Probabilistic Matrix Factorization Recommendation Model Incorporating Multiple Weighting Factors
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摘要: 针对个性化推荐精度较低、对冷启动敏感等问题，该文提出一种融合多权重因素的低秩概率矩阵分解推荐模型MWFPMF。模型利用给定的社交网络构建信任网络，借助Page rank算法和信任传递机制求取用户间信任度；基于Page rank计算用户社会地位，利用活动评分和评分时间修正用户间关系权重；引入词频-逆文本频率技术(TF-IDF)求取用户标签，通过标签相似性表征用户间同质性；将用户间信任度、用户社会地位影响力和用户同质性3因素融入低秩概率矩阵分解中，从而使用户偏好和活动特征映射到同一低秩空间，实现用户-活动评分矩阵的分解，在正则化约束下，最终完成低秩特征矩阵对用户评分缺失的有效预测。利用豆瓣同城北京和Ciao数据集确定各模块的参数设置值。通过仿真对比实验可知，本推荐模型获得了较高的推荐精度，与其他5种传统推荐算法相比，平均绝对误差至少降低了6.58%，均方差误差至少降低了6.27%，与深度学习推进算法相比，推荐精度基本接近；在冷启动用户推荐上优势明显，与其他推荐算法相比，平均绝对误差至少降低了0.89%，均方差误差至少降低了3.01%。Abstract: Considering the problems of low accuracy of personalized recommendation and sensitivity to cold start, low-rank Probabilistic Matrix Factorization recommendation model incorporating Multiple Weighting Factors (MWFPMF) is proposed; The trust network is constructed using a given social network, and the trust between users is calculated using the Page rank algorithm and trust transfer mechanism; The user’s social status is calculated based on Page rank, and the weight of the relationship between users is modified using activity scores and scoring time; Term Frequency-Inverse Document Frequency(TF-IDF) is introduced to take user tags, and the homogeneity between users is characterized by tag similarity; The three factors of trust among users, influence of users’ social status, and user homogeneity are integrated into the low-rank probability matrix decomposition, so that user preferences and activity characteristics are mapped to the same low-rank space, and the user-activity scoring matrix is decomposed. Under the premise of regularization as a constraint, the effective prediction of the lack of user ratings by the low-rank feature matrix is finally completed. The data sets of Douban Beijing and Ciao are used to determine the parameter settings of each module. Through simulation and comparison experiments, it can be seen that this recommendation model obtains higher recommendation model accuracy. Compared with the other five traditional recommendation algorithms, the mean absolute error is reduced by at least 6.58%, and the mean square error is reduced by at least 6.27%, compared with the deep learning advancing algorithm, the recommendation accuracy is almost the same; It has obvious advantages in cold-start user recommendation. Compared with other recommendation algorithms, the average absolute error is reduced by at least 0.89%, and the mean square error is reduced by at least 3.01%.
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表 1 参数设置
参数 值 参数 值 用户特征正则化控制参数${\lambda _{{\boldsymbol{Ut}}} }$ 0.1 用户同质性调节参数${\lambda _H}$ 0.5 活动特征正则化控制参数${\lambda _{{\boldsymbol{St}}} }$ 0.1 用户信任网络跳出率$\rho $ 0.85 用户社会影响力调节参数${\lambda _W}$ 5 隐特征矩阵维度$d$ 15 梯度学习速率$\beta $ 0.01 跳数阈值${h_\theta }$ 3 同质相似性阈值$\alpha $ 0.8 时间衰减参数$\delta$ 0.5 
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表 2 各算法对冷启动用户的推荐性能比较
推荐算法 豆瓣北京数据集 Ciao数据集 ${\rm{MAE}}$ ${\rm{RMSE}}$ ${\rm{MAE}}$ ${\rm{RMSE}}$ MWFPMF 0.8417 1.0526 0.8333 1.0348 AODR 0.8493 1.0843 0.8407 1.0695 CA-NCF 0.8654 1.0949 0.8537 1.0814 CSIT 0.8892 1.1377 0.8945 1.1229 AutoTrustRec 0.8988 1.1432 0.8964 1.1291 MIMFCF 0.9168 1.1637 0.9125 1.1339 RSNMF 0.9349 1.1938 0.9368 1.1954 ISSMF 1.0102 1.2651 0.9929 1.2695 PMF 1.0273 1.3081 1.0169 1.3096
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