For graph learning tasks, many existing methods utilize a message-passing mechanism where vertex features are updated iteratively by aggregation of neighbor information. This strategy provides an efficient means for graph features extraction, but obtained features after many iterations might contain too much information from other vertices, and tend to be similar to each other. This makes their representations less expressive. Learning graphs using paths, on the other hand, can be less adversely affected by this problem because it does not involve all vertex neighbors. However, most of them can only compare paths with the same length, which might engender information loss. To resolve this difficulty, we propose a new Graph Kernel based on a Longest Common Subsequence (LCS) similarity. Moreover, we found that the widely-used $\mathcal{R}$-convolution framework is unsuitable for path-based Graph Kernel because a huge number of comparisons between dissimilar paths might deteriorate graph distances calculation. Therefore, we propose a novel metric space by exploiting the proposed LCS-based similarity, and compute a new Wasserstein-based graph distance in this metric space, which emphasizes more the comparison between similar paths. Furthermore, to reduce the computational cost, we propose an adjacent point merging operation to sparsify point clouds in the metric space.

对于图学习任务，许多现有方法利用消息传递机制，其中顶点特征通过邻居信息的聚合迭代更新。这种策略为图特征提取提供了一种有效的手段，但是经过多次迭代得到的特征可能包含太多来自其他顶点的信息，并且往往彼此相似。这使得它们的表示不那么具有表现力。另一方面，使用路径学习图受此问题的不利影响较小，因为它不涉及所有顶点邻居。然而，它们中的大多数只能比较相同长度的路径，这可能会导致信息丢失。为了解决这个困难，我们提出了一种基于最长公共子序列（LCS）相似性的新图内核。此外，我们发现广泛使用的$\mathcal{电阻}$-convolution 框架不适合基于路径的图内核，因为不同路径之间的大量比较可能会影响图距离计算。因此，我们通过利用所提出的基于 LCS 的相似性提出了一个新的度量空间，并在这个度量空间中计算了一个新的基于 Wasserstein 的图距离，这更加强调了相似路径之间的比较。此外，为了降低计算成本，我们提出了一种相邻点合并操作来稀疏度量空间中的点云。