With the rapid development of Internet, the amount of information on the Web grows explosively, people often feel puzzled and helpless in finding and getting the information they really need. For overcoming this problem, recommender systems such as singular value decomposition (SVD) method help users finding relevant information, products or services by providing personalized recommendations based on their profiles. SVD is a powerful technique for dimensionality reduction. However, due to its expensive computational requirements and weak performance for large sparse matrices, it has been considered inappropriate for practical applications involving massive data. Thus, to extract information in which the user is interested from a massive amount of data, we propose a personalized recommendation algorithm which is called ApproSVD algorithm based on approximating SVD in this paper. The trick behind our algorithm is to sample some rows of a user-item matrix, rescale each row by an appropriate factor to form a relatively smaller matrix, and then reduce the dimensionality of the smaller matrix. Finally, we present an empirical study to compare the prediction accuracy of our proposed algorithm with that of Drineas's LINEARTIMESVD algorithm and the standard SVD algorithm on MovieLens dataset and Flixster dataset, and show that our method has the best prediction quality. Furthermore, in order to show the superiority of the ApproSVD algorithm, we also conduct an empirical study to compare the prediction accuracy and running time between ApproSVD algorithm and incremental SVD algorithm on MovieLens dataset and Flixster dataset, and demonstrate that our proposed method has better performance overall.
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