Self-organization and associative memory: 3rd edition
Self-organization and associative memory: 3rd edition
A Bayesian interpretation for the exponential correlation associative memory
Pattern Recognition Letters
Asymptotic Level Density of the Elastic Net Self-Organizing Feature Map
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Annealing and the normalized N-cut
Pattern Recognition
Hierarchical, unsupervised learning with growing via phase transitions
Neural Computation
Neural Computation
Differential priors for elastic nets
IDEAL'05 Proceedings of the 6th international conference on Intelligent Data Engineering and Automated Learning
Registration of microscopic iris image sequences using probabilistic mesh
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Object recognition with constrained elastic models
Mathematical and Computer Modelling: An International Journal
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
An elastic net clustering algorithm for non-linearly separable data
ACIIDS'13 Proceedings of the 5th Asian conference on Intelligent Information and Database Systems - Volume Part I
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This paper analyzes the elastic net approach (Durbin and Willshaw 1987) to the traveling salesman problem of finding the shortest path through a set of cities. The elastic net approach jointly minimizes the length of an arbitrary path in the plane and the distance between the path points and the cities. The tradeoff between these two requirements is controlled by a scale parameter K. A global minimum is found for large K, and is then tracked to a small value. In this paper, we show that (1) in the small K limit the elastic path passes arbitrarily close to all the cities, but that only one path point is attracted to each city, (2) in the large K limit the net lies at the center of the set of cities, and (3) at a critical value of K the energy function bifurcates. We also show that this method can be interpreted in terms of extremizing a probability distribution controlled by K. The minimum at a given K corresponds to the maximum a posteriori (MAP) Bayesian estimate of the tour under a natural statistical interpretation. The analysis presented in this paper gives us a better understanding of the behavior of the elastic net, allows us to better choose the parameters for the optimization, and suggests how to extend the underlying ideas to other domains.