Abstract: For the problems of low recommendation accuracy, data sparsity and malicious recommendation, a new recommendation model based on Probability Matrix Factorization (PMF) and fusing trust was proposed. Firstly, by establishing a Collaborative Filtering Model based on Trust Similarity (CFMTS), the improved trust mechanism was integrated into the collaborative filtering recommendation algorithm. The trust value was obtained through global trust and local trust calculation. The local trust was obtained by calculating the direct trust value and the indirect trust value of the user by the trust propagation mechanism, the global trust was calculated by the trust directed graph. Then, the trust value was combined with the score similarity to solve the problems of data sparsity and malicious recommendation. At the same time, CFMTS was integrated into the PMF model to establish a new recommendation model-Model based on Probability Matrix Factorization and Fusing Trust (MPMFFT). The user feature vectors and the project feature vectors were calculated by the gradient descent algorithm to generate the predicted scores, further improving the accuracy of the recommender system. Through experiments, the proposed MPMFFT was compared with the classical models such as PMF, Social Matrix Factorization (SocialMF), Social Recommendation (SoRec) and Recommendations with Social Trust Ensemble (RSTE). The proposed model has the Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) decreased by 2.9% and 1.5% respectively compared with the optimal model RSTE on the open real dataset Epinions, and has the MAE and RMSE decreased by 1.1% and 1.8% respectively compared with the optimal SocialMF model on open real dataset Ciao, verifying that the proposed model is significantly improved on the above indicators. The results confirme that the propose model can resolve the problem of data sparseness and malicious recommendation to some extent, and effectively improved the recommendation quality.

Key words: recommender system, trust relationship, Probability Matrix Factorization (PMF), feature vector

摘要： 针对推荐精度不准确、数据稀疏、恶意推荐的问题，提出融合信任基于概率矩阵分解（PMF）的新推荐模型。首先，通过建立基于信任的协同过滤模型（CFMTS）将改进的信任机制融入到协同过滤推荐算法中。信任值通过全局信任及局部信任计算获得，其中局部信任利用了信任传播机制计算用户的直接信任值和间接信任值得到，全局信任采用信任有向图的方式计算得到。然后，将信任值与评分相似度融合以解决数据稀疏、恶意推荐的问题。同时，将CFMTS融入到PMF模型中以建立新的推荐模型——融合信任基于概率矩阵分解模型（MPMFFT），通过梯度下降算法对用户特征向量和项目特征向量进行计算以产生预测评分值，进一步提高推荐系统的精准度。通过实验将提出的MPMFFT与经典的PMF、社交信息的矩阵分解（SocialMF）、社交信息的推荐（SoRec）、加权社交信息的推荐（RSTE）等模型进行了结果的对比和分析，在公开的真实数据集Epinions上MPMFFT的平均绝对误差（MAE）和均方根误差（RMSE）比最优的RSTE模型分别降低2.9%和1.5%，同时在公开的真实数据集Ciao上MPMFFT的MAE和RMSE比最优的SocialMF模型分别降低1.1%和1.8%，结果证实了模型能在一定程度上解决数据稀疏、恶意推荐问题，有效提高推荐质量。

关键词: 推荐系统, 信任关系, 概率矩阵分解, 特征向量