Advances in Graph Learning and Network Structure Inference

The field of graph learning and network structure inference is moving towards more innovative and effective methods for analyzing and interpreting complex network data. Recent developments have focused on improving the expressiveness and robustness of graph neural networks, as well as developing new methods for thresholding and parameter selection. Topological data analysis has emerged as a key tool for identifying optimal network parameters and preserving meaningful topological structure. Additionally, there is a growing interest in developing more interpretable graph learning methods, including those that can identify rationale substructures in graphs. Notable papers include:

  • One paper proposes a novel algorithm for label propagation and self-training using fractional heat kernel dynamics, which has been shown to be effective in cases where only a small number of labeled training examples are present.
  • Another paper introduces a systematic thresholding algorithm that leverages topological data analysis to identify optimal network parameters, allowing users to specify minimum requirements for topological features.
  • A third paper proposes a topological framework for graph learning that leverages persistent homology to identify persistent rationale subgraphs, providing theoretical guarantees and demonstrating effectiveness in tackling key challenges.

Sources

Fractional Heat Kernel for Semi-Supervised Graph Learning with Small Training Sample Size

Diffusion-Assisted Distillation for Self-Supervised Graph Representation Learning with MLPs

Higher-Order Network Structure Inference: A Topological Approach to Network Selection

TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration

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