回顧經典卷積的操作：采樣（即構建鄰域）+聚合（聚合鄰居結點的信息）。將固定數量的鄰域結點排序后，與相同數量的卷積核參數相乘求和。
對於圖結構數據如何定義卷積操作？
1）構建鄰域；
2）對鄰域的點與卷積核參數內積；
GNN，構建鄰域的大小為p，p個固定數量的卷積核參數。GNN使用隨機游走的方法，為每個結點選取了最緊密相連的p個結點作為鄰域，然后與固定大小的卷積核參數進行內積。
Comparison Between Spectral and Spatial Models [1]:
Spatial models are preferred over spectral models due to efficiency, generality, and flexibility issues.
為什么空域圖卷積更受到大家的關注？原因：效率，泛化性，靈活性。
First, spectral models are less efficient than spatial models. Spectral models either need to perform eigenvector computation or handle the whole graph at the same time. Spatial models are more scalable to large graphs as they directly perform convolutions in the graph domain via information propagation. The computationcan be performed in a batch of nodes instead of the whole graph.
1、譜域圖卷積需要處理整張圖的Laplace矩陣，同時譜分解是高復雜度的。空余圖卷積則更適合於大規模的圖，因為其直接再結點域執行卷積操作（信息的傳播）。而且是針對每一個節點，具有局部性。
Second, spectral models that rely on a graph Fourier basis generalize poorly to new graphs. They assume a fixed graph. Any perturbations to a graph would result in a change of eigenbasis. Spatial-based models, on the other hand, perform graph convolutions locally on each node, where weights can be easily shared across different locations and structures.
2、譜域圖卷積高度依賴於Laplace矩陣的圖傅里葉變換正交基，因此，只能針對固定的圖。空域圖卷積則針對節點的鄰域進行卷積操作（信息的加權聚合），同時也可以實現參數共享。
Third, spectral-based models are limited to operate on undirected graphs. Spatial-based models are more flexible to handle multisource graph inputs, such as edge inputs directed graphs signed graphs and heterogeneous graphs because these graph inputs can be incorporated into the aggregation function easily.
3、由於Laplace矩陣的特征值分解的需要，因此，譜域圖卷積只能針對於無向圖（保證Laplace矩陣為對稱半正定矩陣，從而一定可以譜分解），但空域圖卷積不存在這樣的約束，可以處理更多類型的輸入，更加的靈活。
[1]: A Comprehensive Survey on Graph Neural Networks