{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T22:22:13Z","timestamp":1649110933885},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Neur. Syst."],"published-print":{"date-parts":[[1991,1]]},"abstract":"<jats:p> Based on the assumption that most probability densities in real life can be approximated by a mixture of Gaussian densities, we propose here a three-layer adaptive network with each neuron in the lower hidden layer representing a Gaussian basis function (covariance matrix equal to [Formula: see text] where I is a unit matrix) to estimate various probability densities and serve as a Bayes classifier. The width of the basis function [Formula: see text] may be the same for all neurons in this layer or it may vary from one neuron to another. This paper investigates the effectiveness of the network for both cases and presents a localized learning algorithm to adjust the network parameters. The network was trained with artificial data derived from known mixtures of memoryless Gaussian sources as well as exponential and Gamma densities. The performance of the network as a pattern density estimator was measured in terms of the relative difference between the target probability density function (p.d.f.) which generates the training and testing data and the network output representing the estimation. Samples from two mixtures corresponding to two classes were used to test the network capability as a classifier by comparing its error rate against that of a Bayes classifier. Both one- and two-dimensional cases were explored. The successfulness of the network depended on how well the target p.d.f.\u2019s were represented by the training samples, the number of hidden neurons employed in the network and how thoroughly the network was trained. It was also found that allowing each basis function to have an independent width had a predominant effect on the network performance. <\/jats:p>","DOI":"10.1142\/s0129065791000194","type":"journal-article","created":{"date-parts":[[2004,11,24]],"date-time":"2004-11-24T19:50:24Z","timestamp":1101325824000},"page":"211-220","source":"Crossref","is-referenced-by-count":5,"title":["A THREE-LAYER ADAPTIVE NETWORK FOR PATTERN DENSITY ESTIMATION AND CLASSIFICATION"],"prefix":"10.1142","volume":"02","author":[{"given":"Jian-xiong","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Computer Science University of Hong Kong, Hong Kong"},{"name":"Institute of Image Processing and Pattern Recognition Shanghai Jiaotong University, P.R.C"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chorkin","family":"Chan","sequence":"additional","affiliation":[{"name":"Department of Computer Science University of Hong Kong, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"container-title":["International Journal of Neural Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129065791000194","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T12:20:44Z","timestamp":1565180444000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129065791000194"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,1]]},"references-count":0,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[1991,1]]}},"alternative-id":["10.1142\/S0129065791000194"],"URL":"https:\/\/doi.org\/10.1142\/s0129065791000194","relation":{},"ISSN":["0129-0657","1793-6462"],"issn-type":[{"value":"0129-0657","type":"print"},{"value":"1793-6462","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,1]]}}}