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Networks and the Best Approximation Property

dc.date.accessioned2004-10-04T14:36:01Z
dc.date.accessioned2018-11-24T10:11:32Z
dc.date.available2004-10-04T14:36:01Z
dc.date.available2018-11-24T10:11:32Z
dc.date.issued1989-10-01en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/6017
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/1721.1/6017
dc.description.abstractNetworks can be considered as approximation schemes. Multilayer networks of the backpropagation type can approximate arbitrarily well continuous functions (Cybenko, 1989; Funahashi, 1989; Stinchcombe and White, 1989). We prove that networks derived from regularization theory and including Radial Basis Function (Poggio and Girosi, 1989), have a similar property. From the point of view of approximation theory, however, the property of approximating continous functions arbitrarily well is not sufficient for characterizing good approximation schemes. More critical is the property of best approximation. The main result of this paper is that multilayer networks, of the type used in backpropagation, are not best approximation. For regularization networks (in particular Radial Basis Function networks) we prove existence and uniqueness of best approximation.en_US
dc.format.extent22 p.en_US
dc.format.extent104037 bytes
dc.format.extent421671 bytes
dc.language.isoen_US
dc.subjectlearningen_US
dc.subjectnetworksen_US
dc.subjectregularizationen_US
dc.subjectbest approximationen_US
dc.subjectsapproximation theoryen_US
dc.titleNetworks and the Best Approximation Propertyen_US


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