简化图卷积笔记

1 Title

Simplifying Graph Convolutional Networks（Felix Wu、Tianyi Zhang、Amauri Holanda de、 Souza Jr、Christopher Fifty、Tao Yu、Kilian Q. Weinberger）【ICML 2019】

2 Conclusion

This paper proposes a simplified graph convolutional method. By eliminating the nonlinear computation between GCN layers, reducing the additional complexity of GCN by folding the obtained function into a linear transformation, and obtaining the theoretical support of SGC from the root of graph convolution-spectrum analysis, it is proved that SGC is equivalent to a fixed low-channel filter and a linear classifier

3 Good Sentence

1、However, possibly because GCNs were proposed after the recent “renaissance” of neural networks, they tend to be a rare exception to this trend. GCNs are built upon multi-layer
neural networks, and were never an extension of a simpler (insufficient) linear counterpart（GCNs are not linear, making them not easy to optimize and interpret）
2、In contrast to its nonlinear counterparts, the SGC is intuitively interpretable and we provide a theoretical analysis from the graph convolution perspective. Notably, feature extraction in SGC corresponds to a single fixed filter applied to each feature dimension（The advantages of SGC when compared with GCN）
3、The algorithm is almost trivial, a graph based pre-processing step followed by standard multi-class logistic regression. However, the performance of SGC rivals — if not surpasses — the performance of GCNs and state-of-the-art graph neural network models across a wide range of graph learning tasks（The contribution of SGC）

本文的目的是把非线性的GCN转化成一个简单的线性模型SGC，通过反复消除GCN层之间的非线性并将得到的函数折叠成一个线性变换来减少GCNs的额外复杂度。

在GCN中，每一层的操作可以表示为： $H^{l+1} =\sigma (D^{-1/2} A D^{-1/2} H^{l} W^l)$ 其中，A是邻接矩阵，D是度矩阵， $H^I$ 是第l层的隐藏状态， $W^I$ 是第l层的权重，σ是非线性激活函数。在SGC中，我们省略了非线性激活函数σ，因此每一层的操作变为： $H^{l+1} = D^{-1/2} A D^{-1/2} H^l W^l$ 这样，所有层的操作可以合并为一个操作，即： $H^K = {(D^{-1/2} A D^{-1/2})}^K H^0 W$ 其中，K是层数， $H^0$ 是输入特征，W是一个需要学习的权重矩阵。这种方法的优点是计算效率高，因为所有层的操作可以预先计算并存储为一个矩阵。此外，由于省略了非线性激活函数，SGC的训练过程也更稳定。然而，这也意味着SGC可能无法捕捉到一些复杂的非线性模式。