From 229023b69cf9855340b7241ac8a9b43df47cfc92 Mon Sep 17 00:00:00 2001 From: neingeist Date: Mon, 17 Nov 2014 21:58:10 +0100 Subject: [PATCH] Add exercise 7 --- ex7.pdf | Bin 0 -> 748655 bytes ex7/bird_small.mat | Bin 0 -> 45606 bytes ex7/bird_small.png | Bin 0 -> 33031 bytes ex7/computeCentroids.m | 40 +++ ex7/displayData.m | 59 ++++ ex7/drawLine.m | 8 + ex7/ex7.m | 174 +++++++++++ ex7/ex7_pca.m | 235 +++++++++++++++ ex7/ex7data1.mat | Bin 0 -> 995 bytes ex7/ex7data2.mat | Bin 0 -> 4784 bytes ex7/ex7faces.mat | Bin 0 -> 11027767 bytes ex7/featureNormalize.m | 17 ++ ex7/findClosestCentroids.m | 33 +++ ex7/kMeansInitCentroids.m | 26 ++ ex7/pca.m | 31 ++ ex7/plotDataPoints.m | 14 + ex7/plotProgresskMeans.m | 27 ++ ex7/projectData.m | 26 ++ ex7/recoverData.m | 28 ++ ex7/runkMeans.m | 64 +++++ ex7/submit.m | 576 +++++++++++++++++++++++++++++++++++++ ex7/submitWeb.m | 20 ++ 22 files changed, 1378 insertions(+) create mode 100644 ex7.pdf create mode 100644 ex7/bird_small.mat create mode 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example_width) / max_val; + curr_ex = curr_ex + 1; + end + if curr_ex > m, + break; + end +end + +% Display Image +h = imagesc(display_array, [-1 1]); + +% Do not show axis +axis image off + +drawnow; + +end diff --git a/ex7/drawLine.m b/ex7/drawLine.m new file mode 100644 index 0000000..85e6c41 --- /dev/null +++ b/ex7/drawLine.m @@ -0,0 +1,8 @@ +function drawLine(p1, p2, varargin) +%DRAWLINE Draws a line from point p1 to point p2 +% DRAWLINE(p1, p2) Draws a line from point p1 to point p2 and holds the +% current figure + +plot([p1(1) p2(1)], [p1(2) p2(2)], varargin{:}); + +end \ No newline at end of file diff --git a/ex7/ex7.m b/ex7/ex7.m new file mode 100644 index 0000000..3a095ae --- /dev/null +++ b/ex7/ex7.m @@ -0,0 +1,174 @@ +%% Machine Learning Online Class +% Exercise 7 | Principle Component Analysis and K-Means Clustering +% +% Instructions +% ------------ +% +% This file contains code that helps you get started on the +% exercise. You will need to complete the following functions: +% +% pca.m +% projectData.m +% recoverData.m +% computeCentroids.m +% findClosestCentroids.m +% kMeansInitCentroids.m +% +% For this exercise, you will not need to change any code in this file, +% or any other files other than those mentioned above. +% + +%% Initialization +clear ; close all; clc + +%% ================= Part 1: Find Closest Centroids ==================== +% To help you implement K-Means, we have divided the learning algorithm +% into two functions -- findClosestCentroids and computeCentroids. In this +% part, you shoudl complete the code in the findClosestCentroids function. +% +fprintf('Finding closest centroids.\n\n'); + +% Load an example dataset that we will be using +load('ex7data2.mat'); + +% Select an initial set of centroids +K = 3; % 3 Centroids +initial_centroids = [3 3; 6 2; 8 5]; + +% Find the closest centroids for the examples using the +% initial_centroids +idx = findClosestCentroids(X, initial_centroids); + +fprintf('Closest centroids for the first 3 examples: \n') +fprintf(' %d', idx(1:3)); +fprintf('\n(the closest centroids should be 1, 3, 2 respectively)\n'); + +fprintf('Program paused. Press enter to continue.\n'); +pause; + +%% ===================== Part 2: Compute Means ========================= +% After implementing the closest centroids function, you should now +% complete the computeCentroids function. +% +fprintf('\nComputing centroids means.\n\n'); + +% Compute means based on the closest centroids found in the previous part. +centroids = computeCentroids(X, idx, K); + +fprintf('Centroids computed after initial finding of closest centroids: \n') +fprintf(' %f %f \n' , centroids'); +fprintf('\n(the centroids should be\n'); +fprintf(' [ 2.428301 3.157924 ]\n'); +fprintf(' [ 5.813503 2.633656 ]\n'); +fprintf(' [ 7.119387 3.616684 ]\n\n'); + +fprintf('Program paused. Press enter to continue.\n'); +pause; + + +%% =================== Part 3: K-Means Clustering ====================== +% After you have completed the two functions computeCentroids and +% findClosestCentroids, you have all the necessary pieces to run the +% kMeans algorithm. In this part, you will run the K-Means algorithm on +% the example dataset we have provided. +% +fprintf('\nRunning K-Means clustering on example dataset.\n\n'); + +% Load an example dataset +load('ex7data2.mat'); + +% Settings for running K-Means +K = 3; +max_iters = 10; + +% For consistency, here we set centroids to specific values +% but in practice you want to generate them automatically, such as by +% settings them to be random examples (as can be seen in +% kMeansInitCentroids). +initial_centroids = [3 3; 6 2; 8 5]; + +% Run K-Means algorithm. The 'true' at the end tells our function to plot +% the progress of K-Means +[centroids, idx] = runkMeans(X, initial_centroids, max_iters, true); +fprintf('\nK-Means Done.\n\n'); + +fprintf('Program paused. Press enter to continue.\n'); +pause; + +%% ============= Part 4: K-Means Clustering on Pixels =============== +% In this exercise, you will use K-Means to compress an image. To do this, +% you will first run K-Means on the colors of the pixels in the image and +% then you will map each pixel on to it's closest centroid. +% +% You should now complete the code in kMeansInitCentroids.m +% + +fprintf('\nRunning K-Means clustering on pixels from an image.\n\n'); + +% Load an image of a bird +A = double(imread('bird_small.png')); + +% If imread does not work for you, you can try instead +% load ('bird_small.mat'); + +A = A / 255; % Divide by 255 so that all values are in the range 0 - 1 + +% Size of the image +img_size = size(A); + +% Reshape the image into an Nx3 matrix where N = number of pixels. +% Each row will contain the Red, Green and Blue pixel values +% This gives us our dataset matrix X that we will use K-Means on. +X = reshape(A, img_size(1) * img_size(2), 3); + +% Run your K-Means algorithm on this data +% You should try different values of K and max_iters here +K = 16; +max_iters = 10; + +% When using K-Means, it is important the initialize the centroids +% randomly. +% You should complete the code in kMeansInitCentroids.m before proceeding +initial_centroids = kMeansInitCentroids(X, K); + +% Run K-Means +[centroids, idx] = runkMeans(X, initial_centroids, max_iters); + +fprintf('Program paused. Press enter to continue.\n'); +pause; + + +%% ================= Part 5: Image Compression ====================== +% In this part of the exercise, you will use the clusters of K-Means to +% compress an image. To do this, we first find the closest clusters for +% each example. After that, we + +fprintf('\nApplying K-Means to compress an image.\n\n'); + +% Find closest cluster members +idx = findClosestCentroids(X, centroids); + +% Essentially, now we have represented the image X as in terms of the +% indices in idx. + +% We can now recover the image from the indices (idx) by mapping each pixel +% (specified by it's index in idx) to the centroid value +X_recovered = centroids(idx,:); + +% Reshape the recovered image into proper dimensions +X_recovered = reshape(X_recovered, img_size(1), img_size(2), 3); + +% Display the original image +subplot(1, 2, 1); +imagesc(A); +title('Original'); + +% Display compressed image side by side +subplot(1, 2, 2); +imagesc(X_recovered) +title(sprintf('Compressed, with %d colors.', K)); + + +fprintf('Program paused. Press enter to continue.\n'); +pause; + diff --git a/ex7/ex7_pca.m b/ex7/ex7_pca.m new file mode 100644 index 0000000..de98b13 --- /dev/null +++ b/ex7/ex7_pca.m @@ -0,0 +1,235 @@ +%% Machine Learning Online Class +% Exercise 7 | Principle Component Analysis and K-Means Clustering +% +% Instructions +% ------------ +% +% This file contains code that helps you get started on the +% exercise. You will need to complete the following functions: +% +% pca.m +% projectData.m +% recoverData.m +% computeCentroids.m +% findClosestCentroids.m +% kMeansInitCentroids.m +% +% For this exercise, you will not need to change any code in this file, +% or any other files other than those mentioned above. +% + +%% Initialization +clear ; close all; clc + +%% ================== Part 1: Load Example Dataset =================== +% We start this exercise by using a small dataset that is easily to +% visualize +% +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 ('ex7data1.mat'); + +% Visualize the example dataset +plot(X(:, 1), X(:, 2), 'bo'); +axis([0.5 6.5 2 8]); axis square; + +fprintf('Program paused. Press enter to continue.\n'); +pause; + + +%% =============== Part 2: Principal Component Analysis =============== +% You should now implement PCA, a dimension reduction technique. You +% should complete the code in pca.m +% +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)); +fprintf('\n(you should expect to see -0.707107 -0.707107)\n'); + +fprintf('Program paused. Press enter to continue.\n'); +pause; + + +%% =================== Part 3: Dimension Reduction =================== +% You should now implement the projection step to map the data onto the +% first k eigenvectors. The code will then plot the data in this reduced +% dimensional space. This will show you what the data looks like when +% using only the corresponding eigenvectors to reconstruct it. +% +% You should complete the code in projectData.m +% +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)); +fprintf('\n(this value should be about 1.481274)\n\n'); + +X_rec = recoverData(Z, U, K); +fprintf('Approximation of the first example: %f %f\n', X_rec(1, 1), X_rec(1, 2)); +fprintf('\n(this value should be about -1.047419 -1.047419)\n\n'); + +% 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 + +fprintf('Program paused. Press enter to continue.\n'); +pause; + +%% =============== Part 4: Loading and Visualizing Face Data ============= +% We start the exercise by first loading and visualizing the dataset. +% The following code will load the dataset into your environment +% +fprintf('\nLoading face dataset.\n\n'); + +% Load Face dataset +load ('ex7faces.mat') + +% Display the first 100 faces in the dataset +displayData(X(1:100, :)); + +fprintf('Program paused. Press enter to continue.\n'); +pause; + +%% =========== Part 5: PCA on Face Data: Eigenfaces =================== +% Run PCA and visualize the eigenvectors which are in this case eigenfaces +% We display the first 36 eigenfaces. +% +fprintf(['\nRunning PCA on face dataset.\n' ... + '(this mght 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)'); + +fprintf('Program paused. Press enter to continue.\n'); +pause; + + +%% ============= Part 6: Dimension Reduction for Faces ================= +% Project images to the eigen space using the top k eigenvectors +% If you are applying a machine learning algorithm +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)); + +fprintf('\n\nProgram paused. Press enter to continue.\n'); +pause; + +%% ==== Part 7: Visualization of Faces after PCA Dimension Reduction ==== +% Project images to the eigen space using the top K eigen vectors and +% visualize only using those K dimensions +% Compare to the original input, which is also displayed + +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; + +fprintf('Program paused. Press enter to continue.\n'); +pause; + + +%% === Part 8(a): Optional (ungraded) Exercise: PCA for Visualization === +% One useful application of PCA is to use it to visualize high-dimensional +% data. In the last K-Means exercise you ran K-Means on 3-dimensional +% pixel colors of an image. We first visualize this output in 3D, and then +% apply PCA to obtain a visualization in 2D. + +close all; close all; clc + +% Re-load 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('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); + +% Sample 1000 random indexes (since working with all the data is +% too expensive. 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