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. Unlike 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. The code is available at https://github.com/navid-naderi/WEGL.
翻译:我们提出瓦瑟斯坦图学嵌入嵌入器(WEGL),这是将整张图表嵌入矢量空间的新而快速的框架,在矢量空间中,各种机器学习模型适用于图形级的预测任务。我们利用新的洞察力来界定图表之间的相似性,这是其结点嵌入分布的相似性函数。具体地说,我们使用瓦瑟斯坦距离来测量不同图表结点嵌入的不相同性。与以往的工作不同,我们避免对图表之间的距离进行对称计算,并在图表数量中将计算的复杂性从二次到线性。WEGL从每个节点嵌入的引用分布中计算蒙古地图,并在这些地图的基础上创建了该图的固定尺寸矢量代表。我们评估了我们新的图形嵌入方法,以显示不同基准的图形-丙酸预测任务为标准,同时具有较高的计算效率。该代码可在 https://github.com/navid-naderi/WEGL上查阅。