{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T00:15:00Z","timestamp":1767917700565,"version":"3.49.0"},"reference-count":40,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Neur. Syst."],"published-print":{"date-parts":[[2009,8]]},"abstract":"<jats:p> In this paper, a fully complex-valued radial basis function (FC-RBF) network with a fully complex-valued activation function has been proposed, and its complex-valued gradient descent learning algorithm has been developed. The fully complex activation function, sech(.) of the proposed network, satisfies all the properties needed for a complex-valued activation function and has Gaussian-like characteristics. It maps C<jats:sup>n<\/jats:sup> \u2192 C, unlike the existing activation functions of complex-valued RBF network that maps C<jats:sup>n<\/jats:sup> \u2192 R. Since the performance of the complex-RBF network depends on the number of neurons and initialization of network parameters, we propose a K-means clustering based neuron selection and center initialization scheme. First, we present a study on convergence using complex XOR problem. Next, we present a synthetic function approximation problem and the two-spiral classification problem. Finally, we present the results for two practical applications, viz., a non-minimum phase equalization and an adaptive beam-forming problem. The performance of the network was compared with other well-known complex-valued RBF networks available in literature, viz., split-complex CRBF, CMRAN and the CELM. The results indicate that the proposed fully complex-valued network has better convergence, approximation and classification ability. <\/jats:p>","DOI":"10.1142\/s0129065709002026","type":"journal-article","created":{"date-parts":[[2009,9,2]],"date-time":"2009-09-02T04:09:31Z","timestamp":1251864571000},"page":"253-267","source":"Crossref","is-referenced-by-count":103,"title":["A FULLY COMPLEX-VALUED RADIAL BASIS FUNCTION NETWORK AND ITS LEARNING ALGORITHM"],"prefix":"10.1142","volume":"19","author":[{"given":"R.","family":"SAVITHA","sequence":"first","affiliation":[{"name":"School of Electrical and Electronics Engineering, Nanyang Technological University, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"SURESH","sequence":"additional","affiliation":[{"name":"CIST, Korea University, Seoul, Republic of South Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N.","family":"SUNDARARAJAN","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronics Engineering, Nanyang Technological University, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0129065708001464"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0129065708001415"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0129065708001439"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0129065708001403"},{"key":"rf5","first-page":"165","volume":"18","author":"Rao V. 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