A Theoretical Analysis of Neural Networks with Nonzero Diagonal Elements

Masaya OHTA  Yoichiro ANZAI  Shojiro YONEDA  Akio OGIHARA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A   No.3   pp.284-291
Publication Date: 1993/03/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on the 5th Karuizawa Workshop on Circuits and Systems)
neural networks,  combinatorial optimization problems,  nonzero diagonal elements,  eigen value,  eigen vector,  

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This article analyzes the property of the fully interconnected neural networks as a method of solving combinatorial optimization problems in general. In particular, in order to escape local minimums in this model, we analyze theoretically the relation between the diagonal elements of the connection matrix and the stability of the networks. It is shown that the position of the global minimum point of the energy function on the hyper sphere in n dimensional space is given by the eigen vector corresponding the maximum eigen value of the connection matrix. Then it is shown that the diagonal elements of the connection matrix can be improved without loss of generality. The equilibrium points of the improved networks are classified according to their properties, and their stability is investigated. In order to show that the change of the diagonal elements improves the potential for the global minimum search, computer simulations are carried out by using the theoretical values. In according to the simulation result on 10 neurons, the success rate to get the optimum solution is 97.5%. The result shows that the improvement of the diagonal elements has potential for minimum search.