[Paper Review] Exploring Structure-Adaptive Graph Learning for Robust Semi-Supervised Classification

Xiang Gao, Wei Hu+1 more|arXiv (Cornell University)|Apr 23, 2019

Advanced Graph Neural Networks30 references4 citations

TL;DR

This paper proposes Graph Learning Neural Networks (GLNNs), which jointly optimize graph structure and edge weights via a structure-adaptive regularization based on the Graph Laplacian Regularizer (GLR) within a GCNN framework. The method enhances robustness in semi-supervised node classification, especially under low label rates, outperforming state-of-the-art methods on citation and social network datasets by learning data- and task-driven graphs end-to-end.

ABSTRACT

Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to graph-structured data, in which convolution is guided by the graph topology. In many cases where graphs are unavailable, existing methods manually construct graphs or learn task-driven adaptive graphs. In this paper, we propose Graph Learning Neural Networks (GLNNs), which exploit the optimization of graphs (the adjacency matrix in particular) from both data and tasks. Leveraging on spectral graph theory, we propose the objective of graph learning from a sparsity constraint, properties of a valid adjacency matrix as well as a graph Laplacian regularizer via maximum a posteriori estimation. The optimization objective is then integrated into the loss function of the GCNN, which adapts the graph topology to not only labels of a specific task but also the input data. Experimental results show that our proposed GLNN outperforms state-of-the-art approaches over widely adopted social network datasets and citation network datasets for semi-supervised classification.

Motivation & Objective

• To address the challenge of suboptimal graph construction in semi-supervised learning when ground-truth graphs are unavailable or unreliable.
• To improve model robustness in low-label-rate scenarios common in real-world graph data.
• To jointly optimize graph topology (connectivities and weights) and classification performance using both data and label information.
• To integrate structure-adaptive graph learning into GCNNs via a differentiable, end-to-end training framework.
• To demonstrate the superiority of GLR-based graph learning over fixed or edge-weight-only learned graphs in semi-supervised node classification.

Proposed method

• Formulate graph learning as a Maximum a Posteriori (MAP) estimation problem for the adjacency matrix, incorporating GLR as a likelihood function.
• Introduce a prior distribution enforcing sparsity, symmetry, normalization, and absence of self-loops for valid adjacency matrices.
• Integrate the graph learning objective into the GCNN's cross-entropy loss, enabling joint optimization of graph structure and classification.
• Design a GLNN framework with a Graph Learning Layer followed by two GCN layers for feature extraction and classification.
• Use spectral graph theory to define the Graph Laplacian Regularizer (GLR), which promotes smoothness of node features over the learned graph.
• Optimize the adjacency matrix end-to-end using backpropagation, allowing the model to adapt graph structure based on input data and labels.

Experimental results

Research questions

• RQ1 Can structure-adaptive graph learning improve semi-supervised node classification performance, especially when labels are scarce?
• RQ2 How does incorporating the Graph Laplacian Regularizer (GLR) enhance the robustness of GCNNs in low-label regimes?
• RQ3 To what extent does joint optimization of graph structure and classification loss outperform methods that fix or only adapt edge weights?
• RQ4 Does the proposed GLNN learn adjacency matrices that are both structurally similar to ground truth and sparser over training?
• RQ5 How sensitive is the performance to the hyperparameter weighting the GLR loss term?

Key findings

• GLNN achieves state-of-the-art performance on citation networks (Cora, Citeseer, PubMed) and social networks (TerroristsRel, TerrorAttack), with accuracy improvements over GCN and ChebNet.
• On Cora and Citeseer, GLNN maintains classification accuracy above 58% and 51.8% respectively even at a label rate of 0.005, significantly outperforming baseline models.
• The model's performance improves with increasing GLR weighting (λ₀), peaking at λ₀ = 1.0, demonstrating the critical role of GLR in enhancing classification accuracy.
• Ablation studies show that removing the GLR loss term results in a substantial performance drop, validating its effectiveness.
• Visualization confirms that the learned adjacency matrix converges toward the ground truth over training epochs and becomes sparser, aligning with the sparsity constraint.
• The GLNN framework successfully learns meaningful, sparse, and task-aware graph structures without relying on pre-defined or manually constructed graphs.