Frequency Analysis for Graph Convolution Network
In this work, we develop quantitative results to the learnablity of a two-layers Graph Convolutional Network (GCN). Instead of analyzing GCN under some classes of functions, our approach provides a quantitative gap between a two-layers GCN and a two-layers MLP model. Our analysis is based on the graph signal processing (GSP) approach, which can provide much more useful insights than the message-passing computational model. Interestingly, based on our analysis, we have been able to empirically demonstrate a few case when GCN and other state-of-the-art models cannot learn even when true vertex features are extremely low-dimensional. To demonstrate our theoretical findings and propose a solution to the aforementioned adversarial cases, we build a proof of concept graph neural network model with stacked filters named Graph Filters Neural Network (gfNN).
Code (0)
등록된 구현이 없습니다.
Tasks
Graph Neural NetworkMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Signed Graph Neural Networks: A Frequency Perspective
Graph convolutional networks (GCNs) and its variants are designed for unsigned graphs containing only positive links. Many existing GCNs have been derived from the spectral domain analysis of signals lying over (unsigned…
Link Sign PredictionNode ClassificationStability to Deformations of Manifold Filters and Manifold Neural Networks
The paper defines and studies manifold (M) convolutional filters and neural networks (NNs). \emph{Manifold} filters and MNNs are defined in terms of the Laplace-Beltrami operator exponential and are such that \emph{graph…
Epileptic Seizure Detection in Separate Frequency Bands Using Feature Analysis and Graph Convolutional Neural Network (GCN) from Electroencephalogram (EEG) Signals
Epileptic seizures are neurological disorders characterized by abnormal and excessive electrical activity in the brain, resulting in recurrent seizure events. Electroencephalogram (EEG) signals are widely used for seizur…
Seizure DetectionA Generalization of the Convolution Theorem and its Connections to Non-Stationarity and the Graph Frequency Domain
In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters. Specifically, we show how a node…
Not All Low-Pass Filters are Robust in Graph Convolutional Networks
Graph Convolutional Networks (GCNs) are promising deep learning approaches in learning representations for graph-structured data. Despite the proliferation of such methods, it is well known that they are vulnerable to ca…
All