[Paper Review] RobustGCNs: Robust Norm Graph Convolutional Networks in the Presence of Node Missing Data and Large Noises

Bo Jiang, Ziyan Zhang|arXiv (Cornell University)|Mar 23, 2020

Advanced Graph Neural Networks4 citations

TL;DR

This paper proposes RobustGCNs, a novel graph convolutional network architecture that integrates robust norm-based feature learning into graph convolutions to handle node attribute missing data and large noises. By reinterpreting graph convolution as a data reconstruction process on graphs and applying robust norms (e.g., L1 or Huber) to the propagation function, the method improves robustness against outliers and missing features, achieving superior performance on noisy benchmark datasets.

ABSTRACT

Graph Convolutional Networks (GCNs) have been widely studied for attribute graph data representation and learning. In many applications, graph node attribute/feature may contain various kinds of noises, such as gross corruption, outliers and missing values. Existing graph convolutions (GCs) generally focus on feature propagation on structured graph which i) fail to address the graph data with missing values and ii) often perform susceptibility to the large feature errors/noises and outliers. To address this issue, in this paper, we propose to incorporate robust norm feature learning mechanism into graph convolution and present Robust Graph Convolutions (RGCs) for graph data in the presence of feature noises and missing values. Our RGCs is proposed based on the interpretation of GCs from a propagation function aspect of 'data reconstruction on graph'. Based on it, we then derive our RGCs by exploiting robust norm based propagation functions into GCs. Finally, we incorporate the derived RGCs into an end-to-end network architecture and propose a kind of RobustGCNs for graph data learning. Experimental results on several noisy datasets demonstrate the effectiveness and robustness of the proposed RobustGCNs.

Motivation & Objective

• Address the limitation of existing graph convolutions in handling missing node attributes and large feature noise.
• Improve robustness of GCNs under real-world data imperfections such as gross corruption and outliers.
• Develop a new graph convolution mechanism that is resilient to noisy and incomplete node features.
• Integrate the robust convolution into an end-to-end deep learning framework for graph representation learning.
• Demonstrate the effectiveness of the proposed method on real-world noisy graph datasets.

Proposed method

• Reinterpret graph convolution as a data reconstruction process on the graph structure, framing feature propagation as minimizing reconstruction error.
• Replace standard L2-based propagation with robust norm-based (e.g., L1 or Huber) loss functions to reduce sensitivity to outliers and noise.
• Design Robust Graph Convolutions (RGCs) by incorporating robust norm-based propagation functions into the GCN framework.
• Formulate the RGC layer as a differentiable module that minimizes a robust objective function over node features during message passing.
• Integrate RGCs into a deep neural network architecture to enable end-to-end training on graph-structured data with noisy features.
• Optimize the full network using standard backpropagation, with robust norms stabilizing gradients during training under noisy inputs.

Experimental results

Research questions

• RQ1 Can robust norm-based feature learning improve the robustness of graph convolutions under missing node attributes?
• RQ2 How does the proposed RGC mechanism perform compared to standard GCNs when exposed to large feature noise and outliers?
• RQ3 To what extent does the robust norm formulation enhance model generalization on noisy graph datasets?
• RQ4 Does the proposed method maintain performance under varying levels of missing data and noise intensity?
• RQ5 Can the robust norm-based propagation function be effectively integrated into an end-to-end GCN framework?

Key findings

• The proposed RobustGCNs significantly outperform standard GCNs on datasets with missing node features and large noise.
• RobustGCNs demonstrate improved robustness to outliers and gross corruption in node attributes, maintaining high performance under extreme noise conditions.
• The use of robust norms (e.g., L1 or Huber) in the propagation function reduces sensitivity to large errors in input features.
• Experimental results show consistent performance gains across multiple noisy benchmark datasets, validating the effectiveness of the robust norm approach.
• The end-to-end training of RobustGCNs enables stable optimization even when input features are corrupted or incomplete.