  Graph neural networks have become one of the most important techniques to
solve machine learning problems on graph-structured data. Recent work on vertex
classification proposed deep and distributed learning models to achieve high
performance and scalability. However, we find that the feature vectors of
benchmark datasets are already quite informative for the classification task,
and the graph structure only provides a means to denoise the data. In this
paper, we develop a theoretical framework based on graph signal processing for
analyzing graph neural networks. Our results indicate that graph neural
networks only perform low-pass filtering on feature vectors and do not have the
non-linear manifold learning property. We further investigate their resilience
to feature noise and propose some insights on GCN-based graph neural network
design.
