Performance evaluation of Hopfield network for simple examples

Author

Urahama, Kiichi

Author_Institution

Dept. of Comput. Sci. & Electron., Kyushu Inst. of Technol., Iizuka, Japan

fYear

1991

fDate

11-14 Jun 1991

Firstpage

1412

Abstract

The performance guarantees of the Hopfield network are given for two simple graph problems. A lower bound of cutsize is evaluated for the maximum cut problem through the analysis of eigenvalues at equilibrium states. The condition of constraint satisfaction and an upper bound of the cutsize are given for the graph bipartitioning problem. In addition, an effective numerical scheme is proposed to integrate the differential equations of the Hopfield network by using the backward Euler formula with one-step Gauss-Seidel relaxation. Theoretical estimates of the performance of the algorithm are verified experimentally

Keywords

graph theory; neural nets; topology; Hopfield network; backward Euler formula; constraint satisfaction; cutsize; differential equations; eigenvalues; equilibrium states; graph bipartitioning problem; graph problems; maximum cut problem; one-step Gauss-Seidel relaxation; performance guarantees; Computer science; Differential equations; Eigenvalues and eigenfunctions; Estimation theory; Gaussian processes; Hopfield neural networks; Hypercubes; Neural networks; Neurons; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 1991., IEEE International Sympoisum on

Print_ISBN

0-7803-0050-5

Type

conf

DOI

10.1109/ISCAS.1991.176637

Filename

176637