基于点割集图分割的矩阵变换与分解的推荐算法  

Matrix Transformation and Factorization Based on Graph Partitioning by Vertex Separator for Recommendation

作　　者：何亦琛 毛宜军[1] 谢贤芬[2] 古万荣 HE Yi-chen;MAO Yi-jun;XIE Xian-fen;GU Wan-rong(School of Mathematics and Information,South China Agricultural University,Guangzhou 510642,China;School of Economy,Jinan University,Guangzhou 510632,China)

机构地区：[1]华南农业大学数学与信息学院,广州510642 [2]暨南大学经济学院,广州510632

出　　处：《计算机科学》2022年第S01期272-279,共8页Computer Science

基　　金：全国统计科学研究项目(2020LY018);全国统计科学研究重点项目(2019LZ37);广东省社会科学项目(GD19CGL34);国家重点研发计划(2017YFC1601701);广东省农业厅创新团队项目(2019KJ130)。

摘　　要：基于模型的协同过滤算法通过矩阵分解来将用户偏好以及物品属性用隐变量来表示,但现有的矩阵分解算法很难应对个性化推荐系统中严重的数据稀疏性以及数据变化性所带来的问题。针对上述问题,提出了基于双边块对角矩阵的矩阵分解算法。首先通过基于社区发现的点割集图分割算法将原始的稀疏矩阵转换成双边块对角矩阵,将具有相同偏好的用户以及相似特征的物品归并到同一个对角块中,然后将结构中的对角块和双边拼接成数个密度较高的子矩阵。实验结果表明,对这几个密度有提高的子矩阵进行并行分解,基于其分解结果进行原始矩阵的预测,能够有效缓解矩阵分解中数据稀疏性所带来的问题,既能提升预测的精度,又能提高推荐结果的可解释性。同时,每个子对角块都能并行独立分解,能达到提高算法效率的目的。Model-based collaborative filtering algorithms usually express user’s preferences and item’s attributes by latent factors through matrix factorization,but the traditional matrix factorization algorithm is difficult to deal with the serious data sparsity and data variability problems in the recommendation system.To solve the above problem,a matrix factorization algorithm based on bordered block diagonal matrix is proposed.Firstly,the original sparse matrix is transformed into bordered block diagonal matrix by a graph partitioning algorithm based on community discovery,which merges users with the same preference and items with similar characteristics into the same diagonal block,and then splices the diagonal blocks and the bordered into several sub-diagonal matrices which have higher densities.The experimental results show that,by decomposing the sub-diagonal matrices in parallel can not only improve the precision of prediction,but also improve the interpretability of the recommendation results.At the same time,each sub-diagonal matrix can be decomposed independently and in parallel,which can improve the efficiency of the algorithm.

关 键 词：社区发现 矩阵分解 协同过滤 推荐系统 

分 类 号：TP391.3[自动化与计算机技术—计算机应用技术]