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

Volume

6

Issue

6

fYear

1995

fDate

11/1/1995 12:00:00 AM

Firstpage

1365

Lastpage

1374

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;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/72.471371

Filename

471371