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Matlab code to produce PCA animations
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| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| % Matlab code to produce PCA animations shown here: | |
| % http://stats.stackexchange.com/questions/2691 | |
| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| % Static image | |
| clear all | |
| rng(42) | |
| X = randn(100,2); | |
| X = X*chol([1 0.6; 0.6 0.6]); | |
| X = bsxfun(@minus, X, mean(X)); | |
| [a,b] = eig(cov(X)); | |
| fig = figure('Position', [100 100 1000 400]); | |
| set(gcf,'color','w'); | |
| axis([-3.5 3.5 -3.5 3.5]) | |
| axis square | |
| hold on | |
| scatter(X(:,1), X(:,2), 'b', 'filled') | |
| %% Rotating animation | |
| fig = figure('Position', [100 100 1000 400]); | |
| set(gcf,'color','w'); | |
| axis([-3.5 3.5 -3.5 3.5]) | |
| axis square | |
| hold on | |
| for alpha = 1:1:179 | |
| w = [cosd(alpha) sind(alpha)]; | |
| z = X*w'*w; | |
| cla | |
| for i=1:100 | |
| plot([X(i,1) z(i,1)], [X(i,2) z(i,2)], 'r') | |
| end | |
| plot(w(1)*3.5*[-1 1], w(2)*3.5*[-1 1], 'k') | |
| plot(-w(2)*2*[-1 1], w(1)*2*[-1 1], 'Color', [.6 .6 .6]) | |
| scatter(z(:,1), z(:,2), 'r', 'filled') | |
| scatter(X(:,1), X(:,2), 'b', 'filled') | |
| scatter(0,0,65,'k','filled', 'LineWidth', 2, 'MarkerFaceColor', [1 1 1], 'MarkerEdgeColor', [0 0 0]) | |
| a1 = 3.5; | |
| a2 = 4.5; | |
| plot(a(1,2)*[-a2 -a1], a(2,2)*[-a2 -a1], 'm', 'LineWidth', 2) | |
| plot(a(1,2)*[ a1 a2], a(2,2)*[ a1 a2], 'm', 'LineWidth', 2) | |
| drawnow | |
| frame = getframe(fig); | |
| if alpha == 1 | |
| [imind,map] = rgb2ind(frame.cdata,16,'nodither'); | |
| else | |
| imind(:,:,1,alpha) = rgb2ind(frame.cdata,map,'nodither'); | |
| end | |
| end | |
| imwrite(imind,map, 'animation_pca.gif', 'DelayTime', 0, 'LoopCount', inf) | |
| %% Pendulum animation | |
| fig = figure('Position', [100 100 1000 400]); | |
| set(gcf,'color','w'); | |
| axis([-3.5 3.5 -3.5 3.5]) | |
| axis square | |
| hold on | |
| alpha = -45; | |
| omega = 0; | |
| for t = 1:1:1000 | |
| w = [cosd(alpha) sind(alpha)]; | |
| z = X*w'*w; | |
| M = sum(sum((z * [0 1; -1 0]) .* (X-z), 2)); | |
| omega = omega + M; | |
| omega = omega * 0.93; | |
| alpha = alpha + omega/40; | |
| if(abs(omega)<1 && abs(alpha-abs(atand(a(2,2)/a(1,2)))) < 1) | |
| break | |
| end | |
| cla | |
| for i=1:100 | |
| plot([X(i,1) z(i,1)], [X(i,2) z(i,2)], 'r') | |
| end | |
| plot(w(1)*3.5*[-1 1], w(2)*3.5*[-1 1], 'k') | |
| plot(-w(2)*2*[-1 1], w(1)*2*[-1 1], 'Color', [.6 .6 .6]) | |
| scatter(z(:,1), z(:,2), 'r', 'filled') | |
| scatter(X(:,1), X(:,2), 'b', 'filled') | |
| scatter(0,0,65,'k','filled', 'LineWidth', 2, 'MarkerFaceColor', [1 1 1], 'MarkerEdgeColor', [0 0 0]) | |
| a1 = 3.5; | |
| a2 = 4.5; | |
| plot(a(1,2)*[-a2 -a1], a(2,2)*[-a2 -a1], 'm', 'LineWidth', 2) | |
| plot(a(1,2)*[ a1 a2], a(2,2)*[ a1 a2], 'm', 'LineWidth', 2) | |
| pause(0.01) | |
| drawnow | |
| frame = getframe(fig); | |
| if t == 1 | |
| [imind,map] = rgb2ind(frame.cdata,16,'nodither'); | |
| else | |
| imind(:,:,1,t) = rgb2ind(frame.cdata,map,'nodither'); | |
| end | |
| end | |
| imwrite(imind,map, 'animation_pca_pendulum.gif', 'DelayTime', 0, 'LoopCount', inf) |
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