《智能控制智能控制智能控制 (36).pdf》由会员分享,可在线阅读,更多相关《智能控制智能控制智能控制 (36).pdf(11页珍藏版)》请在得力文库 - 分享文档赚钱的网站上搜索。
1、Introduction Radial basis function(RBF)NN is artificial neural networks for application toproblems of supervised learning:Regression Classification Time series prediction System controlD.S.BroomheadDavid LoweLinear-separabilityNot linearly separableBasic Architecture of RBFperforms a non-linear mapp
2、ing from input space into higher dimensional spaceGaussian functionHidden layer Input layer Hidden layer Hidden units provide a set of basis function High dimensionality Output layer Linear combination of hidden functionsGaussians in RBF Gaussian Distribution Gaussian para.In RBF Gaussian centers uj
3、 Standard deviation?Alinear combination of Gaussians to approximate any function.22()()exp()2jjxuh xFinding the RBF Parameters Use the K-means algorithm to find ujOutcome:There are K clusters with means representing the centroid of each clusters.Advantages:(1)A fast and simple algorithm.(2)Reduce th
4、e effects of noisy samples.Finding the RBF Parameters Use K nearest neighbor rule to find the function width The objective is to cover the training points so that a smooth fit of the training samples can be achieved211KkikiccKk-th nearest neighbor of ciFinding the RBF Parameters Determining weights
5、w using the least square method210()NMpjjpjpjEywxu0 Ewwyp:the desired output for pattern pRBF Learning ProcessX,YK-meansK-NearestNeighborGaussianFunctionleast square methodujujwRBF Learning Process Updating by gradient descent We have the following update equations:w tw te xxiMw tw te xitte xwxxctct
6、cte xwxxctiiwpippNiiwppNijijpiippjijijpNijijcpiippjijijpN()()()(),()()()()()()()()()()()()()11 210111123121 when when Radial basis function network:uses radial basis functions as activation functions.The output of the network:linear combination of radial basis functions of the inputs andneuron parameters.Summary