CayleyNets : graph convolutional neural networks with complex rational spectral filters

• المؤلفون الرئيسيون: Levie, Ron, Monti, Federico, Bresson, Xavier, Bronstein, Michael M.
• مؤلفون آخرون: School of Computer Science and Engineering
• التنسيق: مقال
• اللغة: English
• منشور في: 2020
• الموضوعات: Engineering::Computer science and engineering; Geometric Deep Learning; Graph Convolution Neural Networks
• الوصول للمادة أونلاين: https://hdl.handle.net/10356/139445

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.