Mercurial > hg > machine-learning-hw7
changeset 0:ded78d0b4987
init
| author | Jordi Gutiérrez Hermoso <jordigh@octave.org> |
|---|---|
| date | Mon, 05 Dec 2011 00:19:20 -0500 |
| parents | |
| children | 90d2a292663c |
| files | bird_small.png computeCentroids.m displayData.m drawLine.m ex7.m ex7_pca.m ex7data1.mat ex7data2.mat featureNormalize.m findClosestCentroids.m kMeansInitCentroids.m pca.m plotDataPoints.m plotProgresskMeans.m projectData.m recoverData.m runkMeans.m submit.m submitWeb.m |
| diffstat | 19 files changed, 1462 insertions(+), 0 deletions(-) [+] |
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new file mode 100644 --- /dev/null +++ b/computeCentroids.m @@ -0,0 +1,40 @@ +function centroids = computeCentroids(X, idx, K) +%COMPUTECENTROIDS returs the new centroids by computing the means of the +%data points assigned to each centroid. +% centroids = COMPUTECENTROIDS(X, idx, K) returns the new centroids by +% computing the means of the data points assigned to each centroid. It is +% given a dataset X where each row is a single data point, a vector +% idx of centroid assignments (i.e. each entry in range [1..K]) for each +% example, and K, the number of centroids. You should return a matrix +% centroids, where each row of centroids is the mean of the data points +% assigned to it. +% + +% Useful variables +[m n] = size(X); + +% You need to return the following variables correctly. +centroids = zeros(K, n); + + +% ====================== YOUR CODE HERE ====================== +% Instructions: Go over every centroid and compute mean of all points that +% belong to it. Concretely, the row vector centroids(i, :) +% should contain the mean of the data points assigned to +% centroid i. +% +% Note: You can use a for-loop over the centroids to compute this. +% + + + + + + + + +% ============================================================= + + +end +
new file mode 100644 --- /dev/null +++ b/displayData.m @@ -0,0 +1,59 @@ +function [h, display_array] = displayData(X, example_width) +%DISPLAYDATA Display 2D data in a nice grid +% [h, display_array] = DISPLAYDATA(X, example_width) displays 2D data +% stored in X in a nice grid. It returns the figure handle h and the +% displayed array if requested. + +% Set example_width automatically if not passed in +if ~exist('example_width', 'var') || isempty(example_width) + example_width = round(sqrt(size(X, 2))); +end + +% Gray Image +colormap(gray); + +% Compute rows, cols +[m n] = size(X); +example_height = (n / example_width); + +% Compute number of items to display +display_rows = floor(sqrt(m)); +display_cols = ceil(m / display_rows); + +% Between images padding +pad = 1; + +% Setup blank display +display_array = - ones(pad + display_rows * (example_height + pad), ... + pad + display_cols * (example_width + pad)); + +% Copy each example into a patch on the display array +curr_ex = 1; +for j = 1:display_rows + for i = 1:display_cols + if curr_ex > m, + break; + end + % Copy the patch + + % Get the max value of the patch + max_val = max(abs(X(curr_ex, :))); + display_array(pad + (j - 1) * (example_height + pad) + (1:example_height), ... + pad + (i - 1) * (example_width + pad) + (1:example_width)) = ... + reshape(X(curr_ex, :), example_height, 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
new file mode 100644 --- /dev/null +++ b/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
new file mode 100644 --- /dev/null +++ b/ex7.m @@ -0,0 +1,170 @@ +%% 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')); +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; +
new file mode 100644 --- /dev/null +++ b/ex7_pca.m @@ -0,0 +1,231 @@ +%% 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')); +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. 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'); +fprintf('Program paused. Press enter to continue.\n'); +pause; + +%% === Part 8(b): Optional (ungraded) Exercise: PCA for Visualization === +% Use PCA to project this cloud to 2D for visualization + +% 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'); +fprintf('Program paused. Press enter to continue.\n'); +pause;
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new file mode 100644 --- /dev/null +++ b/featureNormalize.m @@ -0,0 +1,17 @@ +function [X_norm, mu, sigma] = featureNormalize(X) +%FEATURENORMALIZE Normalizes the features in X +% FEATURENORMALIZE(X) returns a normalized version of X where +% the mean value of each feature is 0 and the standard deviation +% is 1. This is often a good preprocessing step to do when +% working with learning algorithms. + +mu = mean(X); +X_norm = bsxfun(@minus, X, mu); + +sigma = std(X_norm); +X_norm = bsxfun(@rdivide, X_norm, sigma); + + +% ============================================================ + +end
new file mode 100644 --- /dev/null +++ b/findClosestCentroids.m @@ -0,0 +1,33 @@ +function idx = findClosestCentroids(X, centroids) +%FINDCLOSESTCENTROIDS computes the centroid memberships for every example +% idx = FINDCLOSESTCENTROIDS (X, centroids) returns the closest centroids +% in idx for a dataset X where each row is a single example. idx = m x 1 +% vector of centroid assignments (i.e. each entry in range [1..K]) +% + +% Set K +K = size(centroids, 1); + +% You need to return the following variables correctly. +idx = zeros(size(X,1), 1); + +% ====================== YOUR CODE HERE ====================== +% Instructions: Go over every example, find its closest centroid, and store +% the index inside idx at the appropriate location. +% Concretely, idx(i) should contain the index of the centroid +% closest to example i. Hence, it should be a value in the +% range 1..K +% +% Note: You can use a for-loop over the examples to compute this. +% + + + + + + + +% ============================================================= + +end +
new file mode 100644 --- /dev/null +++ b/kMeansInitCentroids.m @@ -0,0 +1,26 @@ +function centroids = kMeansInitCentroids(X, K) +%KMEANSINITCENTROIDS This function initializes K centroids that are to be +%used in K-Means on the dataset X +% centroids = KMEANSINITCENTROIDS(X, K) returns K initial centroids to be +% used with the K-Means on the dataset X +% + +% You should return this values correctly +centroids = zeros(K, size(X, 2)); + +% ====================== YOUR CODE HERE ====================== +% Instructions: You should set centroids to randomly chosen examples from +% the dataset X +% + + + + + + + + +% ============================================================= + +end +
new file mode 100644 --- /dev/null +++ b/pca.m @@ -0,0 +1,31 @@ +function [U, S] = pca(X) +%PCA Run principal component analysis on the dataset X +% [U, S, X] = pca(X) computes eigenvectors of the covariance matrix of X +% Returns the eigenvectors U, the eigenvalues (on diagonal) in S +% + +% Useful values +[m, n] = size(X); + +% You need to return the following variables correctly. +U = zeros(n); +S = zeros(n); + +% ====================== YOUR CODE HERE ====================== +% Instructions: You should first compute the covariance matrix. Then, you +% should use the "svd" function to compute the eigenvectors +% and eigenvalues of the covariance matrix. +% +% Note: When computing the covariance matrix, remember to divide by m (the +% number of examples). +% + + + + + + + +% ========================================================================= + +end
new file mode 100644 --- /dev/null +++ b/plotDataPoints.m @@ -0,0 +1,14 @@ +function plotDataPoints(X, idx, K) +%PLOTDATAPOINTS plots data points in X, coloring them so that those with the same +%index assignments in idx have the same color +% PLOTDATAPOINTS(X, idx, K) plots data points in X, coloring them so that those +% with the same index assignments in idx have the same color + +% Create palette +palette = hsv(K + 1); +colors = palette(idx, :); + +% Plot the data +scatter(X(:,1), X(:,2), 15, colors); + +end
new file mode 100644 --- /dev/null +++ b/plotProgresskMeans.m @@ -0,0 +1,27 @@ +function plotProgresskMeans(X, centroids, previous, idx, K, i) +%PLOTPROGRESSKMEANS is a helper function that displays the progress of +%k-Means as it is running. It is intended for use only with 2D data. +% PLOTPROGRESSKMEANS(X, centroids, previous, idx, K, i) plots the data +% points with colors assigned to each centroid. With the previous +% centroids, it also plots a line between the previous locations and +% current locations of the centroids. +% + +% Plot the examples +plotDataPoints(X, idx, K); + +% Plot the centroids as black x's +plot(centroids(:,1), centroids(:,2), 'x', ... + 'MarkerEdgeColor','k', ... + 'MarkerSize', 10, 'LineWidth', 3); + +% Plot the history of the centroids with lines +for j=1:size(centroids,1) + drawLine(centroids(j, :), previous(j, :)); +end + +% Title +title(sprintf('Iteration number %d', i)) + +end +
new file mode 100644 --- /dev/null +++ b/projectData.m @@ -0,0 +1,26 @@ +function Z = projectData(X, U, K) +%PROJECTDATA Computes the reduced data representation when projecting only +%on to the top k eigenvectors +% Z = projectData(X, U, K) computes the projection of +% the normalized inputs X into the reduced dimensional space spanned by +% the first K columns of U. It returns the projected examples in Z. +% + +% You need to return the following variables correctly. +Z = zeros(size(X, 1), K); + +% ====================== YOUR CODE HERE ====================== +% Instructions: Compute the projection of the data using only the top K +% eigenvectors in U (first K columns). +% For the i-th example X(i,:), the projection on to the k-th +% eigenvector is given as follows: +% x = X(i, :)'; +% projection_k = x' * U(:, k); +% + + + + +% ============================================================= + +end
new file mode 100644 --- /dev/null +++ b/recoverData.m @@ -0,0 +1,28 @@ +function X_rec = recoverData(Z, U, K) +%RECOVERDATA Recovers an approximation of the original data when using the +%projected data +% X_rec = RECOVERDATA(Z, U, K) recovers an approximation the +% original data that has been reduced to K dimensions. It returns the +% approximate reconstruction in X_rec. +% + +% You need to return the following variables correctly. +X_rec = zeros(size(Z, 1), size(U, 1)); + +% ====================== YOUR CODE HERE ====================== +% Instructions: Compute the approximation of the data by projecting back +% onto the original space using the top K eigenvectors in U. +% +% For the i-th example Z(i,:), the (approximate) +% recovered data for dimension j is given as follows: +% v = Z(i, :)'; +% recovered_j = v' * U(j, 1:K)'; +% +% Notice that U(j, 1:K) is a row vector. +% + + + +% ============================================================= + +end
new file mode 100644 --- /dev/null +++ b/runkMeans.m @@ -0,0 +1,64 @@ +function [centroids, idx] = runkMeans(X, initial_centroids, ... + max_iters, plot_progress) +%RUNKMEANS runs the K-Means algorithm on data matrix X, where each row of X +%is a single example +% [centroids, idx] = RUNKMEANS(X, initial_centroids, max_iters, ... +% plot_progress) runs the K-Means algorithm on data matrix X, where each +% row of X is a single example. It uses initial_centroids used as the +% initial centroids. max_iters specifies the total number of interactions +% of K-Means to execute. plot_progress is a true/false flag that +% indicates if the function should also plot its progress as the +% learning happens. This is set to false by default. runkMeans returns +% centroids, a Kxn matrix of the computed centroids and idx, a m x 1 +% vector of centroid assignments (i.e. each entry in range [1..K]) +% + +% Set default value for plot progress +if ~exist('plot_progress', 'var') || isempty(plot_progress) + plot_progress = false; +end + +% Plot the data if we are plotting progress +if plot_progress + figure; + hold on; +end + +% Initialize values +[m n] = size(X); +K = size(initial_centroids, 1); +centroids = initial_centroids; +previous_centroids = centroids; +idx = zeros(m, 1); + +% Run K-Means +for i=1:max_iters + + % Output progress + fprintf('K-Means iteration %d/%d...\n', i, max_iters); + if exist('OCTAVE_VERSION') + fflush(stdout); + end + + % For each example in X, assign it to the closest centroid + idx = findClosestCentroids(X, centroids); + + % Optionally, plot progress here + if plot_progress + plotProgresskMeans(X, centroids, previous_centroids, idx, K, i); + previous_centroids = centroids; + fprintf('Press enter to continue.\n'); + pause; + end + + % Given the memberships, compute new centroids + centroids = computeCentroids(X, idx, K); +end + +% Hold off if we are plotting progress +if plot_progress + hold off; +end + +end +
new file mode 100644 --- /dev/null +++ b/submit.m @@ -0,0 +1,336 @@ +function submit(partId) +%SUBMIT Submit your code and output to the ml-class servers +% SUBMIT() will connect to the ml-class server and submit your solution + + fprintf('==\n== [ml-class] Submitting Solutions | Programming Exercise %s\n==\n', ... + homework_id()); + if ~exist('partId', 'var') || isempty(partId) + partId = promptPart(); + end + + % Check valid partId + partNames = validParts(); + if ~isValidPartId(partId) + fprintf('!! Invalid homework part selected.\n'); + fprintf('!! Expected an integer from 1 to %d.\n', numel(partNames) + 1); + fprintf('!! Submission Cancelled\n'); + return + end + + [login password] = loginPrompt(); + if isempty(login) + fprintf('!! Submission Cancelled\n'); + return + end + + fprintf('\n== Connecting to ml-class ... '); + if exist('OCTAVE_VERSION') + fflush(stdout); + end + + % Setup submit list + if partId == numel(partNames) + 1 + submitParts = 1:numel(partNames); + else + submitParts = [partId]; + end + + for s = 1:numel(submitParts) + % Submit this part + partId = submitParts(s); + + % Get Challenge + [login, ch, signature] = getChallenge(login); + if isempty(login) || isempty(ch) || isempty(signature) + % Some error occured, error string in first return element. + fprintf('\n!! Error: %s\n\n', login); + return + end + + % Attempt Submission with Challenge + ch_resp = challengeResponse(login, password, ch); + [result, str] = submitSolution(login, ch_resp, partId, output(partId), ... + source(partId), signature); + + fprintf('\n== [ml-class] Submitted Homework %s - Part %d - %s\n', ... + homework_id(), partId, partNames{partId}); + fprintf('== %s\n', strtrim(str)); + if exist('OCTAVE_VERSION') + fflush(stdout); + end + end + +end + +% ================== CONFIGURABLES FOR EACH HOMEWORK ================== + +function id = homework_id() + id = '7'; +end + +function [partNames] = validParts() + partNames = { + 'Find Closest Centroids (k-Means)', ... + 'Compute Centroid Means (k-Means)' ... + 'PCA', ... + 'Project Data (PCA)', ... + 'Recover Data (PCA)' ... + }; +end + +function srcs = sources() + % Separated by part + srcs = { { 'findClosestCentroids.m' }, ... + { 'computeCentroids.m' }, ... + { 'pca.m' }, ... + { 'projectData.m' }, ... + { 'recoverData.m' } ... + }; +end + +function out = output(partId) + % Random Test Cases + X = reshape(sin(1:165), 15, 11); + Z = reshape(cos(1:121), 11, 11); + C = Z(1:5, :); + idx = (1 + mod(1:15, 3))'; + if partId == 1 + idx = findClosestCentroids(X, C); + out = sprintf('%0.5f ', idx(:)); + elseif partId == 2 + centroids = computeCentroids(X, idx, 3); + out = sprintf('%0.5f ', centroids(:)); + elseif partId == 3 + [U, S] = pca(X); + out = sprintf('%0.5f ', abs([U(:); S(:)])); + elseif partId == 4 + X_proj = projectData(X, Z, 5); + out = sprintf('%0.5f ', X_proj(:)); + elseif partId == 5 + X_rec = recoverData(X(:,1:5), Z, 5); + out = sprintf('%0.5f ', X_rec(:)); + end +end + +function url = challenge_url() + url = 'http://www.ml-class.org/course/homework/challenge'; +end + +function url = submit_url() + url = 'http://www.ml-class.org/course/homework/submit'; +end + +% ========================= CHALLENGE HELPERS ========================= + +function src = source(partId) + src = ''; + src_files = sources(); + if partId <= numel(src_files) + flist = src_files{partId}; + for i = 1:numel(flist) + fid = fopen(flist{i}); + while ~feof(fid) + line = fgets(fid); + src = [src line]; + end + fclose(fid); + src = [src '||||||||']; + end + end +end + +function ret = isValidPartId(partId) + partNames = validParts(); + ret = (~isempty(partId)) && (partId >= 1) && (partId <= numel(partNames) + 1); +end + +function partId = promptPart() + fprintf('== Select which part(s) to submit:\n', ... + homework_id()); + partNames = validParts(); + srcFiles = sources(); + for i = 1:numel(partNames) + fprintf('== %d) %s [', i, partNames{i}); + fprintf(' %s ', srcFiles{i}{:}); + fprintf(']\n'); + end + fprintf('== %d) All of the above \n==\nEnter your choice [1-%d]: ', ... + numel(partNames) + 1, numel(partNames) + 1); + selPart = input('', 's'); + partId = str2num(selPart); + if ~isValidPartId(partId) + partId = -1; + end +end + +function [email,ch,signature] = getChallenge(email) + str = urlread(challenge_url(), 'post', {'email_address', email}); + + str = strtrim(str); + [email, str] = strtok (str, '|'); + [ch, str] = strtok (str, '|'); + [signature, str] = strtok (str, '|'); +end + + +function [result, str] = submitSolution(email, ch_resp, part, output, ... + source, signature) + + params = {'homework', homework_id(), ... + 'part', num2str(part), ... + 'email', email, ... + 'output', output, ... + 'source', source, ... + 'challenge_response', ch_resp, ... + 'signature', signature}; + + str = urlread(submit_url(), 'post', params); + + % Parse str to read for success / failure + result = 0; + +end + +% =========================== LOGIN HELPERS =========================== + +function [login password] = loginPrompt() + % Prompt for password + [login password] = basicPrompt(); + + if isempty(login) || isempty(password) + login = []; password = []; + end +end + + +function [login password] = basicPrompt() + login = input('Login (Email address): ', 's'); + password = input('Password: ', 's'); +end + + +function [str] = challengeResponse(email, passwd, challenge) + salt = ')~/|]QMB3[!W`?OVt7qC"@+}'; + str = sha1([challenge sha1([salt email passwd])]); + sel = randperm(numel(str)); + sel = sort(sel(1:16)); + str = str(sel); +end + + +% =============================== SHA-1 ================================ + +function hash = sha1(str) + + % Initialize variables + h0 = uint32(1732584193); + h1 = uint32(4023233417); + h2 = uint32(2562383102); + h3 = uint32(271733878); + h4 = uint32(3285377520); + + % Convert to word array + strlen = numel(str); + + % Break string into chars and append the bit 1 to the message + mC = [double(str) 128]; + mC = [mC zeros(1, 4-mod(numel(mC), 4), 'uint8')]; + + numB = strlen * 8; + if exist('idivide') + numC = idivide(uint32(numB + 65), 512, 'ceil'); + else + numC = ceil(double(numB + 65)/512); + end + numW = numC * 16; + mW = zeros(numW, 1, 'uint32'); + + idx = 1; + for i = 1:4:strlen + 1 + mW(idx) = bitor(bitor(bitor( ... + bitshift(uint32(mC(i)), 24), ... + bitshift(uint32(mC(i+1)), 16)), ... + bitshift(uint32(mC(i+2)), 8)), ... + uint32(mC(i+3))); + idx = idx + 1; + end + + % Append length of message + mW(numW - 1) = uint32(bitshift(uint64(numB), -32)); + mW(numW) = uint32(bitshift(bitshift(uint64(numB), 32), -32)); + + % Process the message in successive 512-bit chs + for cId = 1 : double(numC) + cSt = (cId - 1) * 16 + 1; + cEnd = cId * 16; + ch = mW(cSt : cEnd); + + % Extend the sixteen 32-bit words into eighty 32-bit words + for j = 17 : 80 + ch(j) = ch(j - 3); + ch(j) = bitxor(ch(j), ch(j - 8)); + ch(j) = bitxor(ch(j), ch(j - 14)); + ch(j) = bitxor(ch(j), ch(j - 16)); + ch(j) = bitrotate(ch(j), 1); + end + + % Initialize hash value for this ch + a = h0; + b = h1; + c = h2; + d = h3; + e = h4; + + % Main loop + for i = 1 : 80 + if(i >= 1 && i <= 20) + f = bitor(bitand(b, c), bitand(bitcmp(b), d)); + k = uint32(1518500249); + elseif(i >= 21 && i <= 40) + f = bitxor(bitxor(b, c), d); + k = uint32(1859775393); + elseif(i >= 41 && i <= 60) + f = bitor(bitor(bitand(b, c), bitand(b, d)), bitand(c, d)); + k = uint32(2400959708); + elseif(i >= 61 && i <= 80) + f = bitxor(bitxor(b, c), d); + k = uint32(3395469782); + end + + t = bitrotate(a, 5); + t = bitadd(t, f); + t = bitadd(t, e); + t = bitadd(t, k); + t = bitadd(t, ch(i)); + e = d; + d = c; + c = bitrotate(b, 30); + b = a; + a = t; + + end + h0 = bitadd(h0, a); + h1 = bitadd(h1, b); + h2 = bitadd(h2, c); + h3 = bitadd(h3, d); + h4 = bitadd(h4, e); + + end + + hash = reshape(dec2hex(double([h0 h1 h2 h3 h4]), 8)', [1 40]); + + hash = lower(hash); + +end + +function ret = bitadd(iA, iB) + ret = double(iA) + double(iB); + ret = bitset(ret, 33, 0); + ret = uint32(ret); +end + +function ret = bitrotate(iA, places) + t = bitshift(iA, places - 32); + ret = bitshift(iA, places); + ret = bitor(ret, t); +end
new file mode 100644 --- /dev/null +++ b/submitWeb.m @@ -0,0 +1,352 @@ +function submitWeb(partId) +%SUBMITWEB Generates a base64 encoded string for web-based submissions +% SUBMITWEB() will generate a base64 encoded string so that you can submit your +% solutions via a web form + + fprintf('==\n== [ml-class] Submitting Solutions | Programming Exercise %s\n==\n', ... + homework_id()); + if ~exist('partId', 'var') || isempty(partId) + partId = promptPart(); + end + + % Check valid partId + partNames = validParts(); + if ~isValidPartId(partId) + fprintf('!! Invalid homework part selected.\n'); + fprintf('!! Expected an integer from 1 to %d.\n', numel(partNames)); + fprintf('!! Submission Cancelled\n'); + return + end + + [login] = loginPrompt(); + if isempty(login) + fprintf('!! Submission Cancelled\n'); + return + end + + [result] = submitSolution(login, partId, output(partId), ... + source(partId)); + result = base64encode(result); + + fprintf('\nSave as submission file [submit_ex%s_part%d.txt]: ', ... + homework_id(), partId); + saveAsFile = input('', 's'); + if (isempty(saveAsFile)) + saveAsFile = sprintf('submit_ex%s_part%d.txt', homework_id(), partId); + end + + fid = fopen(saveAsFile, 'w'); + if (fid) + fwrite(fid, result); + fclose(fid); + fprintf('\nSaved your solutions to %s.\n\n', saveAsFile); + fprintf(['You can now submit your solutions through the web \n' ... + 'form in the programming exercises. Select the corresponding \n' ... + 'programming exercise to access the form.\n']); + + else + fprintf('Unable to save to %s\n\n', saveAsFile); + fprintf(['You can create a submission file by saving the \n' ... + 'following text in a file: (press enter to continue)\n\n']); + pause; + fprintf(result); + end + +end + +% ================== CONFIGURABLES FOR EACH HOMEWORK ================== + +function id = homework_id() + id = '7'; +end + +function [partNames] = validParts() + partNames = { + 'Find Closest Centroids (k-Means)', ... + 'Compute Centroid Means (k-Means)' ... + 'PCA', ... + 'Project Data (PCA)', ... + 'Recover Data (PCA)' ... + }; +end + +function srcs = sources() + % Separated by part + srcs = { { 'findClosestCentroids.m' }, ... + { 'computeCentroids.m' }, ... + { 'pca.m' }, ... + { 'projectData.m' }, ... + { 'recoverData.m' } ... + }; +end + +function out = output(partId) + % Random Test Cases + X = reshape(sin(1:165), 15, 11); + Z = reshape(cos(1:121), 11, 11); + C = Z(1:5, :); + idx = (1 + mod(1:15, 3))'; + if partId == 1 + idx = findClosestCentroids(X, C); + out = sprintf('%0.5f ', idx(:)); + elseif partId == 2 + centroids = computeCentroids(X, idx, 3); + out = sprintf('%0.5f ', centroids(:)); + elseif partId == 3 + [U, S] = pca(X); + out = sprintf('%0.5f ', abs([U(:); S(:)])); + elseif partId == 4 + X_proj = projectData(X, Z, 5); + out = sprintf('%0.5f ', X_proj(:)); + elseif partId == 5 + X_rec = recoverData(X(:,1:5), Z, 5); + out = sprintf('%0.5f ', X_rec(:)); + end +end + + +% ========================= SUBMIT HELPERS ========================= + +function src = source(partId) + src = ''; + src_files = sources(); + if partId <= numel(src_files) + flist = src_files{partId}; + for i = 1:numel(flist) + fid = fopen(flist{i}); + while ~feof(fid) + line = fgets(fid); + src = [src line]; + end + fclose(fid); + src = [src '||||||||']; + end + end +end + +function ret = isValidPartId(partId) + partNames = validParts(); + ret = (~isempty(partId)) && (partId >= 1) && (partId <= numel(partNames)); +end + +function partId = promptPart() + fprintf('== Select which part(s) to submit:\n', ... + homework_id()); + partNames = validParts(); + srcFiles = sources(); + for i = 1:numel(partNames) + fprintf('== %d) %s [', i, partNames{i}); + fprintf(' %s ', srcFiles{i}{:}); + fprintf(']\n'); + end + fprintf('\nEnter your choice [1-%d]: ', ... + numel(partNames)); + selPart = input('', 's'); + partId = str2num(selPart); + if ~isValidPartId(partId) + partId = -1; + end +end + + +function [result, str] = submitSolution(email, part, output, source) + + result = ['a:5:{' ... + p_s('homework') p_s64(homework_id()) ... + p_s('part') p_s64(part) ... + p_s('email') p_s64(email) ... + p_s('output') p_s64(output) ... + p_s('source') p_s64(source) ... + '}']; + +end + +function s = p_s(str) + s = ['s:' num2str(numel(str)) ':"' str '";']; +end + +function s = p_s64(str) + str = base64encode(str, ''); + s = ['s:' num2str(numel(str)) ':"' str '";']; +end + +% =========================== LOGIN HELPERS =========================== + +function [login] = loginPrompt() + % Prompt for password + [login] = basicPrompt(); +end + + +function [login] = basicPrompt() + login = input('Login (Email address): ', 's'); +end + + +% =========================== Base64 Encoder ============================ +% Thanks to Peter John Acklam +% + +function y = base64encode(x, eol) +%BASE64ENCODE Perform base64 encoding on a string. +% +% BASE64ENCODE(STR, EOL) encode the given string STR. EOL is the line ending +% sequence to use; it is optional and defaults to '\n' (ASCII decimal 10). +% The returned encoded string is broken into lines of no more than 76 +% characters each, and each line will end with EOL unless it is empty. Let +% EOL be empty if you do not want the encoded string broken into lines. +% +% STR and EOL don't have to be strings (i.e., char arrays). The only +% requirement is that they are vectors containing values in the range 0-255. +% +% This function may be used to encode strings into the Base64 encoding +% specified in RFC 2045 - MIME (Multipurpose Internet Mail Extensions). The +% Base64 encoding is designed to represent arbitrary sequences of octets in a +% form that need not be humanly readable. A 65-character subset +% ([A-Za-z0-9+/=]) of US-ASCII is used, enabling 6 bits to be represented per +% printable character. +% +% Examples +% -------- +% +% If you want to encode a large file, you should encode it in chunks that are +% a multiple of 57 bytes. This ensures that the base64 lines line up and +% that you do not end up with padding in the middle. 57 bytes of data fills +% one complete base64 line (76 == 57*4/3): +% +% If ifid and ofid are two file identifiers opened for reading and writing, +% respectively, then you can base64 encode the data with +% +% while ~feof(ifid) +% fwrite(ofid, base64encode(fread(ifid, 60*57))); +% end +% +% or, if you have enough memory, +% +% fwrite(ofid, base64encode(fread(ifid))); +% +% See also BASE64DECODE. + +% Author: Peter John Acklam +% Time-stamp: 2004-02-03 21:36:56 +0100 +% E-mail: pjacklam@online.no +% URL: http://home.online.no/~pjacklam + + if isnumeric(x) + x = num2str(x); + end + + % make sure we have the EOL value + if nargin < 2 + eol = sprintf('\n'); + else + if sum(size(eol) > 1) > 1 + error('EOL must be a vector.'); + end + if any(eol(:) > 255) + error('EOL can not contain values larger than 255.'); + end + end + + if sum(size(x) > 1) > 1 + error('STR must be a vector.'); + end + + x = uint8(x); + eol = uint8(eol); + + ndbytes = length(x); % number of decoded bytes + nchunks = ceil(ndbytes / 3); % number of chunks/groups + nebytes = 4 * nchunks; % number of encoded bytes + + % add padding if necessary, to make the length of x a multiple of 3 + if rem(ndbytes, 3) + x(end+1 : 3*nchunks) = 0; + end + + x = reshape(x, [3, nchunks]); % reshape the data + y = repmat(uint8(0), 4, nchunks); % for the encoded data + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % Split up every 3 bytes into 4 pieces + % + % aaaaaabb bbbbcccc ccdddddd + % + % to form + % + % 00aaaaaa 00bbbbbb 00cccccc 00dddddd + % + y(1,:) = bitshift(x(1,:), -2); % 6 highest bits of x(1,:) + + y(2,:) = bitshift(bitand(x(1,:), 3), 4); % 2 lowest bits of x(1,:) + y(2,:) = bitor(y(2,:), bitshift(x(2,:), -4)); % 4 highest bits of x(2,:) + + y(3,:) = bitshift(bitand(x(2,:), 15), 2); % 4 lowest bits of x(2,:) + y(3,:) = bitor(y(3,:), bitshift(x(3,:), -6)); % 2 highest bits of x(3,:) + + y(4,:) = bitand(x(3,:), 63); % 6 lowest bits of x(3,:) + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % Now perform the following mapping + % + % 0 - 25 -> A-Z + % 26 - 51 -> a-z + % 52 - 61 -> 0-9 + % 62 -> + + % 63 -> / + % + % We could use a mapping vector like + % + % ['A':'Z', 'a':'z', '0':'9', '+/'] + % + % but that would require an index vector of class double. + % + z = repmat(uint8(0), size(y)); + i = y <= 25; z(i) = 'A' + double(y(i)); + i = 26 <= y & y <= 51; z(i) = 'a' - 26 + double(y(i)); + i = 52 <= y & y <= 61; z(i) = '0' - 52 + double(y(i)); + i = y == 62; z(i) = '+'; + i = y == 63; z(i) = '/'; + y = z; + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % Add padding if necessary. + % + npbytes = 3 * nchunks - ndbytes; % number of padding bytes + if npbytes + y(end-npbytes+1 : end) = '='; % '=' is used for padding + end + + if isempty(eol) + + % reshape to a row vector + y = reshape(y, [1, nebytes]); + + else + + nlines = ceil(nebytes / 76); % number of lines + neolbytes = length(eol); % number of bytes in eol string + + % pad data so it becomes a multiple of 76 elements + y = [y(:) ; zeros(76 * nlines - numel(y), 1)]; + y(nebytes + 1 : 76 * nlines) = 0; + y = reshape(y, 76, nlines); + + % insert eol strings + eol = eol(:); + y(end + 1 : end + neolbytes, :) = eol(:, ones(1, nlines)); + + % remove padding, but keep the last eol string + m = nebytes + neolbytes * (nlines - 1); + n = (76+neolbytes)*nlines - neolbytes; + y(m+1 : n) = ''; + + % extract and reshape to row vector + y = reshape(y, 1, m+neolbytes); + + end + + % output is a character array + y = char(y); + +end