4.7 Article

Perturbation of the Normalized Laplacian Matrix for the Prediction of Missing Links in Real Networks

期刊

出版社

IEEE COMPUTER SOC
DOI: 10.1109/TNSE.2021.3137862

关键词

Laplace equations; Perturbation methods; Symmetric matrices; Predictive models; Prediction algorithms; Indexes; Eigenvalues and eigenfunctions; Complex networks; link prediction; perturbation theory; normalized Laplacian matrix

资金

  1. Alexander von Humboldt Foundation
  2. Spanish Agencia Estatal de Investigacion Project [PID2019-106290GBC22/AEI]
  3. Generalitat de Catalunya [2017SGR1064]

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This paper presents a link prediction method called Laplacian Perturbation Method (LPM) based on perturbation theory, which significantly improves prediction accuracy and outperforms other methods.
The problem of predicting missing links in real-world networks is an active and challenging research area in both science and engineering. The goal is to model the process of link formation in a complex network based on its observed structure to unveil lost or unseen interactions. In this paper, we use perturbation theory to develop a general link prediction procedure, called Laplacian Perturbation Method (LPM), that relies on relevant structural information encoded in the normalized Laplacian matrix of the network. We implement a general algorithm for our perturbation method valid for different Laplacian-based link prediction schemes that successfully surpass the prediction accuracy of their standard non-perturbed versions in real-world and model networks. The suggested LPM for link prediction also exhibits higher accuracy compared to other extensively used local and global state-of-the-art techniques and, in particular, it outperform the Structural Perturbation Method (SPM), a popular procedure that perturbs the adjacency matrix of a network for inferring missing links, in many real-world and in synthetic networks. Taken together, our results show that perturbation methods can significantly improve Laplacian-based link prediction techniques, and feeds the debate on which representation, Laplacian or adjacency, better represents structural information for link prediction tasks in networks.

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