test_ams.m

MATLAB2007科学计算与工程分析代码

function test_ams()
  n = 200;   % Number of training points
  nt = 1000; % Number of test points
  
  % We construct a 2D toy problem which looks like a checkboard.
  % But there is more variation on the 2nd component (and the length
  %   scale should be smaller)
  X = rand(n,2);
  Y = sign((X(:,1)-0.5).*(mod(3*X(:,2),1)-0.5));
  Xt = rand(nt,2);
  Yt = sign((Xt(:,1)-0.5).*(mod(3*Xt(:,2),1)-0.5));  
  
  % Normalize by the standard deviation on each component
  s = std(X);
  X  = X./repmat(s,n,1);
  Xt = Xt./repmat(s,nt,1);
  
  % Plot the toy problem
  plot(X(Y== 1,1),X(Y== 1,2),'b+'); hold on;  
  plot(X(Y==-1,1),X(Y==-1,2),'ro'); hold off; pause(1); drawnow;
  
  % We now try the four different model selection criterion
  meth = {'loo' 'rm' 'val' 'ev'};
  for i=1:4
    [sig,C,alpha,b] = ams(X,Y,meth{i},0); % Do the model selection
    Kt = compute_kernel(Xt,X,sig); % Compute the test kernel...
    te = mean(Yt.*(Kt*alpha+b)<0); % ... and the test error
    fprintf('Method = %s,\t sigma_1 = %.3f, sigma_2 = %.3f, test error = %.3f\n',...
            meth{i},sig(1),sig(2),te);
  end;
  
  fprintf(['All methods give comparable error rates and find that the ' ...
           'length scale should be smaller on the 2nd component.\n']);

function K = compute_kernel(X,Y,sig)
  % Compute the RBF kernel matrix
  if length(sig)==1
    X = X / sig;
    Y = Y / sig;
  else
    X = X ./ repmat(sig',size(X,1),1);
    Y = Y ./ repmat(sig',size(Y,1),1);
  end;

  normX = sum(X.^2,2);
  normY = sum(Y.^2,2);

  K = exp(-0.5*(repmat(normX ,1,size(Y,1)) + ...
                repmat(normY',size(X,1),1) - 2*X*Y'));