of a Kalman filter implementation of the SOM coupled with a recursive parameter estimation method. The Kalman filter trains the neurons' weights with estimated learning coefficients so as to minimize the variance of the estimation error. The recursive parameter estimation method estimates the width of the neighborhood function by minimizing the prediction error variance of the Kalman filter. In addition, the "topographic function" is incorporated to measure neighborhood violations and prevent the map's converging to configurations with neighborhood violations. It is demonstrated that neighborhoods can be preserved in both mapping directions as desired for dimension-reducing applications. The development of neighborhood-preserving maps and their convergence behavior is demonstrated by three examples accounting for the basic applications of self-organizing feature maps.