融合有向结构和非负矩阵分解的链路预测

Link prediction combing nonnegative matrix factorization and directed structure

现存有向网络链路预测方法仅考虑单类型网络结构而忽略一些关键网络结构,导致预测准确度下降。针对此问题,提出一个融合多类型有向网络结构和非负矩阵分解的链路预测框架去保持局部和全局结构信息。首先,将有向网络的邻接矩阵映射到低维潜在空间保持原始网络的方向链接;其次,通过2-范数和规范化拉普拉斯融合四个关键有向结构相似度包括有向共同邻居(DCN)、有向Adamic-Adar(DAA)、有向资源分配(DRA)和势理论(BF)去保持多类型网络结构信息,分别提出四个有向网络的链路预测模型NMF-DNS-DCN、NMF-DNS-DAA、NMF-DNS-DRA和NMF-DNS-BF;最后,启用乘法更新规则去学习四个模型参数并证明所提算法的收敛性。在八个真实世界有向网络上与现存的代表性方法相比较,该模型的AUC、recall和F_(1)分别最大提高5.3%、7.8%和6%。

The existing link prediction methods for directed networks only consider single-type network structures but ignore some key network structures,which leads to the decrease of prediction accuracy.To solve this problem,this paper proposed a link prediction framework which combined multi-type directed network structure and non-negative matrix factorization to preserve local and global structure information.Firstly,it mapped the adjacency matrix of directed network to the low-dimensional latent space to preserve the directional link of the original network.Secondly,it fused four key directed structural similarities including DCN,DAA,DRA and potential theory(BF)by 2-norm and normalised Laplacian to maintain information on the structure of multi-type networks.Then,it proposed four link prediction models NMF-DNS-DCN,NMF-DNS-DAA,NMF-DNS-DRA and NMF-DNS-BF respectively.Finally,this paper enabled multiplicative update rules to learn the parameters of the four models and proved the convergence of the proposed algorithms.Compared with the existing representative methods on 8 real-world directed networks,the AUC,recall and F_(1) of the proposed model is increased by 5.3%,7.8%and 6%,respectively.