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

摘要： 推荐系统根据用户对项目的历史评分实施推荐，评分矩阵的稀疏性导致推荐的先验知识不足，降低推荐准确率。粗糙集理论能够利用不完备知识实施有效推理，从而提出了基于人口统计学的概率粗糙集推荐模型，使用概率粗糙集理论划分等价类，降低了评分矩阵稀疏性对推荐结果的影响。使用基于最大期望（expectation maximization，EM）思想的参数求解算法求解参数α和β的最优值，将Pawlak粗糙集的边界域分解到正域或负域中，提升推荐效果。实验结果表明，概率粗糙集模型能够有效提高在评分矩阵非常稀疏情况下的推荐准确率，其在MovieLens数据集上的推荐准确率最高达到71.42%，覆盖率指标最高达到99.18%。

关键词: 粗糙集, 推荐算法, 参数求解, 最大期望（EM）算法