35 lines
971 B
Mathematica
35 lines
971 B
Mathematica
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% CSCI 5521 Introduction to Machine Learning
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% Rui Kuang
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% Demonstration of 2-D Gaussians
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%Try Sigma = [0.5, 0;0, 0.5];Sigma = [0.7, 0;0, 0.3];Sigma = [0.7, 0.2;0.2, 0.3]
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mu = [0 0];
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Sigma = [0.7, 0.2;0.2, 0.3];
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x1 = -3:.2:3; x2 = -3:.2:3;
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[X1,X2] = meshgrid(x1,x2);
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%pdf
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F = mvnpdf([X1(:) X2(:)],mu,Sigma);
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F = reshape(F,length(x2),length(x1));
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subplot(1,2,1);
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surf(x1,x2,F);
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caxis([min(F(:))-.5*range(F(:)),max(F(:))]);
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axis([-3 3 -3 3 0 .4])
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xlabel('x1'); ylabel('x2'); zlabel('Probability Density');
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subplot(1,2,2);
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contour(x1,x2,F,[.0001 .001 .01 .05:.1:.95 .99 .999 .9999],'ShowText','on');
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%contour
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figure
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i=1;
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for rho = -0.8:0.4:0.8
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Sigma(1,2)=rho*sqrt(Sigma(1,1)*Sigma(2,2));
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Sigma(2,1)=Sigma(1,2);
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F = mvnpdf([X1(:) X2(:)],mu,Sigma);
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F = reshape(F,length(x2),length(x1));
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subplot(1,5,i);
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i=i+1;
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contour(x1,x2,F,[.0001 .001 .01 .05:.1:.95 .99 .999 .9999]);
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title (sprintf('rho = %f',rho));
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xlabel('x1'); ylabel('x2');
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end
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