ml_ex8

ex8:

%% Machine Learning Online Class
%  Exercise 8 | Anomaly Detection and Collaborative Filtering
%% Initialization
clear ; close all; clc

%% ================== Part 1: Load Example Dataset  ===================
%  The following command loads the dataset. You should now have the
%  variables X, Xval, yval in your environment
load('ex8data1.mat');

%% ================== Part 2: Estimate the dataset statistics ===================
%  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);

%% ================== Part 3: Find Outliers ===================

pval = multivariateGaussian(Xval, mu, sigma2);

[epsilon F1] = selectThreshold(yval, pval);

%  Find the outliers in the training set and plot the
outliers = find(p < epsilon);

%% ================== Part 4: Multidimensional Outliers ===================
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);

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);

mu = (sum(X)./m)';

sigma2 = (sum((X-mu').^2)./m)';

end

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)
    
    tp = sum((pval<epsilon)&(yval));
    fp = sum((pval<epsilon)&(~yval));
    fn = sum((pval>=epsilon)&(yval));
    prec = tp/(tp+fp);
    rec = tp/(tp+fn);
    F1 = 2*prec*rec/(prec+rec);

    if F1 > bestF1
       bestF1 = F1;
       bestEpsilon = epsilon;
    end
end

end

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));

J = sum(sum((((X*Theta'-Y).^2).*R)))/2 + ...
    (lambda/2)*(sum(sum(X.^2))+sum(sum(Theta.^2)));
X_grad = ((X*Theta'-Y).*R)*Theta + lambda.*X;
Theta_grad = ((X*Theta'-Y).*R)'*X + lambda.*Theta;
grad = [X_grad(:); Theta_grad(:)];

end