DOI: 10.5176/978-981-08-7656-2ATAI2010-32
Authors: Shuli Han, Yujiu Yang, Wenhuang Liu
Abstract:
Collaborative Filtering (CF) is one of the most popular methods for recommendation problem. The key idea is to predict further the interests of a user (ratings) based on the available rating information from many users. Recently, matrix factorization(MF) based approaches, one branch of collaborative filtering, have proven successful for the rating prediction issues. As is well known, most of the MF models follow one of the following frames: (1) to fit a linear factor model overall observed ratings respect to the Frobenius norm with a positive regularization item, (2) to fit a linear factor model over all observed ratings respect to the Frobenius norm with a non negative constraint added. Differing from the exiting MF models, which model only on the observed ratings, the proposed variant of MF, referred to as Probabilistic Prior Non negative Matrix Factorization (PPNMF) in this paper, utilizes the prior information of the missing elements via treating each missing as a random variable; the probability distribution of each element is calculated with some specific scheme. Compared with the traditional Matrix Factorization for Collaborative Filtering, our empirical studies show that the proposed algorithm makes more accurate predictions of user ratings and is more robust with respect to the initial setting. With this method, we analyze the mechanism of its learning process, which shows that the algorithm will first go through a damping vibration process to make an adjustment, and then converges.
Keywords: Collaborative Filtering, Matrix Factorization, Miss-ing Data, Prior Information
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