Hyperparameter selection for self-organizing maps
Neural Computation
GTM: the generative topographic mapping
Neural Computation
Neural Processing Letters
Kernel-based equiprobabilistic topographic map formation
Neural Computation
Learning and Design of Principal Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Clustering by Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Unified Model for Probabilistic Principal Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Data Mining and Knowledge Discovery
Computers and Operations Research
Kernel-based topographic map formation by local density modeling
Neural Computation
Self Organizing Map and Sammon Mapping for Asymmetric Proximities
ICANN '01 Proceedings of the International Conference on Artificial Neural Networks
Data visualisation and manifold mapping using the ViSOM
Neural Networks - New developments in self-organizing maps
Convergence and Ordering of Kohonen's Batch Map
Neural Computation
Kernel class-wise locality preserving projection
Information Sciences: an International Journal
Visualizing asymmetric proximities with SOM and MDS models
Neurocomputing
An experimental study on asymmetric self-organizing map
IDEAL'11 Proceedings of the 12th international conference on Intelligent data engineering and automated learning
Electricity load forecasting using self organizing maps
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part II
Probabilistic principal surface classifier
FSKD'05 Proceedings of the Second international conference on Fuzzy Systems and Knowledge Discovery - Volume Part II
Clustering based on principal curve
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Extending the SOM algorithm to visualize word relationships
IDA'05 Proceedings of the 6th international conference on Advances in Intelligent Data Analysis
A new SOM algorithm for electricity load forecasting
ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I
Journal of Medical Systems
Information Sciences: an International Journal
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Kohonen's self-organizing map, when described in a batchprocessing mode, can be interpreted as a statistical kernelsmoothing problem. The batch SOM algorithm consists of two steps.First, the training data are partitioned according to the Voronoiregions of the map unit locations. Second, the units are updated bytaking weighted centroids of the data falling into the Voronoiregions, with the weighing function given by the neighborhood.Then, the neighborhood width is decreased and steps 1, 2 arerepeated. The second step can be interpreted as a statisticalkernel smoothing problem where the neighborhood functioncorresponds to the kernel and neighborhood width corresponds tokernel span. To determine the new unit locations, kernel smoothingis applied to the centroids of the Voronoi regions in thetopological space. This interpretation leads to some new insightsconcerning the role of the neighborhood and dimensionalityreduction. It also strengthens the algorithm's connection with thePrincipal Curve algorithm. A generalized self-organizing algorithmis proposed, where the kernel smoothing step is replaced with anarbitrary nonparametric regression method.