We present Wasserstein Embedding for Graph Learning (WEGL), a novel and fast framework for embedding entire graphs in a vector space, in which various machine learning models are applicable for graph-level prediction tasks. We leverage new insights on defining similarity between graphs as a function of the similarity between their node embedding distributions. Specifically, we use the Wasserstein distance to measure the dissimilarity between node embeddings of different graphs. Different from prior work, we avoid pairwise calculation of distances between graphs and reduce the computational complexity from quadratic to linear in the number of graphs. WEGL calculates Monge maps from a reference distribution to each node embedding and, based on these maps, creates a fixed-sized vector representation of the graph. We evaluate our new graph embedding approach on various benchmark graph-property prediction tasks, showing state-of-the-art classification performance, while having superior computational efficiency.

本研究提出了针对图学习的 Wasserstein Embedding 方法，并应用不同的机器学习模型来进行图预测任务，利用节点嵌入分布的相似度来定义图之间的相似性，并用 Wasserstein 距离度量两者之间的差异，不同于现有方法，避免了两两计算不同的图之间的距离，将计算复杂度从二次线性降至一次线性，并证明了该方法在各项基准图属性预测任务中具有优秀的分类表现及计算效率。

基于Wasserstein嵌入的图学习