Title :
Performance evaluation of Hopfield network for simple examples
Author_Institution :
Dept. of Comput. Sci. & Electron., Kyushu Inst. of Technol., Iizuka, Japan
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;
Conference_Titel :
Circuits and Systems, 1991., IEEE International Sympoisum on
Print_ISBN :
0-7803-0050-5
DOI :
10.1109/ISCAS.1991.176637
