CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters
This work addresses the need for efficient and effective deep learning models on non-Euclidean domains like social and biological networks, representing an incremental improvement in spectral graph convolutional neural networks.
The authors tackled the problem of generalizing deep learning to graph-structured data by introducing CayleyNets, a spectral domain convolutional architecture using complex rational spectral filters, which achieved superior performance on tasks like spectral image classification and community detection compared to other spectral methods.
The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in generalizing deep learning models to non-Euclidean domains. In this paper, we introduce a new spectral domain convolutional architecture for deep learning on graphs. The core ingredient of our model is a new class of parametric rational complex functions (Cayley polynomials) allowing to efficiently compute spectral filters on graphs that specialize on frequency bands of interest. Our model generates rich spectral filters that are localized in space, scales linearly with the size of the input data for sparsely-connected graphs, and can handle different constructions of Laplacian operators. Extensive experimental results show the superior performance of our approach, in comparison to other spectral domain convolutional architectures, on spectral image classification, community detection, vertex classification and matrix completion tasks.