Graph Convolutional Neural Networks Sensitivity Under Probabilistic Error Model

Xinjue Wang

doi:10.1109/TSIPN.2024.3485532

Graph Convolutional Neural Networks Sensitivity Under Probabilistic Error Model

2024-01-01

0

OA

AI

DOI：10.1109/TSIPN.2024.3485532

Original

Original request for help

Save

Abstract

En 中文

Graph Neural Networks (GNNs), particularly Graph Convolutional Neural Networks (GCNNs), have emerged as pivotal instruments in machine learning and signal processing for processing graph-structured data. This paper proposes an analysis framework to investigate the sensitivity of GCNNs to probabilistic graph perturbations, directly impacting the graph shift operator (GSO). Our study establishes tight expected GSO error bounds, which are explicitly linked to the error model parameters, and reveals a linear relationship between GSO perturbations and the resulting output differences at each layer of GCNNs. This linearity demonstrates that a single-layer GCNN maintains stability under graph edge perturbations, provided that the GSO errors remain bounded, regardless of the perturbation scale. For multilayer GCNNs, the dependency of system's output difference on GSO perturbations is shown to be a recursion of linearity. Finally, we exemplify the framework with the Graph Isomorphism Network (GIN) and Simple Graph Convolution Network (SGCN). Experiments validate our theoretical derivations and the effectiveness of our approach.

Keywords:

Perturbation methods

Filters

Sensitivity analysis

Probabilistic logic

Convolution

Laplace equations

Vectors

Information processing

Analytical models

Accuracy

Graph convolutional neural network

graph shift operator

sensitivity analysis

structural perturbation

Graph Convolutional Neural Networks Sensitivity Under Probabilistic Error Model

Abstract

Journal

Organization