appendix_b.m

用于函数逼近的BP算法程序

%用于函数逼近的BP算法程序
%作者魏海坤，摘自《神经网络结构设计的方法与理论》
% function main()
SamNum = 100;               %....训练样本数
TestSamNum = 101;           %....测试样本数
HiddenUnitNum = 10;         %....隐节点数
InDim = 1;                  %....样本输入维数
OutDim = 1;                 %....样本输出维数
%........................根据目标函数获得样本输入输出
rand('state',sum(100*clock))
NoiseVar = 0.1;
Noise = NoiseVar * randn(1,SamNum);
SamIn = 8 * rand(1,SamNum) - 4;
SamOutNoNoise = 1.1 * (1 - SamIn + 2*SamIn.^2) .* exp(-SamIn.^2/2);
SamOut = SamOutNoNoise + Noise;

TestSamIn = -4:0.08:4;
TestSamOut = 1.1 * (1 - TestSamIn + 2*TestSamIn.^2) .* exp(-TestSamIn.^2/2);

MaxEpochs = 30000;            %....最大训练次数
lr = 0.003;                   %....学习率
E0 = 0.5;                     %....目标误差

W1 = 0.2 * rand(HiddenUnitNum,InDim) - 0.1;     %....输入层到隐层的初始权值
B1 = 0.2 * rand(HiddenUnitNum,1) - 0.1;         %....隐节点初始偏移
W2 = 0.2 * rand(OutDim,HiddenUnitNum) - 0.1;    %....隐层到输出层的初始权值
B2 = 0.2 * rand(OutDim,1) -0.1;                 %....输出层初始偏移
%.........................................................
W1Ex = [W1 B1];                                 %....输入层到隐层的初始权值扩展
W2Ex = [W2 B2];                                 %....隐层到输出层的初始权值扩展

SamInEx = [SamIn; ones(1,SamNum)];             %....样本输入扩展
ErrHistory = [];                                %....用于记录每次权值调整后的训练误差
for i = 1:MaxEpochs
    
    %....正向传播计算网络输出
    HiddenOut = logsig( W1Ex * SamInEx );
    HiddenOutEx = [HiddenOut; ones(1,SamNum)];
    NetworkOut = W2Ex * HiddenOutEx;
    
    %....停止学习判断
    Error = SamOut - NetworkOut;
    SSE = sumsqr(Error);
    
    %....记录每次权值调整后的训练误差
    ErrHistory = [ErrHistory SSE];
    
    if SSE < E0
        break
    end
    
    %....计算反向传播误差
    Delta2 = Error;
    Delta1 = W2' * Delta2 .* HiddenOut .* ( 1-HiddenOut );
    
    %....计算权值调节量
    dW2Ex = Delta2 * HiddenOutEx';
    dW1Ex = Delta1 * SamInEx';
    
    %....权值调节
    W1Ex = W1Ex + lr * dW1Ex;
    W2Ex = W2Ex + lr * dW2Ex;
    
    %....分离隐层到输出层的初始权值，以便后面用
    W2 = W2Ex(:,1:HiddenUnitNum);
end

figure
hold on
grid
plot(SamIn,SamOut,'r+');
plot(TestSamIn,TestSamOut,'b--');
xlabel('Input x');
ylabel('Output y');

%....显示计算结果
W1 = W1Ex(:,1:InDim)
B1 = W1Ex(:,InDim+1)
W2
B2 = W2Ex(:,1+HiddenUnitNum)

%....测试
TestHiddenOut = logsig( W1 * TestSamIn + repmat( B1,1,TestSamNum ));
TestNNOut = W2 * TestHiddenOut + repmat( B2,1,TestSamNum );
plot(TestSamIn,TestNNOut,'g-');

%....绘制学习误差曲线
figure
hold on
grid
[xx,Num] = size(ErrHistory);
plot(1:Num,ErrHistory,'k-');