目前的圖(graph)的嵌入模型雖然可以產生對做圖的相 關問題時表現不錯的向量，但是在模型在學習如何產生圖 的嵌入向量的時候，是否能同時學習對任務有用的其他資 訊，卻是鮮少被探討的問題。
在這篇論文中，我們考慮在嵌入時同時偵測對監督任務 有決定性影響的「關鍵結構」的可能性。我們提出一個由 局部到全局的嵌入模型「Ego-CNNs」，主要想法是利用到 卷積網路(CNNs)的特性，將局部的嵌入向量，再透過一 層層的 Ego-Convolution 層之後，擴張成能覆蓋整張圖的向 量，其中這向量代表的是由不同的點(node)為中心出發看 待整張圖的觀點。只要跟監督任務模型(supervised task model)結合就能偵測出其中的關鍵結構。
我們呈現的結果有:(1)Ego-CNN 能得不比目前最好 的嵌入模型差的表現。(2)Ego-CNN 可以利用現有的卷積 網路視覺化的技術來呈現偵測到的結構。(3)Ego-CNN 在 計算上很有效率並且可以加入現實社群網路中常見的無尺 度(scale-free)的特性進一步提升學模型的學習效率。

While existing graph embedding models can generate useful embedding vectors for graph-related tasks, what valuable information can be jointly learned from a graph embedding model is less discussed. In this paper, we consider the possibility of detecting critical structures by a graph embedding model. We propose Ego-CNN to embed graphs, which works in a local-to- global manner to take ad- vantages of CNNs that gradually expands the detectable local regions on the graph as the network depth increases. Critical structures can be detected if Ego-CNN is combined with a supervised task model. We show that Ego- CNN is (1) competitive to state-of-the-art graph embeddings models, (2) can work nicely with CNNs visualization techniques to show the detected structures, and (3) is efficient and can incorporate with scale-free priors, which commonly occurs in social network datasets, to further improve the training efficiency.

1. INTRODUCTION ..............................................................6
2. RELATED WORK .............................................................10
Graph Kernels .....................................................................10
Graphical Models ................................................................11
Convolution-based Methods................................................11
3. EGO-CNN ........................................................................14
Effective Receptive Field on Ambient Graph .......................16
4. ADVANTAGES OF EGO-CNN ...........................................18
DETECTING CRITICAL STRUCTURES ..................................18
EFFICIENCY AND THE SCALE-FREE PRIOR .........................18
5. EXPERIMENTS .................................................................20
GRAPH CLASSIFICATION .....................................................20
SCALE-FREE REGULARIZER .................................................21
VISUALIZATION OF CRITICAL STRUCTURES .......................22
6. CONCLUSIONS .................................................................25
REFERENCES ........................................................................26

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