Plot hotelling's confidence ellipse in PCA

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karthik
karthik 2014-3-25
回答： Aditya 2025-3-3
Can anyone tell me how to draw an ellipse error on a pca plot. The princomp function gives us the distances from each point to the center of the group, but how can we use this information to draw the corresponding ellipse's?

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回答（1 个）

Aditya
Aditya 2025-3-3
Hi Karthik,
To draw an error ellipse on a PCA plot, you can use the covariance matrix of the principal component scores to determine the shape and orientation of the ellipse.
Here is the sample code for the same:
% Sample data
data = randn(100, 3); % 100 observations with 3 variables
% Perform PCA
[coeff, score, latent] = pca(data);
% Calculate the covariance matrix of the scores
covariance = cov(score(:, 1:2)); % Use the first two principal components
% Calculate the mean of the scores
mean_score = mean(score(:, 1:2));
% Eigen decomposition of the covariance matrix
[eigenvec, eigenval] = eig(covariance);
% Calculate the ellipse parameters
chi_square_val = 2.4477; % For 95% confidence interval
theta = linspace(0, 2*pi, 100);
ellipse_x = chi_square_val * sqrt(eigenval(1,1)) * cos(theta);
ellipse_y = chi_square_val * sqrt(eigenval(2,2)) * sin(theta);
% Rotation matrix
R = [cos(atan2(eigenvec(2,1), eigenvec(1,1))), -sin(atan2(eigenvec(2,1), eigenvec(1,1)));
sin(atan2(eigenvec(2,1), eigenvec(1,1))), cos(atan2(eigenvec(2,1), eigenvec(1,1)))];
% Rotate the ellipse
ellipse = [ellipse_x; ellipse_y]' * R;
% Plot the PCA scores
figure;
scatter(score(:, 1), score(:, 2), 'b.');
hold on;
% Plot the error ellipse
plot(mean_score(1) + ellipse(:, 1), mean_score(2) + ellipse(:, 2), 'r-', 'LineWidth', 2);
% Add labels and title
xlabel('Principal Component 1');
ylabel('Principal Component 2');
title('PCA with Error Ellipse');
axis equal;
grid on;
hold off;

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