1、按一下以編輯母片標題樣式,*,按一下以編輯母片,第二層,第三層,第四層,第五層,函數的近似,函數近似(,function approximation),：,在於使用,linear projection theorem,去描述一個實數向量,x,的函數,f(x)：,及,其中 稱為基底函數(,basis function),神經網路與函數的近似,神經網路與函數的近似,函數近似的主要工作：,選擇基底函數 計算,weights wi,決定基底函數的個數,N,多層前饋式神經網路的基底函數：,RBF,神經網路學習,RBF,神經網路的學習機制：,誤差倒傳遞+,Gaussian,中心(,Mean),和變異數(,
2、Variance),的調整,監督式學習：使用誤差倒傳遞同時調整,weight、Gaussian,中心和變異數,自組織學習：兩階段學習。第一階段根據輸入資料做叢聚分析(,clustering),例如,K-means,或,SOM,方法，每個叢聚的中心和變異數即可求出；第一階段再以誤差倒傳遞調整,weight。,基底函數個數的,Trade-off,個數太少，可能無法涵蓋整個,domain,如果個數太多而且資料夾帶許多雜訊，則函數可能會被雜訊掩蓋。,機率式神經網路(,PNN),Gaussian,機率密度函數的估測：,：,平滑參數,PNN,的,特色,:,1.選擇適當平滑參數,值。,2.使用,Bayesi
3、an,最佳化。,3.,容許資料誤差。,4.,適合稀疏取樣,(,sparse sampling),。,5.,當資料數目增加時,可將參數,較小，不須重新訓練。,Bias-Variance,矛盾,RNFN v.s.FIS,Both the RBFN and the FIS under consideration use the same aggregation method(namely,either weighted average or weighted sum)to derive their overall outputs.,The number of receptive field unit
4、s in the RBFN is equal to the number of fuzzy if-then rules in the FIS.,Each radial basis function of the RBFN is equal to a multidimensional composite MF of the premise part of a fuzzy rule in the FIS.One way to achieve this is to use Gaussian MFs with the same variance in a fuzzy rule,and apply pr
5、oduct to calculate the firing strength.The multiplication of these Gaussian MFs becomes a multidimensional Gaussian function a radial basis function in RBFN.,RNFN v.s.FIS,Corresponding radial basis function and fuzzy rule should have the same response function.That is,they should have the same constant terms(for the original RBFN and zero-order Sugeno FIS)or linear equations(for the extended RBFN and first-order Sugeno FIS).,The functional equivalence between FIS and RBFN cross-fertilizes both computing paradigms.Further details are presented in Section 12.4.,
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