一、ex8.m

%% Machine Learning Online Class % Exercise 8 | Anomaly Detection and Collaborative Filtering % % Instructions % ------------ % % This file contains code that helps you get started on the % exercise. You will need to complete the following functions: % % estimateGaussian.m % selectThreshold.m % cofiCostFunc.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 easy to % visualize. % % Our example case consists of 2 network server statistics across % several machines: the latency and throughput of each machine. % This exercise will help us find possibly faulty (or very fast) machines. %fprintf('Visualizing example dataset for outlier detection.\n\n');% The following command loads the dataset. You should now have the % variables X, Xval, yval in your environment load('ex8data1.mat');% Visualize the example dataset plot(X(:, 1), X(:, 2), 'bx'); axis([0 30 0 30]); xlabel('Latency (ms)'); ylabel('Throughput (mb/s)');fprintf('Program paused. Press enter to continue.\n'); pause%% ================== Part 2: Estimate the dataset statistics =================== % For this exercise, we assume a Gaussian distribution for the dataset. % % We first estimate the parameters of our assumed Gaussian distribution, % then compute the probabilities for each of the points and then visualize % both the overall distribution and where each of the points falls in % terms of that distribution. % fprintf('Visualizing Gaussian fit.\n\n');% Estimate my and sigma2 [mu sigma2] = estimateGaussian(X);% Returns the density of the multivariate normal at each data point (row) % of X p = multivariateGaussian(X, mu, sigma2);% Visualize the fit visualizeFit(X, mu, sigma2); xlabel('Latency (ms)'); ylabel('Throughput (mb/s)');fprintf('Program paused. Press enter to continue.\n'); pause;%% ================== Part 3: Find Outliers =================== % Now you will find a good epsilon threshold using a cross-validation set % probabilities given the estimated Gaussian distribution % pval = multivariateGaussian(Xval, mu, sigma2);[epsilon F1] = selectThreshold(yval, pval); fprintf('Best epsilon found using cross-validation: %e\n', epsilon); fprintf('Best F1 on Cross Validation Set: %f\n', F1); fprintf(' (you should see a value epsilon of about 8.99e-05)\n\n');% Find the outliers in the training set and plot the outliers = find(p < epsilon);% Draw a red circle around those outliers hold on plot(X(outliers, 1), X(outliers, 2), 'ro', 'LineWidth', 2, 'MarkerSize', 10); hold offfprintf('Program paused. Press enter to continue.\n'); pause;%% ================== Part 4: Multidimensional Outliers =================== % We will now use the code from the previous part and apply it to a % harder problem in which more features describe each datapoint and only % some features indicate whether a point is an outlier. %% Loads the second dataset. You should now have the % variables X, Xval, yval in your environment load('ex8data2.mat');% Apply the same steps to the larger dataset [mu sigma2] = estimateGaussian(X);% Training set p = multivariateGaussian(X, mu, sigma2);% Cross-validation set pval = multivariateGaussian(Xval, mu, sigma2);% Find the best threshold [epsilon F1] = selectThreshold(yval, pval);fprintf('Best epsilon found using cross-validation: %e\n', epsilon); fprintf('Best F1 on Cross Validation Set: %f\n', F1); fprintf('# Outliers found: %d\n', sum(p < epsilon)); fprintf(' (you should see a value epsilon of about 1.38e-18)\n\n'); pause

二、ex8_cofi.m

%% Machine Learning Online Class % Exercise 8 | Anomaly Detection and Collaborative Filtering % % Instructions % ------------ % % This file contains code that helps you get started on the % exercise. You will need to complete the following functions: % % estimateGaussian.m % selectThreshold.m % cofiCostFunc.m % % For this exercise, you will not need to change any code in this file, % or any other files other than those mentioned above. %%% =============== Part 1: Loading movie ratings dataset ================ % You will start by loading the movie ratings dataset to understand the % structure of the data. % fprintf('Loading movie ratings dataset.\n\n');% Load data load ('ex8_movies.mat');% Y is a 1682x943 matrix, containing ratings (1-5) of 1682 movies on % 943 users % % R is a 1682x943 matrix, where R(i,j) = 1 if and only if user j gave a % rating to movie i% From the matrix, we can compute statistics like average rating. fprintf('Average rating for movie 1 (Toy Story): %f / 5\n\n', ...mean(Y(1, R(1, :))));% We can "visualize" the ratings matrix by plotting it with imagesc imagesc(Y); ylabel('Movies'); xlabel('Users');fprintf('\nProgram paused. Press enter to continue.\n'); pause;%% ============ Part 2: Collaborative Filtering Cost Function =========== % You will now implement the cost function for collaborative filtering. % To help you debug your cost function, we have included set of weights % that we trained on that. Specifically, you should complete the code in % cofiCostFunc.m to return J.% Load pre-trained weights (X, Theta, num_users, num_movies, num_features) load ('ex8_movieParams.mat');% Reduce the data set size so that this runs faster num_users = 4; num_movies = 5; num_features = 3; X = X(1:num_movies, 1:num_features); Theta = Theta(1:num_users, 1:num_features); Y = Y(1:num_movies, 1:num_users); R = R(1:num_movies, 1:num_users);% Evaluate cost function J = cofiCostFunc([X(:) ; Theta(:)], Y, R, num_users, num_movies, ...num_features, 0);fprintf(['Cost at loaded parameters: %f '...'\n(this value should be about 22.22)\n'], J);fprintf('\nProgram paused. Press enter to continue.\n'); pause;%% ============== Part 3: Collaborative Filtering Gradient ============== % Once your cost function matches up with ours, you should now implement % the collaborative filtering gradient function. Specifically, you should % complete the code in cofiCostFunc.m to return the grad argument. % fprintf('\nChecking Gradients (without regularization) ... \n');% Check gradients by running checkNNGradients checkCostFunction;fprintf('\nProgram paused. Press enter to continue.\n'); pause;%% ========= Part 4: Collaborative Filtering Cost Regularization ======== % Now, you should implement regularization for the cost function for % collaborative filtering. You can implement it by adding the cost of % regularization to the original cost computation. % % Evaluate cost function J = cofiCostFunc([X(:) ; Theta(:)], Y, R, num_users, num_movies, ...num_features, 1.5);fprintf(['Cost at loaded parameters (lambda = 1.5): %f '...'\n(this value should be about 31.34)\n'], J);fprintf('\nProgram paused. Press enter to continue.\n'); pause;%% ======= Part 5: Collaborative Filtering Gradient Regularization ====== % Once your cost matches up with ours, you should proceed to implement % regularization for the gradient. %% fprintf('\nChecking Gradients (with regularization) ... \n');% Check gradients by running checkNNGradients checkCostFunction(1.5);fprintf('\nProgram paused. Press enter to continue.\n'); pause;%% ============== Part 6: Entering ratings for a new user =============== % Before we will train the collaborative filtering model, we will first % add ratings that correspond to a new user that we just observed. This % part of the code will also allow you to put in your own ratings for the % movies in our dataset! % movieList = loadMovieList();% Initialize my ratings my_ratings = zeros(1682, 1);% Check the file movie_idx.txt for id of each movie in our dataset % For example, Toy Story (1995) has ID 1, so to rate it "4", you can set my_ratings(1) = 4;% Or suppose did not enjoy Silence of the Lambs (1991), you can set my_ratings(98) = 2;% We have selected a few movies we liked / did not like and the ratings we % gave are as follows: my_ratings(7) = 3; my_ratings(12)= 5; my_ratings(54) = 4; my_ratings(64)= 5; my_ratings(66)= 3; my_ratings(69) = 5; my_ratings(183) = 4; my_ratings(226) = 5; my_ratings(355)= 5;fprintf('\n\nNew user ratings:\n'); for i = 1:length(my_ratings)if my_ratings(i) > 0 fprintf('Rated %d for %s\n', my_ratings(i), ...movieList{i});end endfprintf('\nProgram paused. Press enter to continue.\n'); pause;%% ================== Part 7: Learning Movie Ratings ==================== % Now, you will train the collaborative filtering model on a movie rating % dataset of 1682 movies and 943 users %fprintf('\nTraining collaborative filtering...\n');% Load data load('ex8_movies.mat');% Y is a 1682x943 matrix, containing ratings (1-5) of 1682 movies by % 943 users % % R is a 1682x943 matrix, where R(i,j) = 1 if and only if user j gave a % rating to movie i% Add our own ratings to the data matrix Y = [my_ratings Y]; R = [(my_ratings ~= 0) R];% Normalize Ratings [Ynorm, Ymean] = normalizeRatings(Y, R);% Useful Values num_users = size(Y, 2); num_movies = size(Y, 1); num_features = 10;% Set Initial Parameters (Theta, X) X = randn(num_movies, num_features); Theta = randn(num_users, num_features);initial_parameters = [X(:); Theta(:)];% Set options for fmincg options = optimset('GradObj', 'on', 'MaxIter', 100);% Set Regularization lambda = 10; theta = fmincg (@(t)(cofiCostFunc(t, Y, R, num_users, num_movies, ...num_features, lambda)), ...initial_parameters, options);% Unfold the returned theta back into U and W X = reshape(theta(1:num_movies*num_features), num_movies, num_features); Theta = reshape(theta(num_movies*num_features+1:end), ...num_users, num_features);fprintf('Recommender system learning completed.\n');fprintf('\nProgram paused. Press enter to continue.\n'); pause;%% ================== Part 8: Recommendation for you ==================== % After training the model, you can now make recommendations by computing % the predictions matrix. %p = X * Theta'; my_predictions = p(:,1) + Ymean;movieList = loadMovieList();[r, ix] = sort(my_predictions, 'descend'); fprintf('\nTop recommendations for you:\n'); for i=1:10j = ix(i);fprintf('Predicting rating %.1f for movie %s\n', my_predictions(j), ...movieList{j}); endfprintf('\n\nOriginal ratings provided:\n'); for i = 1:length(my_ratings)if my_ratings(i) > 0 fprintf('Rated %d for %s\n', my_ratings(i), ...movieList{i});end end

三、estimateGaussian.m

function [mu sigma2] = estimateGaussian(X) %ESTIMATEGAUSSIAN This function estimates the parameters of a %Gaussian distribution using the data in X % [mu sigma2] = estimateGaussian(X), % The input X is the dataset with each n-dimensional data point in one row % The output is an n-dimensional vector mu, the mean of the data set % and the variances sigma^2, an n x 1 vector % % Useful variables [m, n] = size(X);% You should return these values correctly mu = zeros(n, 1); sigma2 = zeros(n, 1);% ====================== YOUR CODE HERE ====================== % Instructions: Compute the mean of the data and the variances % In particular, mu(i) should contain the mean of % the data for the i-th feature and sigma2(i) % should contain variance of the i-th feature. %mu = mean(X); sigma2 = var(X,opt=1);% =============================================================end

四、selectThreshold.m

function [bestEpsilon bestF1] = selectThreshold(yval, pval) %SELECTTHRESHOLD Find the best threshold (epsilon) to use for selecting %outliers % [bestEpsilon bestF1] = SELECTTHRESHOLD(yval, pval) finds the best % threshold to use for selecting outliers based on the results from a % validation set (pval) and the ground truth (yval). %bestEpsilon = 0; bestF1 = 0; F1 = 0;stepsize = (max(pval) - min(pval)) / 1000; for epsilon = min(pval):stepsize:max(pval)% ====================== YOUR CODE HERE ======================% Instructions: Compute the F1 score of choosing epsilon as the% threshold and place the value in F1. The code at the% end of the loop will compare the F1 score for this% choice of epsilon and set it to be the best epsilon if% it is better than the current choice of epsilon.% % Note: You can use predictions = (pval < epsilon) to get a binary vector% of 0's and 1's of the outlier predictionspredictions = (pval < epsilon);truePositives = sum((predictions == 1) & (yval == 1));falsePositives = sum((predictions == 1) & (yval == 0));falseNegatives = sum((predictions == 0) & (yval == 1));precision = truePositives / (truePositives + falsePositives);recall = truePositives / (truePositives + falseNegatives);F1 = (2 * precision * recall) / (precision + recall);% =============================================================if F1 > bestF1bestF1 = F1;bestEpsilon = epsilon;end endend

五、cofiCostFunc.m

function [J, grad] = cofiCostFunc(params, Y, R, num_users, num_movies, ...num_features, lambda) %COFICOSTFUNC Collaborative filtering cost function % [J, grad] = COFICOSTFUNC(params, Y, R, num_users, num_movies, ... % num_features, lambda) returns the cost and gradient for the % collaborative filtering problem. %% Unfold the U and W matrices from params X = reshape(params(1:num_movies*num_features), num_movies, num_features); Theta = reshape(params(num_movies*num_features+1:end), ...num_users, num_features);% You need to return the following values correctly J = 0; X_grad = zeros(size(X)); Theta_grad = zeros(size(Theta));% ====================== YOUR CODE HERE ====================== % Instructions: Compute the cost function and gradient for collaborative % filtering. Concretely, you should first implement the cost % function (without regularization) and make sure it is % matches our costs. After that, you should implement the % gradient and use the checkCostFunction routine to check % that the gradient is correct. Finally, you should implement % regularization. % % Notes: X - num_movies x num_features matrix of movie features % Theta - num_users x num_features matrix of user features % Y - num_movies x num_users matrix of user ratings of movies % R - num_movies x num_users matrix, where R(i, j) = 1 if the % i-th movie was rated by the j-th user % % You should set the following variables correctly: % % X_grad - num_movies x num_features matrix, containing the % partial derivatives w.r.t. to each element of X % Theta_grad - num_users x num_features matrix, containing the % partial derivatives w.r.t. to each element of Theta %errors = (X*Theta' - Y) .* R; regularizationTheta = lambda/2 * sum(sum(Theta.^2)); regularizationX = lambda/2 * sum(sum(X.^2));J = 1/2 * sum(sum(errors .^2)) + regularizationTheta + regularizationX; X_grad = errors * Theta + lambda * X; Theta_grad = errors' * X + lambda * Theta;% =============================================================grad = [X_grad(:); Theta_grad(:)];end

總結

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