6,003 research outputs found
A "Cellular Neuronal" Approach to Optimization Problems
The Hopfield-Tank (1985) recurrent neural network architecture for the
Traveling Salesman Problem is generalized to a fully interconnected "cellular"
neural network of regular oscillators. Tours are defined by synchronization
patterns, allowing the simultaneous representation of all cyclic permutations
of a given tour. The network converges to local optima some of which correspond
to shortest-distance tours, as can be shown analytically in a stationary phase
approximation. Simulated annealing is required for global optimization, but the
stochastic element might be replaced by chaotic intermittency in a further
generalization of the architecture to a network of chaotic oscillators.Comment: -2nd revised version submitted to Chaos (original version submitted
6/07
Winner-relaxing and winner-enhancing Kohonen maps: Maximal mutual information from enhancing the winner
The magnification behaviour of a generalized family of self-organizing
feature maps, the Winner Relaxing and Winner Enhancing Kohonen algorithms is
analyzed by the magnification law in the one-dimensional case, which can be
obtained analytically. The Winner-Enhancing case allows to acheive a
magnification exponent of one and therefore provides optimal mapping in the
sense of information theory. A numerical verification of the magnification law
is included, and the ordering behaviour is analyzed. Compared to the original
Self-Organizing Map and some other approaches, the generalized Winner Enforcing
Algorithm requires minimal extra computations per learning step and is
conveniently easy to implement.Comment: 6 pages, 5 figures. For an extended version refer to cond-mat/0208414
(Neural Computation 17, 996-1009
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