LCS Graph Kernel Based on Wasserstein Distance in Longest Common Subsequence Metric Space

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.