gaus class

gauss_class/gauss2d.m

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

gauss_class/gauss_class_1D.m

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+% CSCI 5521 Introduction to Machine Learning
+% Rui Kuang
+% Demonstration of Classification by 1-D Gaussians 
+
+%mean and standard deviation of class blue
+mu1 = -2;sd1 = 2;
+
+%mean and standard deviation of class red
+mu2 = 2;sd2 = 4;
+
+%generate x-axis
+sd = max(sd1,sd2);
+ix = -6*sd-1:1e-1:6*sd+1; %covers more than 99% of the curve
+
+iy1 = pdf('normal', ix, mu1, sd1);
+iy2 = pdf('normal', ix, mu2, sd2);
+
+subplot(1,2,1);
+plot(ix,iy1,'b'); hold on;
+plot(ix,iy2,'r');
+title('PDF P(X)');
+
+%prior 
+p1=0.8;
+p2=1-p1;
+
+%calculate the posteriors
+iy1_n = p1*iy1 ./ (p1*iy1+p2*iy2);
+iy2_n = p2*iy2 ./ (p1*iy1+p2*iy2);
+subplot(1,2,2);
+plot(ix,iy1_n,'b'); hold on;
+plot(ix,iy2_n,'r');
+title('Posteriors P(C | x)');

gauss_class/gauss_class_2D.m

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+% CSCI 5521 Introduction to Machine Learning
+% Rui Kuang
+% Demonstration of Classification by 2-D Gaussians 
+
+mu1 = [-1 -1];
+mu2 = [1 1];
+
+% Equal diagnoal covariance matrix
+ Sigma1 = [1 0; 0 1];
+ Sigma2 = [1 0; 0 1];
+
+% Diagnoal covariance matrix
+% Sigma1 = [1 0; 0 0.5];
+% Sigma2 = [1 0; 0 0.5];
+
+% Shared covariance matrix
+% Sigma1 = [1 0.3; 0.3 0.5];
+% Sigma2 = [1 0.3; 0.3 0.5];
+
+ x1 = -10:.1:10; x2 = -10:.1:10;
+
+% covariance matrix (increase the range for visualization)
+% Sigma1 = [1 0.1; 0.1 0.5];
+% Sigma2 = [0.5 0.3; 0.3 1];
+% x1 = -40:.1:40; x2 = -40:.1:40;
+
+[X1,X2] = meshgrid(x1,x2);
+%pdf1
+F1 = mvnpdf([X1(:) X2(:)],mu1,Sigma1);
+F1 = reshape(F1,length(x2),length(x1));
+subplot(1,2,1);
+surf(x1,x2,F1); hold on;
+
+%pdf2
+F2 = mvnpdf([X1(:) X2(:)],mu2,Sigma2);
+F2 = reshape(F2,length(x2),length(x1));
+surf(x1,x2,F2);
+caxis([min(F2(:))-.5*range(F2(:)),max(F2(:))]);
+axis([-4 4 -4 4 0 .4])
+xlabel('x1'); ylabel('x2'); zlabel('Probability Density');
+
+%decosopm boundary
+%F1 = mvnpdf([X1(:) X2(:)],mu1,Sigma1);
+%F1 = reshape(F1,length(x2),length(x1));
+%F2 = mvnpdf([X1(:) X2(:)],mu2,Sigma2);
+%F2 = reshape(F2,length(x2),length(x1));
+
+cmp = F1 > F2;
+subplot(1,2,2);
+imagesc(X1(:),X2(:),cmp);
+
+xlabel('x1'); ylabel('x2');