Cold-Start Link Prediction via Weighted Symmetric Nonnegative Matrix Factorization with Graph Regularization

Abstract

Link prediction has attracted wide attention among interdisciplinary researchers as an important issue in complex network. It aims to predict the missing links in current networks and new links that will appear in future networks. Despite the presence of missing links in the target network of link prediction studies, the network it processes remains macroscopically as a large connected graph. However, the complexity of the real world makes the complex networks abstracted from real systems often contain many isolated nodes. This phenomenon leads to existing link prediction methods not to efficiently implement the prediction of missing edges on isolated nodes. Therefore, the cold-start link prediction is favored as one of the most valuable subproblems of traditional link prediction. However, due to the loss of many links in the observation network, the topological information available for completing the link prediction task is extremely scarce. This presents a severe challenge for the study of cold-start link prediction. Therefore, how to mine and fuse more available non-topological information from observed network becomes the key point to solve the problem of cold-start link prediction. In this paper, we propose a framework for solving the cold-start link prediction problem, a joint-weighted symmetric nonnegative matrix factorization model fusing graph regularization information, based on low-rank approximation algorithms in the field of machine learning. First, the nonlinear features in high-dimensional space of node attributes are captured by the designed graph regularization term. Second, using a weighted matrix, we associate the attribute similarity and first order structure information of nodes and constrain each other. Finally, a unified framework for implementing cold-start link prediction is constructed by using a symmetric nonnegative matrix factorization model to integrate the multiple information extracted together. Extensive experimental validation on five real networks with attributes shows that the proposed model has very good predictive performance when predicting missing edges of isolated nodes.