概
mean 是在 GCN 中是一种常见的 aggregation 方式, 但是作者认为这种方式是不鲁棒的, 很容易受到异常连接的影响.
符号说明
- \(G = (V, E)\), 图;
- \(X_{v}\), node features;
- 一般的 GCN 的每一层可以表述为:\[a_v^{(k)} = f(\{h_u^{(k-1)}: u \in \mathcal{N}_v\}), h_v^{(k)} = \sigma(a_v^{(k)} W^{(k)}). \]其中 \(f\) 为 aggregation function.
本文的方法
- 这里省略本文的 motivation, 即关于
mean不鲁棒的经验验证:
:
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meanaggregation 可以表述为:\[a_v^{(k)} = \sum_{u \in \mathcal{N}_v} w_{uv} h_u^{(k-1)}, w_{uv} = \frac{1}{\sqrt{|\mathcal{N}_u||\mathcal{N}_v|}}. \] -
作者提出用一下两种来替代:
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Median aggregation:
\[a_v = \left \{ \begin{array}{ll} (h_{n / 2} + h_{(n / 2 + 1)}) / 2 & n \text{ is even}; \\ h_{(n+1) / 2} & n \text{ is odd}. \end{array} \right. \]即取中位数, 这里假设 \([h_u]_{u=1}^n\) 是有序的 (按照数值大小进行排序).
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Trimmed mean aggregation:
\[a_v = \frac{1}{n - 2\lfloor n\alpha \rfloor} \sum_{u=s}^t h_u, s = \lfloor n\alpha \rfloor + 1, t = n - \lfloor n\alpha \rfloor, \]即该式只对 \([\alpha, 1 - \alpha]\) 内的取平均.
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代码
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