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A unified temporal link prediction framework based on nonnegative matrix factorization and graph regularization

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Abstract

Complex real-world systems, evolving over time, can be modeled as dynamic networks. Numerous studies have focused on utilizing information about the entities and relationships within networks. Temporal link prediction, a challenging yet critical task for dynamic networks, aims to forecast the appearance and disappearance of links in future snapshots based on the network structure observed in previous snapshots. However, existing works have not fully utilized information from historical networks, such as evolving structures and community data. Additionally, nonnegative matrix factorization (NMF) techniques are unable to automatically extract nonlinear spatial and temporal features from dynamic networks. In this paper, we introduce a unified temporal link prediction framework, EDeepEye, which leverages NMF and graph regularization to predict temporal links. Based on this framework, we propose three novel methods: SDeepEye, GDeepEye, and QDeepEye, which incorporate prior information, weighted matrices, and modularity matrices, respectively. Additionally, we provide effective multiplicative updating rules for the factors of the methods, which learn latent features from the temporal topological structure. Three evaluation metrics, i.e., area under the receiver operator characteristic curve, Precision and root mean squared error, are applied to verify the superiority of the proposed methods. The results of empirical study show that our proposed methods outperform the baseline methods on eight real-world networks and 16 synthetic networks.

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Author information

Authors and Affiliations

  1. College of Computer and Cyber Security, Fujian Normal University, Fuzhou, 350117, China

    Min Li & Gaolin Chen

  2. School of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350117, China

    Shuming Zhou

  3. Key Laboratory of Analytical Mathematics and Applications, Ministry of Education, Fuzhou, 350117, China

    Shuming Zhou

  4. Center for Applied Mathematics of Fujian Province, Fujian Normal University, Fuzhou, 350117, China

    Shuming Zhou

  5. Concord University College, Fujian Normal University, Fuzhou, 350117, China

    Min Li

  6. School of Computing, Montclair State University, Upper Montclair, NJ, 07043, USA

    Dajin Wang

Authors
  1. Min Li
  2. Shuming Zhou
  3. Dajin Wang
  4. Gaolin Chen

Contributions

Min Li was involved in conceptualization, investigation, methodology, software, original draft writing, editing. Shuming Zhou helped in formal analysis, resources, supervision, validation, visualization, review and editing of the manuscript. Dajin Wang contributed to review and editing of the manuscript. Gaolin Chen was involved in software development, visualization.

Corresponding author

Correspondence toShuming Zhou.

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Conflict of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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This work was partly supported by the National Natural Science Foundation of China (Nos. 61977016 and 61572010) and Natural Science Foundation of Fujian Province (Nos. 2020J01164, 2023J01539, 2024J01071). This work was also partly supported by Fujian Alliance of Mathematics (No. 2023SXLMMS04) and China Scholarship Council (CSC No. 202108350054).

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Li, M., Zhou, S., Wang, D.et al. A unified temporal link prediction framework based on nonnegative matrix factorization and graph regularization.J Supercomput81, 774 (2025). https://doi.org/10.1007/s11227-025-07217-7

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