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Gimenez Martinez
Victor

Sanchez Torrubia
Maria Gloria

Torres Blanc
Carmen
A Statistical Convergence Application for the Hopfield Networks
Institute of Information Theories and Applications FOI ITHEA
byncnd
pub
 matematicas
 informatica
public
Learning systems, pattern recognition, graph theory, recurrent neural networks.
When Recurrent Neural Networks (RNN) are going to be used as Pattern Recognition systems, the problem to be considered is how to impose prescribed prototype vectors ctors ξ 1 ,ξ 2 , ...,ξ p , as fixed points. The synaptic matrix W should be interpreted as a sort of sign correlation matrix of the prototypes, In the classical approach. The weak point in this approach, comes from the fact that it does not have the appropriate tools to deal efficiently with the correlation between the state vectors and the prototype vectors The capacity of the net is very poor because one can only know if one given vector is adequately correlated with the prototypes or not and we are not able to know what its exact correlation degree. The interest of our approach lies precisely in the fact that it provides these tools. In this paper, a geometrical vision of the dynamic of states is explained. A fixed point is viewed as a point in the Euclidean plane R2. The retrieving procedure is analyzed trough statistical frequency distribution of the prototypes. The capacity of the net is improved and the spurious states are reduced. In order to clarify and corroborate the theoretical results, together with the formal theory, an application is presented.
published
2008
Information Theory and Applications
15
1
8488
Informatica
Matematica_Aplicada
TRUE
13100513
http://www.foibg.com/ijita/vol15/ijitafv15.htm