rbfnapproximation.m

內涵模糊理論與類神經網路的程式碼...提供初學者做研究參考

% ==========================================================
% 
%           Neural Networks A Classroom Approach
%                     Satish Kumar
%             Copyright Tata McGraw Hill, 2004
%
%     MATLAB code that implements the RBFN approximation
%               Reference: Table 8.9;Page 312
%
% ==========================================================

Q = 10; 			% 10 data points
noise = 0.6;	% additive noise level
x = linspace(-2*pi,2*pi,Q);				% X sample space
scatter = (2*rand(1,Q) - 1)*noise;		% Generate noise
d = (2*sin(x) + x + scatter)';			% Generate Y data
testpts = 100;									% Number of test data
testx = linspace(-2*pi, 2*pi, testpts);% Sample space X test
testy = (2*sin(testx) + testx)';			% Generate Y test data

sigma = .5;			% Set common spread of basis functions

for i = 1:Q			% Generate phi matrix 10 x 5
  k=1;
  for j = 1:Q/2	% Half the data points are basis centers
      phi(i,j) = exp(-(x(i)-x(k))^2/(2*sigma^2));
      k=k+2; 		% choose alternate data point as a basis    
  end
end

% Compute pseudo inverse
pseudoinv = inv(phi' * phi) * phi';
W = pseudoinv * d;	% Compute weights

% Generate phi matrix for test data
for i = 1:testpts
  k=1;
  for j = 1:Q/2
      testphi(i,j) = exp(-(testx(i)-x(k))^2/(2*sigma^2));
      k=k+2; 
  end
end

% Generate approximant
f = testphi* W;

figure(1)
subplot(2,2,1)
hold on
plot(testx, testy,'b')
plot(x, d, 'r^');
plot(testx, f, 'k','LineWidth',2);
axis([-2*pi 2*pi -7 7])
grid on
title('(a)');


sigma = 1;
for i = 1:Q
  k=1;
  for j = 1:Q/2
      phi(i,j) = exp(-(x(i)-x(k))^2/(2*sigma^2));
      k=k+2;     
  end
end

pseudoinv = inv(phi' * phi) * phi';
W = pseudoinv * d;

for i = 1:testpts
  k=1;
  for j = 1:Q/2
      testphi(i,j) = exp(-(testx(i)-x(k))^2/(2*sigma^2));
      k=k+2;     
  end
end

f = testphi* W;

subplot(2,2,2)
hold on
plot(testx, testy,'b')
plot(x, d, 'r^');
plot(testx, f, 'k','LineWidth',2);
axis([-2*pi 2*pi -7 7])
grid on
title('(b)');


sigma = 5;

for i = 1:Q
  k=1;
  for j = 1:Q/2
      phi(i,j) = exp(-(x(i)-x(k))^2/(2*sigma^2));
      k=k+2; %choose each alternate data point as a basis    
  end
end

pseudoinv = inv(phi' * phi) * phi';
W = pseudoinv * d;

for i = 1:testpts
  k=1;
  for j = 1:Q/2
      testphi(i,j) = exp(-(testx(i)-x(k))^2/(2*sigma^2));
      k=k+2; %choose each alternate data point as a basis    
  end
end

f = testphi* W;

subplot(2,2,3)
hold on
plot(testx, testy,'b')
plot(x, d, 'r^');
plot(testx, f, 'k','LineWidth',2);
axis([-2*pi 2*pi -7 7])
grid on
title('(c)');


sigma = 10;

for i = 1:Q
  k=1;
  for j = 1:Q/2
      phi(i,j) = exp(-(x(i)-x(k))^2/(2*sigma^2));
      k=k+2; %choose each alternate data point as a basis    
  end
end

pseudoinv = inv(phi' * phi) * phi';
W = pseudoinv * d;

for i = 1:testpts
  k=1;
  for j = 1:Q/2
      testphi(i,j) = exp(-(testx(i)-x(k))^2/(2*sigma^2));
      k=k+2; %choose each alternate data point as a basis    
  end
end

f = testphi* W;

subplot(2,2,4)
hold on
plot(testx, testy,'b')
plot(x, d, 'r^');
plot(testx, f, 'k','LineWidth',2);
axis([-2*pi 2*pi -7 7])
grid on
title('(d)');