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%% Initialization
clear ; close all; clc
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%% ================== Part 1: Load and Visualize Example Dataset ===================
fprintf('Visualizing example dataset for PCA.\n\n');
% The following command loads the dataset. You should now have the
% variable X in your environment
load ('./data/ex7data1.mat');
% Visualize the example dataset
plot(X(:, 1), X(:, 2), 'bo');
axis([0.5 6.5 2 8]); axis square;
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%% =============== Part 2: Principal Component Analysis ===============
fprintf('\nRunning PCA on example dataset.\n\n');
% Before running PCA, it is important to first normalize X
[X_norm, mu, sigma] = featureNormalize(X);
% Run PCA
[U, S] = pca(X_norm);
% Compute mu, the mean of the each feature
% Draw the eigenvectors centered at mean of data. These lines show the
% directions of maximum variations in the dataset.
hold on;
drawLine(mu, mu + 1.5 * S(1,1) * U(:,1)', '-k', 'LineWidth', 2);
drawLine(mu, mu + 1.5 * S(2,2) * U(:,2)', '-k', 'LineWidth', 2);
hold off;
fprintf('Top eigenvector: \n');
fprintf(' U(:,1) = %f %f \n', U(1,1), U(2,1));
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%% =================== Part 3: Dimension Reduction ===================
fprintf('\nDimension reduction on example dataset.\n\n');
% Plot the normalized dataset (returned from pca)
plot(X_norm(:, 1), X_norm(:, 2), 'bo');
axis([-4 3 -4 3]); axis square
% Project the data onto K = 1 dimension
K = 1;
Z = projectData(X_norm, U, K);
fprintf('Projection of the first example: %f\n', Z(1));
X_rec = recoverData(Z, U, K);
fprintf('Approximation of the first example: %f %f\n', X_rec(1, 1), X_rec(1, 2));
% Draw lines connecting the projected points to the original points
hold on;
plot(X_rec(:, 1), X_rec(:, 2), 'ro');
for i = 1:size(X_norm, 1)
drawLine(X_norm(i,:), X_rec(i,:), '--k', 'LineWidth', 1);
end
hold off
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%% =============== Part 4: Loading and Visualizing Face Data =============
fprintf('\nLoading face dataset.\n\n');
% Load Face dataset
load ('./data/ex7faces.mat')
% Display the first 100 faces in the dataset
displayData(X(1:100, :));
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%% =========== Part 5: PCA on Face Data: Eigenfaces ===================
fprintf(['\nRunning PCA on face dataset.\n' ...
'(this might take a minute or two ...)\n\n']);
% Before running PCA, it is important to first normalize X by subtracting
% the mean value from each feature
[X_norm, mu, sigma] = featureNormalize(X);
% Run PCA
[U, S] = pca(X_norm);
% Visualize the top 36 eigenvectors found
displayData(U(:, 1:36)');
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%% ============= Part 6: Dimension Reduction for Faces =================
fprintf('\nDimension reduction for face dataset.\n\n');
K = 100;
Z = projectData(X_norm, U, K);
fprintf('The projected data Z has a size of: ')
fprintf('%d ', size(Z));
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%% ==== Part 7: Visualization of Faces after PCA Dimension Reduction ====
fprintf('\nVisualizing the projected (reduced dimension) faces.\n\n');
K = 100;
X_rec = recoverData(Z, U, K);
% Display normalized data
subplot(1, 2, 1);
displayData(X_norm(1:100,:));
title('Original faces');
axis square;
% Display reconstructed data from only k eigenfaces
subplot(1, 2, 2);
displayData(X_rec(1:100,:));
title('Recovered faces');
axis square;
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%% ====================== PCA for Visualization ==========================
close all; close all; clc
% Reload the image from the previous exercise and run K-Means on it
% For this to work, you need to complete the K-Means assignment first
A = double(imread('./data/bird_small.png'));
% If imread does not work for you, you can try instead
% load ('bird_small.mat');
A = A / 255;
img_size = size(A);
X = reshape(A, img_size(1) * img_size(2), 3);
K = 16;
max_iters = 10;
initial_centroids = kMeansInitCentroids(X, K);
[centroids, idx] = runkMeans(X, initial_centroids, max_iters);
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% Sample 1000 random indexes (since working with all the data is
% too expensive. If you have a fast computer, you may increase this.
sel = floor(rand(1000, 1) * size(X, 1)) + 1;
% Setup Color Palette
palette = hsv(K);
colors = palette(idx(sel), :);
% Visualize the data and centroid memberships in 3D
figure;
scatter3(X(sel, 1), X(sel, 2), X(sel, 3), 10, colors);
title('Pixel dataset plotted in 3D. Color shows centroid memberships');
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% Subtract the mean to use PCA
[X_norm, mu, sigma] = featureNormalize(X);
% PCA and project the data to 2D
[U, S] = pca(X_norm);
Z = projectData(X_norm, U, 2);
% Plot in 2D
figure;
plotDataPoints(Z(sel, :), idx(sel), K);
title('Pixel dataset plotted in 2D, using PCA for dimensionality reduction');
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