Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
Michael Deffereard, etc.
EPFL
Intro
将CNN放到spectral graph theorem里来讨论。
这篇文章主要有三个贡献
- spectral formulation
- strictly localized filters
- low computational complexity
- efficient pooling
- experimental results
Proposed Methods
Learning Fast Localized Spectral Filters
有两种方法定义convolution filters，或者是spatial approach或者是spectral approach。spatial filter可以在finite size of kernel上进行localization，而graph convolution在spatial domain上相应的操作就很不方便。但另外一方面，spectral approach提供了很好的localization operator，通过在spectral domain上定义的convolution。convolution theorem将convolution定义为linear operators that diagonalize in the Fourier basis (通过Laplacian的特征向量表示)。但是spectral domain上定义的filter没有办法能够自然地localized，且计算要求比较高。这两个limitation都可以通过特殊的filter parameterization克服。
Graph Fourier Transform 后续的和Thomas & Max Welling的很类似（应该是后者和前者很类似），但这里介绍的更加详细。