For graph classification tasks, many methods use a common strategy to aggregate information of vertex neighbors. Although this strategy provides an efficient means of extracting graph topological features, it brings excessive amounts of information that might greatly reduce its accuracy when dealing with large-scale neighborhoods. Learning graphs using paths or walks will not suffer from this difficulty, but many have low utilization of each path or walk, which might engender information loss and high computational costs. To solve this, we propose a graph kernel using a longest common subsequence (LCS kernel) to compute more comprehensive similarity between paths and walks, which resolves substructure isomorphism difficulties. We also combine it with optimal transport theory to extract more in-depth features of graphs. Furthermore, we propose an LCS metric space and apply an adjacent point merge operation to reduce its computational costs. Finally, we demonstrate that our proposed method outperforms many state-of-the-art graph kernel methods.

Inference on a large-scale knowledge graph (KG) is of great importance for KG applications like question answering. The path-based reasoning models can leverage much information over paths other than pure triples in the KG, which face several challenges: all the existing path-based methods are data-driven, lacking explainability for path representation. Besides, some methods either consider only relational paths or ignore the heterogeneity between entities and relations both contained in paths, which cannot capture the rich semantics of paths well. To address the above challenges, in this work, we propose a novel joint semantics and data-driven path representation that balances explainability and generalization in the framework of KG embedding. More specifically, we inject horn rules to obtain the condensed paths by the transparent and explainable path composition procedure. The entity converter is designed to transform the entities along paths into the representations in the semantic level similar to relations for reducing the heterogeneity between entities and relations, in which the KGs both with and without type information are considered. Our proposed model is evaluated on two classes of tasks: link prediction and path query answering task. The experimental results show that it has a significant performance gain over several different state-of-the-art baselines.