N1H111SM's Miniverse

2020/02/25 Share

Materials

# Architecture

## Derivation from ChebNet

ChebNet是利用矩阵上的切比雪夫多项式进行K阶近似的方法。简单来说是将图傅里叶变换中的$g_\theta$进行近似。

Note that this expression is now K-localized since it is a Kth-order polynomial in the Laplacian, i.e. it depends only on nodes that are at maximum K steps away from the central node (Kth-order neighborhood).

K阶近似意味着中心节点的表示仅会被周围距离为K的节点影响。本文的一个重要想法是：我们不需要在单个filter上去定义K阶近似，相反我们限制一个filter就是一阶近似，将这个一阶近似层叠K层也能够达到Kth-order neighborhood的效果。同时估计ChebNet中$\lambda_{\max}\approx 2$。一阶（线性）近似的两个自由变量分别取为相反数$\theta = \theta^ \prime_0 = -\theta^ \prime_1$。这样我们就得到最开始定义的GCN上单通道的卷积操作：

## Semi-Supervised Node Classification

Limitations and Future Work

• For very large and densely connected graph datasets, further approximations might be necessary.
• Our framework currently does not naturally support edge features and is limited to undirected graphs (weighted oo unweighted).
• we implicitly assume locality (dependence on the Kth-order neighborhood for a GCN with K layers) and equal importance of self-connections vs. edges to neighboring nodes. It might be beneficial to introduce a trade-off parameter $\lambda$ in the definition of $\tilde A$: $\tilde A = A + \lambda I_N$.