Title :
Harmonic analysis of homogeneous networks
Author :
Wolfe, William J. ; Rothman, Jay A. ; Chang, Edward H. ; Aultman, William ; Ripton, Garth
Author_Institution :
Dept. of Comput. Sci. & Eng., Colorado Univ., Denver, CO, USA
fDate :
11/1/1995 12:00:00 AM
Abstract :
We introduce a generalization of mutually inhibitory networks called homogeneous networks. Such networks have symmetric connection strength matrices that are circulant (one-dimensional case) or block circulant with circulant blocks (two-dimensional case). Fourier harmonics provide universal eigenvectors, and we apply them to several homogeneous examples: k-wta, k-cluster, on/center off/surround, and the assignment problem. We also analyze one nonhomogeneous case: the subset-sum problem. We present the results of 10000 trials on a 50-node k-cluster problem and 100 trials on a 25-node subset-sum problem
Keywords :
Fourier analysis; Hopfield neural nets; eigenvalues and eigenfunctions; harmonic analysis; Fourier harmonics; assignment problem; block circulant symmetric connection strength matrices; harmonic analysis; homogeneous networks; k-cluster network; k-wta network; mutually inhibitory networks; on/center off/surround network; subset-sum problem; universal eigenvectors; Associative memory; CADCAM; Computer aided manufacturing; Design optimization; Harmonic analysis; Mathematical model; Neurons; Out of order; Retina; Symmetric matrices;
Journal_Title :
Neural Networks, IEEE Transactions on
