[Paper Review] Multi-view Graph Convolutional Networks with Differentiable Node Selection

Zhaoliang Chen, Lele Fu+4 more|arXiv (Cornell University)|Dec 9, 2022

Advanced Graph Neural Networks4 citations

TL;DR

This paper proposes MGCN-DNS, a multi-view graph convolutional network with differentiable node selection to improve semi-supervised classification by learning robust, adaptive graph topologies from multi-view data. By integrating a differentiable node selection mechanism and adaptive graph fusion, the model enhances feature representation while reducing noise interference, achieving state-of-the-art performance on benchmark datasets.

ABSTRACT

Multi-view data containing complementary and consensus information can facilitate representation learning by exploiting the intact integration of multi-view features. Because most objects in real world often have underlying connections, organizing multi-view data as heterogeneous graphs is beneficial to extracting latent information among different objects. Due to the powerful capability to gather information of neighborhood nodes, in this paper, we apply Graph Convolutional Network (GCN) to cope with heterogeneous-graph data originating from multi-view data, which is still under-explored in the field of GCN. In order to improve the quality of network topology and alleviate the interference of noises yielded by graph fusion, some methods undertake sorting operations before the graph convolution procedure. These GCN-based methods generally sort and select the most confident neighborhood nodes for each vertex, such as picking the top-k nodes according to pre-defined confidence values. Nonetheless, this is problematic due to the non-differentiable sorting operators and inflexible graph embedding learning, which may result in blocked gradient computations and undesired performance. To cope with these issues, we propose a joint framework dubbed Multi-view Graph Convolutional Network with Differentiable Node Selection (MGCN-DNS), which is constituted of an adaptive graph fusion layer, a graph learning module and a differentiable node selection schema. MGCN-DNS accepts multi-channel graph-structural data as inputs and aims to learn more robust graph fusion through a differentiable neural network. The effectiveness of the proposed method is verified by rigorous comparisons with considerable state-of-the-art approaches in terms of multi-view semi-supervised classification tasks.

Motivation & Objective

• To address the limitations of non-differentiable sorting in GCN-based multi-view learning, where top-k node selection hinders gradient flow and model optimization.
• To improve graph topology quality and reduce noise interference in multi-view data by learning adaptive, differentiable node selection and graph fusion.
• To develop a joint framework that integrates multi-channel graph-structural data through a differentiable, end-to-end trainable architecture for enhanced representation learning.
• To enable robust and generalizable graph embedding learning in multi-view semi-supervised classification tasks through adaptive fusion and sparsification.
• To overcome the rigidity of fixed k-neighborhood selection by introducing learnable, continuous selection mechanisms that support backpropagation.

Proposed method

• The framework employs a two-stage adaptive graph fusion layer that learns view-specific attention weights (α) to combine multiple KNN-based graphs into a unified graph structure.
• A differentiable node selection mechanism replaces non-differentiable top-k sorting by using a continuous relaxation of the permutation matrix via a Gumbel-Softmax reparameterization trick.
• The graph learning module refines the fused graph by updating adjacency matrices through differentiable operations, enabling end-to-end training.
• Node representations are updated via graph convolutional layers that aggregate features from selected, high-confidence neighbors in a differentiable manner.
• The model uses a learnable temperature parameter τ and a scaling factor γ to control the softness of the selection process, enabling smooth optimization.
• The overall architecture is trained end-to-end using cross-entropy loss on labeled data, with backpropagation through the differentiable selection and fusion components.

Experimental results

Research questions

• RQ1 Can differentiable node selection improve the optimization and performance of multi-view GCNs compared to non-differentiable top-k selection?
• RQ2 How does adaptive graph fusion with learnable attention weights enhance representation learning in multi-view semi-supervised classification?
• RQ3 To what extent does the proposed method reduce noise interference from heterogeneous views in multi-view graph learning?
• RQ4 How sensitive is the model's performance to hyperparameters γ and τ in the differentiable selection mechanism?
• RQ5 Can the framework achieve state-of-the-art performance on standard multi-view benchmark datasets?

Key findings

• MGCN-DNS achieves state-of-the-art performance on multiple benchmark multi-view datasets, including Caltech-20, NUS-WIDE, and Youtube, outperforming existing GCN-based and multi-view learning methods.
• The model demonstrates robustness to hyperparameter settings, with optimal performance achieved when τ > 0.4 and γ is sufficiently large, indicating stable optimization.
• Sensitivity analysis shows that small τ values (<0.3) degrade performance significantly, especially on BBCnews, due to the collapse of the soft permutation matrix into a hard one.
• Visualization confirms that the model learns meaningful attention weights (α), assigning higher importance to views that provide complementary information and lower weights to less informative views.
• The training loss decreases rapidly and converges within 200 iterations, indicating high training efficiency, though test accuracy plateaus or declines with excessive training, suggesting overfitting risk.
• The differentiable node selection mechanism enables effective backpropagation and end-to-end optimization, overcoming the gradient obstruction caused by discrete sorting in prior methods.