{"title":"最优泛化神经网络","authors":"H. Ogawa, E. Oja","doi":"10.1109/IJCNN.1991.170648","DOIUrl":null,"url":null,"abstract":"The problem of approximating a real function f of L variables, given only in terms of its values y/sub 1/,. . .,y/sub M/ at a small set of sample points x/sub 1/,. . .,x/sub M/ in R/sup L/, is studied in the context of multilayer neural networks. Using the theory of reproducing kernels of Hilbert spaces, it is shown that this problem is the inverse of a linear model relating the values y/sub m/ to the function f itself. The authors consider the least-mean-square training criterion for nonlinear multilayer neural network architectures that learn the training set completely. The generalization property of a neural network is defined in terms of function reconstruction and the concept of the optimally generalizing neural network (OGNN) is proposed. It is a network that minimizes a criterion given in terms of the true error between the original function f and the reconstruction f/sub 1/ in the function space, instead of minimizing the error at the sample points only. As an example of the OGNN, a projection filter (PF) criterion is considered and the PFGNN is introduced. The network is of the two-layer nonlinear-linear type.<<ETX>>","PeriodicalId":211135,"journal":{"name":"[Proceedings] 1991 IEEE International Joint Conference on Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1991-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Optimally generalizing neural networks\",\"authors\":\"H. Ogawa, E. Oja\",\"doi\":\"10.1109/IJCNN.1991.170648\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem of approximating a real function f of L variables, given only in terms of its values y/sub 1/,. . .,y/sub M/ at a small set of sample points x/sub 1/,. . .,x/sub M/ in R/sup L/, is studied in the context of multilayer neural networks. Using the theory of reproducing kernels of Hilbert spaces, it is shown that this problem is the inverse of a linear model relating the values y/sub m/ to the function f itself. The authors consider the least-mean-square training criterion for nonlinear multilayer neural network architectures that learn the training set completely. The generalization property of a neural network is defined in terms of function reconstruction and the concept of the optimally generalizing neural network (OGNN) is proposed. It is a network that minimizes a criterion given in terms of the true error between the original function f and the reconstruction f/sub 1/ in the function space, instead of minimizing the error at the sample points only. As an example of the OGNN, a projection filter (PF) criterion is considered and the PFGNN is introduced. The network is of the two-layer nonlinear-linear type.<<ETX>>\",\"PeriodicalId\":211135,\"journal\":{\"name\":\"[Proceedings] 1991 IEEE International Joint Conference on Neural Networks\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-11-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[Proceedings] 1991 IEEE International Joint Conference on Neural Networks\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IJCNN.1991.170648\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[Proceedings] 1991 IEEE International Joint Conference on Neural Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IJCNN.1991.170648","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The problem of approximating a real function f of L variables, given only in terms of its values y/sub 1/,. . .,y/sub M/ at a small set of sample points x/sub 1/,. . .,x/sub M/ in R/sup L/, is studied in the context of multilayer neural networks. Using the theory of reproducing kernels of Hilbert spaces, it is shown that this problem is the inverse of a linear model relating the values y/sub m/ to the function f itself. The authors consider the least-mean-square training criterion for nonlinear multilayer neural network architectures that learn the training set completely. The generalization property of a neural network is defined in terms of function reconstruction and the concept of the optimally generalizing neural network (OGNN) is proposed. It is a network that minimizes a criterion given in terms of the true error between the original function f and the reconstruction f/sub 1/ in the function space, instead of minimizing the error at the sample points only. As an example of the OGNN, a projection filter (PF) criterion is considered and the PFGNN is introduced. The network is of the two-layer nonlinear-linear type.<>