参数自适应的单层 bp 神经网络

% R^m->R^1

%

sigmoid=@(x,a,b)b./(1+exp(-a*x)); % activation function

% input : X,T

x1=linspace(-1,1,5);x2=x1;

[x2,x1]=meshgrid(x2,x1);

X=[x1(:).';x2(:).'];

T=sigmoid(3*X(1,:)+2*X(2,:)-1,3,1);

% or X=[[1;1],[1;0],[0;1],[0;0]];T=[1,0,0,0];

% set the options

tol=0.001;

lr=0.1; % learning rate

% alpha=0.2;

[m,N]=size(X);

W=rand(1,m);theta=rand(1);

b=1;a=1;

Y=sigmoid(W*X-repmat(theta,1,N),a,b);

E=T-Y;

k=0;

%DW0=zeros(1,m);DT0=0;

%Da0=0;Db0=0;

while(norm(E)>tol&&k<10000)

% lr=0.01/(1+k/500);

DW=lr*a/b*((T-Y).*Y.*(b-Y))*X.'; DT=lr*a/b*sum((T-Y).*Y.*(b-Y),2);

Db=lr*sum((T-Y).*Y,2)/b;

Da=lr*sum((T-Y).*Y.*(b-Y).*(W*X),2)/b;

W=W+DW;

theta=theta-DT;

a=a+Da; b=b+Db;

Y=sigmoid(W*X-repmat(theta,1,N),a,b);

E=T-Y;

k=k+1;

end

x1=linspace(-1,1,20);x2=x1;

[x2,x1]=meshgrid(x2,x1);

y=sigmoid(W(1)*x1+W(2)*x2-theta,a,b);

mesh(x1,x2,y);hold on;

plot3(X(1,:),X(2,:),T,'ro');

xlabel('x_1');ylabel('x_2');title('Y/T');