图同态卷积
Graph Homomorphism Convolution
摘要：
本文从图同态的角度研究了图的分类问题。我们考虑从$F$到$G$的同态，其中$G$是感兴趣的图（例如分子或社交网络），而$F$属于某个图族（例如路径或非同构树）。我们表明，图同态数提供了一个自然的不变（同构不变和$\mathcal{F}$不变）嵌入地图，可用于图分类。从$\mathcal{F}$ -不可区分概念的角度考察图分类器的表达能力，证明了图同态向量在逼近$\mathcal{F}$ -不变函数时的普适性。在实践中，通过选择元素具有有界树宽的$\mathcal{F}$，我们证明了与其他方法相比，同态方法是有效的。
英文摘要：
In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some family of graphs (e.g. paths or non-isomorphic trees). We show that graph homomorphism numbers provide a natural invariant (isomorphism invariant and $\mathcal{F}$-invariant) embedding maps which can be used for graph classification. Viewing the expressive power of a graph classifier by the $\mathcal{F}$-indistinguishable concept, we prove the universality property of graph homomorphism vectors in approximating $\mathcal{F}$-invariant functions. In practice, by choosing $\mathcal{F}$ whose elements have bounded tree-width, we show that the homomorphism method is efficient compared with other methods.
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