BP算法——带有详细的说明
function aa=BP()clc
clear all
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% 函数输入 %
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P=-2:0.1:2;
T=1+sin(pi*P/4);
if size(P,2)~=size(T);error('input with ouput of sample not same');end
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% BP算法的参数设置 %
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Lr=0.1; %学习效率
goal=0.001; %期望误差最小值
max_epoch=5; %最大迭代次数
Layer_n=5; %隐含层的神经网络数
%神经网络的调整数：weight=Layer_n * input_n+ output_n * Layer_n
% bias=Layer_n + output_n
% for a network to be able to generalize ,it should have fewer parameters
% than there are data points in the training set
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=size(P);=size(T,1); %初始化隐含层和输出层的权重系数
weight1=rand(Layer_n,input_n);weight2=rand(output_n,Layer_n); %为防止等量调整，权重初始值为随机
bias1=rand(Layer_n,1);bias2=rand(size(output_n,1),1);
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% （二） 神经网络的训练 %
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for interation=1:1:max_epoch %迭代次数
EE=0;
for K=1:1:size(P,2)
p=P(:,K);
a1=fun1(weight1*p+bias1); %计算隐含层输出
a2=fun2(weight2*a1+bias2); %计算输出层输出
E=T(:,K)-a2; %误差计算
=stepdest(E,weight1 ,bias1 ,weight2, bias2,a1,p,Lr);
EE=EE+E.'*E;
end
if EE<goal; break; end
Er(interation,:)=EE; TT(interation,:)=interation; %误差保存
end
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% （三） 神经网络的计算 %
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for K=1:1:size(P,2)
p=P(:,K);
a1=fun1(weight1*p+bias1); %计算隐含层输出
a2=fun2(weight2*a1+bias2); %计算输出层输出
T2(:,K)=a2;
end
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% （四）性能对比
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figure(1)
plot(TT,Er,'r'); grid on; %画误差图像
figure(2)
plot(P,T,'b',P,T2,'r'); %画给的函数图像和神经网络的图像
end
function =stepdest(E,weight1 ,bias1, weight2, bias2,a1,p,Lr)
%标准梯度算法
Sout=-2*dfun2(weight2*a1+bias2).*E; %输出层的灵敏度计算
S1=dfun1(weight1*p+bias1).*(weight2.'*Sout); %第一层灵敏度的计算
weight2=weight2-Lr*Sout*a1.'; %更新权重
bias2=bias2-Lr*Sout;
weight1=weight1-Lr*S1*p.'; %权重更新
bias1=bias1-Lr*S1;
end
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% (五) 神经元的传递函数
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function F=fun1(X)
%Hyperbolic Tangent sigmoid
%F=(exp(X)-exp(-X))./(exp(X)+exp(-X));
%logsid
F=1./(1+exp(-X));
end
function F=dfun1(X)
%Tangent sigmoid 导数
%F=(4*exp(X).*exp(-X))./(exp(X)+exp(-X)).^2;
%dlogsig
F=exp(X)./(exp(X) + 1).^2;
end
function F=fun2(X)
F=X;
end
function F=dfun2(X)
F=ones(size(X));
end
谢了。。。。。。。。。。。。。
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