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function [J, grad] = cofiCostFunc(params, Y, R, num_users, num_movies, ...
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num_features, lambda)
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%COFICOSTFUNC Collaborative filtering cost function
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% [J, grad] = COFICOSTFUNC(params, Y, R, num_users, num_movies, ...
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% num_features, lambda) returns the cost and gradient for the
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% collaborative filtering problem.
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%
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% Unfold the U and W matrices from params
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X = reshape(params(1:num_movies*num_features), num_movies, num_features);
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Theta = reshape(params(num_movies*num_features+1:end), ...
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num_users, num_features);
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% You need to return the following values correctly
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J = 0;
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X_grad = zeros(size(X));
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Theta_grad = zeros(size(Theta));
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% ====================== YOUR CODE HERE ======================
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% Instructions: Compute the cost function and gradient for collaborative
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% filtering. Concretely, you should first implement the cost
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% function (without regularization) and make sure it is
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% matches our costs. After that, you should implement the
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% gradient and use the checkCostFunction routine to check
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% that the gradient is correct. Finally, you should implement
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% regularization.
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%
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% Notes: X - num_movies x num_features matrix of movie features
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% Theta - num_users x num_features matrix of user features
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% Y - num_movies x num_users matrix of user ratings of movies
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% R - num_movies x num_users matrix, where R(i, j) = 1 if the
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% i-th movie was rated by the j-th user
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%
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% You should set the following variables correctly:
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%
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% X_grad - num_movies x num_features matrix, containing the
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% partial derivatives w.r.t. to each element of X
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% Theta_grad - num_users x num_features matrix, containing the
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% partial derivatives w.r.t. to each element of Theta
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%
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J = 0.5 * sum(sum(R.*(X*Theta'-Y).^2)) ...
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+ 0.5 * lambda * sum(sum(Theta.^2)) ...
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+ 0.5 * lambda * sum(sum(X.^2));
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X_grad = (R.*(X*Theta'-Y))*Theta; % mov X user * uxer X feat = mov X feat
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Theta_grad = (R.*(X*Theta'-Y))'*X; % user X mov * mov X feat = user X feat
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% =============================================================
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grad = [X_grad(:); Theta_grad(:)];
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end
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