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@ngosangns
ngosangns committed Feb 23, 2019
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48 changes: 48 additions & 0 deletions ex/ex8/checkCostFunction.m
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function checkCostFunction(lambda)
%CHECKCOSTFUNCTION Creates a collaborative filering problem
%to check your cost function and gradients
% CHECKCOSTFUNCTION(lambda) Creates a collaborative filering problem
% to check your cost function and gradients, it will output the
% analytical gradients produced by your code and the numerical gradients
% (computed using computeNumericalGradient). These two gradient
% computations should result in very similar values.

% Set lambda
if ~exist('lambda', 'var') || isempty(lambda)
lambda = 0;
end

%% Create small problem
X_t = rand(4, 3);
Theta_t = rand(5, 3);

% Zap out most entries
Y = X_t * Theta_t';
Y(rand(size(Y)) > 0.5) = 0;
R = zeros(size(Y));
R(Y ~= 0) = 1;

%% Run Gradient Checking
X = randn(size(X_t));
Theta = randn(size(Theta_t));
num_users = size(Y, 2);
num_movies = size(Y, 1);
num_features = size(Theta_t, 2);

numgrad = computeNumericalGradient( ...
@(t) cofiCostFunc(t, Y, R, num_users, num_movies, ...
num_features, lambda), [X(:); Theta(:)]);

[cost, grad] = cofiCostFunc([X(:); Theta(:)], Y, R, num_users, ...
num_movies, num_features, lambda);

disp([numgrad grad]);
fprintf(['The above two columns you get should be very similar.\n' ...
'(Left-Your Numerical Gradient, Right-Analytical Gradient)\n\n']);

diff = norm(numgrad-grad)/norm(numgrad+grad);
fprintf(['If your cost function implementation is correct, then \n' ...
'the relative difference will be small (less than 1e-9). \n' ...
'\nRelative Difference: %g\n'], diff);

end
59 changes: 59 additions & 0 deletions ex/ex8/cofiCostFunc.m
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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
%

for i = 1:num_movies
for j = 1:num_users
if(R(i, j)==1)
J = J + (Theta(j, :)*transpose(X(i, :))-Y(i, j)).^2;
end;
end;
end;
X = [zeros(num_movies, 1) X(:, 2:end)];
Theta = [zeros(num_movies, 1) Theta(:, 2:end)];
J = J + sum(sum(X.^2)) + sum(sum(Theta.^2));
X(:, 1) = ones(num_movies, 1);

% =============================================================

grad = [X_grad(:); Theta_grad(:)];

end
29 changes: 29 additions & 0 deletions ex/ex8/computeNumericalGradient.m
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function numgrad = computeNumericalGradient(J, theta)
%COMPUTENUMERICALGRADIENT Computes the gradient using "finite differences"
%and gives us a numerical estimate of the gradient.
% numgrad = COMPUTENUMERICALGRADIENT(J, theta) computes the numerical
% gradient of the function J around theta. Calling y = J(theta) should
% return the function value at theta.

% Notes: The following code implements numerical gradient checking, and
% returns the numerical gradient.It sets numgrad(i) to (a numerical
% approximation of) the partial derivative of J with respect to the
% i-th input argument, evaluated at theta. (i.e., numgrad(i) should
% be the (approximately) the partial derivative of J with respect
% to theta(i).)
%

numgrad = zeros(size(theta));
perturb = zeros(size(theta));
e = 1e-4;
for p = 1:numel(theta)
% Set perturbation vector
perturb(p) = e;
loss1 = J(theta - perturb);
loss2 = J(theta + perturb);
% Compute Numerical Gradient
numgrad(p) = (loss2 - loss1) / (2*e);
perturb(p) = 0;
end

end
30 changes: 30 additions & 0 deletions ex/ex8/estimateGaussian.m
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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 = transpose(sum(X))/m;
sigma2 = sum((X.-transpose(mu)).^2)/m;

% =============================================================


end
121 changes: 121 additions & 0 deletions ex/ex8/ex8.m
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%% 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');
fprintf(' (you should see a Best F1 value of 0.875000)\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 off

fprintf('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(' (you should see a value epsilon of about 1.38e-18)\n');
fprintf(' (you should see a Best F1 value of 0.615385)\n');
fprintf('# Outliers found: %d\n\n', sum(p < epsilon));
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