92 lines
2.2 KiB
Matlab
92 lines
2.2 KiB
Matlab
% CSCI 5521 Introduction to Machine Learning
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% Rui Kuang
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% Demonstration of Classification by 2-D Gaussians
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clf;
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prior1 = 0.3;
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prior2 = 0.7;
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% mvndis = @(X, mu, Sigma, prior) ( ...
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% -1/2 * log(2*pi) ...
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% - log(Sigma) ...
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% - power(X - mu, 2) / (2 * power(Sigma, 2)) ...
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% + log(prior) ...
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% );
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mu1 = [-1 -1];
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mu2 = [1 1];
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% Equal diagnoal covariance matrix
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% Sigma1 = [1 0; 0 1];
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% Sigma2 = [1 0; 0 1];
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% Diagnoal covariance matrix
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% Sigma1 = [1 0; 0 0.5];
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% Sigma2 = [1 0; 0 0.5];
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% Shared covariance matrix
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% Sigma1 = [1 0.3; 0.3 0.5];
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% Sigma2 = [1 0.3; 0.3 0.5];
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x1 = -10:.1:10; x2 = -10:.1:10;
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% covariance matrix (increase the range for visualization)
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Sigma1 = [1 0.1; 0.1 0.5];
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Sigma2 = [0.5 0.3; 0.3 1];
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x1 = -40:.1:40; x2 = -40:.1:40;
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[X1,X2] = meshgrid(x1,x2);
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%pdf1
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% F1 = mvnpdf([X1(:) X2(:)],mu1,Sigma1);
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F1 = mvndis([X1(:) X2(:)], mu1, Sigma1, prior1);
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F1 = reshape(F1,length(x2),length(x1));
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subplot(1,2,1);
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surf(x1,x2,F1); hold on;
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%pdf2
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% F2 = mvnpdf([X1(:) X2(:)],mu2,Sigma2);
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F2 = mvndis([X1(:) X2(:)], mu2, Sigma2, prior2);
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F2 = reshape(F2,length(x2),length(x1));
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surf(x1,x2,F2);
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caxis([min(F2(:))-.5*range(F2(:)),max(F2(:))]);
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axis([-4 4 -4 4 0 .4])
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xlabel('x1'); ylabel('x2'); zlabel('Probability Density');
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%decosopm boundary
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%F1 = mvnpdf([X1(:) X2(:)],mu1,Sigma1);
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%F1 = reshape(F1,length(x2),length(x1));
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%F2 = mvnpdf([X1(:) X2(:)],mu2,Sigma2);
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%F2 = reshape(F2,length(x2),length(x1));
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cmp = F1 > F2;
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subplot(1,2,2);
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imagesc(X1(:),X2(:),cmp);
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xlabel('x1'); ylabel('x2');
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function res = mvndis(X, mu, Sigma, prior)
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[len, d] = size(X);
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res = zeros(len, 1);
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for i = 1:len
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x = X(i,:);
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mdist = (x - mu) * inv(Sigma) * (x - mu).';
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res(i) = -d/2*log(2*pi) - 1/2*log(det(Sigma)) - 1/2*mdist + log(prior);
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end
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% 1 x 2
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% (1 x 2) x ((2 x 2) x (2 x 1))
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% X - mu = 40401 x 2
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% (40401 x 2) x (2 x 2) x (2 x 40401)
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% mdist = (X - mu) * inv(Sigma) * (X - mu).';
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% res = -log(2*pi) - 1/2*log(det(Sigma)) - 1/2*mdist + log(prior)
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% res = zeros(size(X));
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% [l1, l2] = size(X);
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%
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% for i1 = 1:l1
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% for i2 = 1:l2
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% cell = -log(2*pi) - 1/2*log(det(Sigma))
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% res(i1, i2) = cell
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% end
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% end
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end
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