framekernelex2.m

神经网络工具箱

%
%   Comparison of RKHS Kernel, Dual Green Kernel and
%   Frame Green Kernel Performance
%
%
%   01/01/2001 Alain Rakotomamonjy 


close all
clear all
verbose=0;
bruit=0.2;
N=100;

lambda1=70;
lambda2=1500;
lambda3=200;
itermax=1;
erreur=zeros(itermax,3);
n=200;
t=linspace(0,10,n)';
uo=1;
a=2^0.25;
bord1=0;
bord2=10;
dilation=[-10];
framematrix=framewav(t,dilation,uo,a,bord1,bord2);
dual=dualframe(framematrix,t);
kernel='numerical';
spanning='wavelet';
dilation=[0 5];
for i=1:itermax
   
    %-------------------creating and plotting data----------------
    x=sort([0.01; 9.99;10*rand(N-2,1)]);
    xf=linspace(0,10,200)';
    x1=x;
    yf=sin(xf)+1*sinc((xf-5))+sinc(5*(xf-2));
    y=sin(x)+1*sinc((x-5))+1*sinc(5*(x-2))+bruit*randn(size(x));
    x2=x;
 
    
    %---------------------Regularization Networks : RKHS Kernel -----------------------
     K=kernelframe(x1,kernel,x2,framematrix,t,dual);
    T=phispan(x,spanning,dilation,uo,a,bord1,bord2);
    [c,d]=regsolve(K,T,y,lambda1);
    x1=xf;
    K=kernelframe(x1,kernel,x2,framematrix,t,dual);
    T=phispan(x1,spanning,dilation,uo,a,bord1,bord2);
    f1=K*c+T*d;
    fprintf('step 1 done\n');
    %---------------------Regularization Networks : Dual Green Function -----------------------
    x1=x;
    K=kernelframe(x1,kernel,x2,dual,t,dual);
    T=phispan(x,spanning,dilation,uo,a,bord1,bord2);
    [c,d]=regsolve(K,T,y,lambda2);
    x1=xf;
    K=kernelframe(x1,kernel,x2,dual,t,dual);
    T=phispan(x1,spanning,dilation,uo,a,bord1,bord2);
    f2=K*c+T*d;
    fprintf('step 2 done\n');
    %---------------------Regularization Networks : Frame Green Kernel -----------------------
    x1=x;
    K=kernelframe(x1,kernel,x2,framematrix,t,framematrix);
    T=phispan(x,spanning,dilation,uo,a,bord1,bord2);
    [c,d]=regsolve(K,T,y,lambda3);
    x1=xf;
    K=kernelframe(x1,kernel,x2,framematrix,t,framematrix);
    T=phispan(x1,spanning,dilation,uo,a,bord1,bord2);
    f3=K*c+T*d;
    fprintf('step 3 done\n');
    %-------------------------Plots--------------------------------------------------
    figure
    hold on
    h = plot(x,y,'g+',xf,yf,'g',xf,f1,'b',xf,f2,'r',xf,f3,'m'); 
    legend('data points', 'original','RKHS Kern.','Dual Green Kern.','Frame Green Kern.');
    set(h,'LineWidth',2);
    title('Regularization Networks with frame Kernels');
    xlabel('x');ylabel('y');
    errrkhs=sum( (yf-f1).^2/200);
    errdual=sum( (yf-f2).^2/200);
    errframe=sum( (yf-f3).^2/200);
    erreur(i,:)=[errrkhs errdual errframe];
    fprintf('i:%d MSE  RKHS Kernel : %f   Dual Green : %f  Frame Green :%f\n',i,errrkhs, errdual, errframe);
end;