关键词: 粗糙集, 推荐算法, 参数求解, 最大期望（EM）算法

Abstract: Recommender systems recommend items to users according to the historical ratings of items. Used to express these historical ratings, the rating matrix usually has the character of sparsity which can lead to the lack of prior knowledge and the decrease of recommendation accuracy. Rough set theory can use incomplete knowledge to effectively reasoning. This paper proposes a recommendation model of probability rough set based on demographic, which is equivalent to the classification of rough set theory, and reduces the effect of sparsity of the rating matrix. This paper uses EM (expectation maximization) algorithm to solve the optimal parameters of α and β, decomposes the Pawlak boundary region into the positive or negative domains according to the parameters, and promotes the recommendation effect. The experimental results show that the probability rough set model can effectively improve the recommendation accuracy. And the recommendation accuracy reaches 71.42%, and the coverage rate reaches 99.18% in the MovieLens test set.

Key words: rough set, recommendation algorithm, solving paramaters, expectation maximization (EM) algorithm