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Improved Dynamic Graph Learning through Fault-Tolerant Sparsification.

Chun Jiang Zhu1, Sabine Storandt2, Kam-Yiu Lam3

  • 1University of Connecticut.

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|July 11, 2022
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Summary
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We introduce fault-tolerant (FT) sparsification for dynamic graphs, reducing computational costs from polynomial to constant per update. This method significantly speeds up graph learning tasks like semisupervised learning and spectral clustering with minimal accuracy loss.

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Area of Science:

  • Graph Machine Learning
  • Computational Graph Theory

Background:

  • Graph sparsification enhances computational efficiency for graph learning tasks such as Laplacian-regularized estimation, semisupervised learning (SSL), and spectral clustering (SC).
  • Dynamic graphs, which change over time, pose computational challenges as repeated sparsification incurs polynomial costs per update.

Purpose of the Study:

  • To introduce a novel fault-tolerant (FT) sparsification technique for dynamic graphs.
  • To significantly reduce the computational cost of graph sparsification from polynomial to constant per update.
  • To analyze the impact of FT sparsification on the accuracy of downstream graph learning tasks.

Main Methods:

  • Development of a new fault-tolerant (FT) sparsification method for dynamic graphs.
  • Theoretical analysis to bound the accuracy loss in Laplacian-regularized estimation, graph SSL, and SC due to FT sparsification.
  • Generalization of FT spectral sparsification to FT cut sparsification for cut-based learning.

Main Results:

  • FT sparsification reduces the computational cost of updating graph sparsifications to a constant.
  • Limited loss in accuracy for subsequent graph learning tasks (Laplacian-regularized estimation, graph SSL, SC) was theoretically bounded.
  • Experimental validation confirmed significant computational efficiencies and maintained accuracy for learning on dynamic graphs.

Conclusions:

  • FT sparsification offers a computationally efficient solution for learning on dynamic graphs.
  • The proposed method enables faster graph learning with minimal compromise on accuracy.
  • FT sparsification is a promising approach for handling evolving graph data structures.