ex8 "Anomaly Detection and Recommender Systems" is done and submitted.

Author: everpeace

ex8/mlclass-ex8/cofiCostFunc.m

@@ -11,7 +11,7 @@
 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));
@@ -21,39 +21,48 @@
 % 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 
+%               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 
+%        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 
+%        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 
+%        Theta_grad - num_users x num_features matrix, containing the
 %                     partial derivatives w.r.t. to each element of Theta
 %
 
+% calculating cost function.
+diff = (X*Theta'-Y);
+J = sum((diff.^2)(R==1))/2;
+J = J + lambda*sum(sum(Theta.^2))/2;  % regularized term of theta.
+J = J + lambda*sum(sum(X.^2))/2;     % regularized term of x.
+
+% calculating gradient of x.
+for i=1:num_movies
+  idx = find(R(i, :)==1);    % users that have rated movie i.
+  Theta_tmp = Theta(idx, :); % user features of movie i.
+  Y_tmp = Y(i, idx);         % user's ratings of movie i.
+  X_grad(i, :) = (X(i, :)*Theta_tmp' - Y_tmp)*Theta_tmp;
+  X_grad(i, :) = X_grad(i, :)+lambda*X(i, :); % regularized term of x.
+end
 
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+% calculating gradient of theta.
+for j=1:num_users
+  idx = find(R(:, j)==1)'; % movies that have rated by user j.
+  X_tmp = X(idx, :);       % features of movies rated by user j.
+  Y_tmp = Y(idx, j);       % user ratings by user j.
+  Theta_grad(j, :) = (X_tmp*Theta(j, :)'-Y_tmp)'*X_tmp;
+  Theta_grad(j, :) = Theta_grad(j, :)+lambda*Theta(j, :); % regularized term of theta.
+end
 
 % =============================================================
 

ex8/mlclass-ex8/estimateGaussian.m

@@ -1,11 +1,11 @@
 function [mu sigma2] = estimateGaussian(X)
-%ESTIMATEGAUSSIAN This function estimates the parameters of a 
+%ESTIMATEGAUSSIAN This function estimates the parameters of a
 %Gaussian distribution using the data in X
-%   [mu sigma2] = estimateGaussian(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);
@@ -21,14 +21,8 @@
 %               should contain variance of the i-th feature.
 %
 
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+mu = mean(X)';
+sigma2 = var(X, 1)';
 
 % =============================================================
 

ex8/mlclass-ex8/selectThreshold.m

@@ -12,28 +12,32 @@
 
 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 predictions
 
+    % yval says it's an anomaly and so algorithm does.
+    tp = sum((yval==1) & (pval<epsilon));
 
+    % yval says it's not an anomaly,  but algorithm says anomaly.
+    fp = sum((yval==0) & (pval<epsilon));
 
+    % yval says it's an anomaly,  but algorithm says not anomaly.
+    fn = sum((yval==1) & (pval>=epsilon));
 
+    % precision and recall
+    prec = tp/(tp+fp);
+    rec = tp/(tp+fn);
 
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+    % F1 value;
+    F1 = (2*prec*rec)/(prec+rec);
 
     % =============================================================