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| import numpy as np | |
| import tensorflow as tf | |
| def normalize(Y, R): | |
| """ | |
| Preprocess data by subtracting mean rating for every book (every row). | |
| Only include real ratings R(i,j)=1. | |
| [Y_norm, Y_mean] = normalize(Y, R) normalized Y so that each book | |
| has a rating of 0 on average. Unrated moves then have a mean rating (0) | |
| Returns the mean rating in Y_mean. | |
| """ | |
| Y_mean = (np.sum(Y * R, axis=1) / (np.sum(R, axis=1) + 1e-12)).reshape(-1, 1) | |
| Y_norm = Y - np.multiply(Y_mean, R) | |
| return Y_norm, Y_mean | |
| def cost_function(X, W, b, Y, R, lambda_): | |
| """ | |
| Returns the cost for the collaborative filtering | |
| Vectorized for speed. Uses tensorflow operations to be compatible with custom training loop. | |
| Args: | |
| X (ndarray (num_books,num_features)): matrix of item features | |
| W (ndarray (num_users,num_features)) : matrix of user parameters | |
| b (ndarray (1, num_users) : vector of user parameters | |
| Y (ndarray (num_books,num_users) : matrix of user ratings of books | |
| R (ndarray (num_books,num_users) : matrix, where R(i, j) = 1 if the i-th books was rated by the j-th user | |
| lambda_ (float): regularization parameter | |
| Returns: | |
| J (float) : Cost | |
| """ | |
| j = (tf.linalg.matmul(X, tf.transpose(W)) + b - Y) * R | |
| J = 0.5 * tf.reduce_sum(j ** 2) + (lambda_ / 2) * (tf.reduce_sum(X ** 2) + tf.reduce_sum(W ** 2)) | |
| return J | |