Hyperparameter selection for self-organizing maps
Neural Computation
GTM: the generative topographic mapping
Neural Computation
Self-Organizing Maps
An analysis of the elastic net approach to the traveling salesman problem
Neural Computation
Arbitrary elastic topologies and ocular dominance
Neural Computation
The elastic net as visual category representation: visualisation and classification
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part II
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The elastic net and related algorithms, such as generative topographic mapping, are key methods for discretized dimension-reduction problems. At their heart are priors that specify the expected topological and geometric properties of the maps. However, up to now, only a very small subset of possible priors has been considered. Here we study a much more general family originating from discrete, high-order derivative operators. We show theoretically that the form of the discrete approximation to the derivative used has a crucial influence on the resulting map. Using a new and more powerful iterative elastic net algorithm, we confirm these results empirically, and illustrate how different priors affect the form of simulated ocular dominance columns.