Abstract: How to improve the accuracy of recommendation is an important issue for the current recommendation system. The matrix decomposition model was studied, and in order to exploit the group structure of the rating data, a Score Similarity based Matrix Factorization recommendation algorithm with Group Sparsity (SSMF-GS) was proposed. Firstly, the scoring matrix was divided into groups according to the users' rating behavior, and the similar user group scoring matrix was obtained. Then, similar users' rating matrix was decomposed in group sparsity by SSMF-GS algorithm. Finally, the alternating optimization algorithm was applied to optimize the proposed model. The latent item features of different user groups could be filtered out and the explanability of latent features was enhanced by the proposed model. Simulation experiments were tested on MovieLens datasets provided by GroupLens website. The experimental results show that the proposed algorithm can improve recommendation accuracy significantly, and the Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) both have good performance.

Key words: group sparsity, matrix factorization, L_2,1-norm regularization, latent feature

摘要： 如何提高系统的推荐精度，是当前推荐系统面临的重要问题。对矩阵分解模型进行了研究，针对评分数据的群结构性问题，提出了一种基于评分相似性的群稀疏矩阵分解模型（SSMF-GS）。首先，根据用户的评分行为对评分数据矩阵进行分群，获得相似用户群评分矩阵；然后，通过SSMF-GS算法对相似用户群评分矩阵进行群稀疏矩阵分解；最后，采用交替优化算法对模型进行求解。所提模型可以筛选出不同用户群的偏好潜在项目特征，提升了潜在特征的可解释性。在GroupLens网站上提供的MovieLens数据集上进行仿真实验，实验结果表明，所提算法可以显著提高预测精度，平均绝对误差（MAE）及均方根误差（RMSE）指标均表现出良好的性能。

关键词: 群稀疏, 矩阵分解, L_2, 1范数正则化, 潜在特征