A personalized collaborative filtering recommendation algorithm based on linear regression

Abstract

This paper attempts to solve the problems with linear regression-based collaborative filtering recommendation algorithm, namely, the difficulty in extracting eigenvalues, the low accuracy and the poor interpretability. For this purpose, the tag weights were introduced as eigenvalues and the prediction accuracy was improved by the principle of collaborative filtering recommendation algorithm, creating a personalized collaborative filtering recommendation algorithm based on linear regression (PCFLR). Firstly, the tag weights for users were computed by term frequency-inverse document frequency (TF-IDF), and taken as the eigenvalues of the linear regression model. Then, the linear regression model was constructed based on the users' historical scores. After that, the cost function was set up by the least squares method, and regularized to prevent over-fitting. Next, the optimal value of the cost function was computed by gradient descent method, yielding the tag weights for items. On this basis, the predicted scores of all unrated items were obtained considering the linear relationship between the tag weights for users and those for items. The mean absolute error (MAE) between the predicted and actual scores was computed, and used to adjust the predicted scores into the final results. In addition, the set of recommendable items for the target user was produced based on the scores rated by all neighboring users, and coupled with the linearly regressed scores to make recommendations to the target user. The experimental results show that the PCFLR outperformed the traditional recommendation algorithms in accuracy and interpretability.