rbffunction.m

RBF网络用于函数逼近的一个程序！内部包含几个关于RBF网络的几个算法。

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  RBF网络用于函数逼近                                 20051218
%%%%  神经网络工具箱
% clear all;clc;
% 
% X = [0:0.1:1];
% T=sin(5*X)+X;
% 
% net = newrb(X,T);
% x1 = [0.05:0.1:0.95];
% Y1 = sim(net,x1);
% T2 = sim(net,X);
% 
% figure(1);
% plot(X,T,'b-',x1,Y1,'r+',X,T2,'g-');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  RBF网络用于函数逼近                                  20051218
%%%%  未使用神经网络工具箱,离线算法
%%%%
% clear;clc;
% 
% X = [0:0.05:1];
% N = length(X);
% Nr = 5;
% T = sin(5*X).^2+X.^2+cos(X);
% 
% %%%% 计算中心矢量
% dc = 1;
% t = 0;
% c = randn(1,Nr);
% while dc>0.0001
%     classNum = zeros(1,Nr);
%     classSum = zeros(1,Nr);
%     for k=1:N
%         d = (X(k)*ones(1,Nr)-c).^2;
%         [m,I] = min(d);
%         classNum(I) = classNum(I)+1;
%         classSum(I) = classSum(I)+X(k);
%     end
%     for i = 1:Nr
%         if classNum(i)>0.5
%             classSum(i) = classSum(i)/classNum(i);
%         else
%             classSum(i)=0;
%         end
%     end
%     c1 = classSum;
%     temp0 = sum((c1-c).^2);
%     temp1 = sum(c1.^2);
%     dc = temp0/temp1;
%     t = t+1;
%     c = c1;
% end
% 
% %%%% 计算方差参数
% classVar = zeros(1,Nr);
% classNum = zeros(1,Nr);
% for k=1:N
%     d = (X(k)*ones-c).^2;
%     [m,I]=min(d);
%     classNum(I) = classNum(I)+1;
%     classVar(I) = classVar(I)+(X(k)-c(I))^2;
% end
% classVar = classVar./classNum;
% %classVar = 2;
% %%%% 学习输出层权植
% dww=1;
% a = 0.2;
% nn = 0;
% W0 = randn(1,Nr);
% while dww>0.01
% dww = 0;
% a = a/(1+nn/1000);
% W = W0;
% for k =1:N
%     R = exp(-(X(k)*ones(1,Nr)-c).^2./classVar/2);
%     y = W*R';
%     dW = a*(T(k)-y)*R;
%     W = W+dW;
% end
% dww = norm(W-W0);
% W0 = W;
% nn= nn+1;
% end
% 
% %%%% 测试学习算法有效性
% t1 = [0:0.05:1];
% Yout1 =zeros(1,N);
% for i =1:N
%     R = exp(-(t1(i)*ones(1,Nr)-c).^2./classVar/2);
%     Yout1(i) = W*R';
% end
% 
% t2 = [0.025:0.05:0.975];
% Yout2 =zeros(1,length(t2));
% for i =1:length(t2)
%     R = exp(-(t2(i)*ones(1,Nr)-c).^2./classVar/2);
%     Yout2(i) = W*R';
% end
% figure(1);
% plot(t1,Yout1,'b-',t2,Yout2,'r+');
% figure(2);
% plot(X,T,'b-');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  RBF网络用于函数逼近                                       20051219    
%%%%  未使用神经网络工具箱,且是实时的,在线算法
%%%%
clear;clc;

X = [0:0.1:1];
N = length(X);
Nr = 6;
T=exp(X)+X.^2+sin(X);
%%%% 计算中心矢量
a = 0.2;
c = randn(1,Nr);
for k =1:N
    d = (X(k)*ones(1,Nr)-c).^2;
    [m,I]=min(d);
    c1 = c;
    c1(I) = c(I)+a*[X(k)-c(I)];
    c = c1;
    a = a/(1+sqrt(k/Nr));
end
%%%% 计算方差
deta = zeros(1,Nr);
for k=1:N
    deta = deta + (X(k)*ones(1,Nr)-c).^2;
end
deta = deta/N;
%%%% 权值迭代
R = zeros(1,Nr);
W0 = 0.2*randn(1,Nr);
dww = 1;
a2 = 0.4;
n2 = 0;
while dww>0.001
W = W0;
y = zeros(1,N);
for k =1:N
    R = exp(-(X(k)*ones(1,Nr)-c).^2./(2*deta));
    y(k) = W*R';%输出
    dW = a2*(T(k)-y(k))*R;
    W = W+dW;  %更新权值
end
dww = norm(W-W0);
n2 = n2+1;
W0 = W;
dE = 0;
for k =1:N
    dE = dE+1/2*(T(k)-y(k))^2;
end
E(n2) = dE;
end
%%%% 测试算法
t1 = [0:0.1:1];
Yout1 =zeros(1,N);
for i =1:N
    R = exp(-(t1(i)*ones(1,Nr)-c).^2./(2*deta));
    Yout1(i) = W*R';
end
t2 = [0:0.05:1];
Yout2 =zeros(1,length(t2));
for i =1:length(t2)
    R = exp(-(t2(i)*ones(1,Nr)-c).^2./(2*deta));
    Yout2(i) = W*R';
end
figure(1);
plot(t1,Yout1,'b-',t2,Yout2,'r+',X,T,'g-');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%