Abstract
Low rank matrices approximations have been used in link prediction for networks, which are usually global optimal methods and lack of using the local information. The block structure is a significant local feature of matrices: entities in the same block have similar values, which implies that links are more likely to be found within dense blocks. We use this insight to give a probabilistic latent variable model for finding missing links by convex nonnegative matrix factorization with block detection. The experiments show that this method gives better prediction accuracy than original method alone. Different from the original low rank matrices approximations methods for link prediction, the sparseness of solutions is in accord with the sparse property for most real complex networks. Scaling to massive size network, we use the block information mapping matrices onto distributed architectures and give a divide-and-conquer prediction method. The experiments show that it gives better results than common neighbors method when the networks have a large number of missing links.
Highlights
As a fundamental problem in the network researches, link prediction attempts to estimate the likelihood of relationship between two individuals by the study of observed links and the property of nodes
To measure the accuracies of link prediction methods, the main metric we use is AUC [21], area under the receiver operating characteristic (ROC) curve, which is widely used in the machine learning and social network communities
Do convex nonnegative matrix factorization (CNMF) with rank min(col(Bi), row(Bi), L) A = A + BiWG//sum the corresponding entities end for Algorithm 2: Algorithm for M-CNMF
Summary
As a fundamental problem in the network researches, link prediction attempts to estimate the likelihood of relationship between two individuals by the study of observed links and the property of nodes. A new measure based on neighbor communities has a good performance with a low complexity [8] Maximum likelihood estimation, such as hierarchical structure model [3] and stochastic block model [9, 10], presuppose some organizing principles of the network structure. Based on the technique of cluster low rank approximation for massive graphs, Shin et al proposed a multiscale link prediction method [18], which captures the information of global structure of network and can handle massive networks quickly. (FG)ij can measure the strength of relationship between object i with feature j and can be used to predict link between i and j
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