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

arXiv: https://arxiv.org/abs/2012.03612 · HTML: https://mlsanity.com/paper/2012.03612/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2020.

## Built on by (most cited first, 7 of 7)

- [Block-coordinate Frank-Wolfe algorithm and convergence analysis for semi-relaxed optimal transport problem](https://mlsanity.com/paper/2205.13766/) (2022)
- [Wasserstein Graph Distance Based on L1-Approximated Tree Edit Distance between Weisfeiler-Lehman Subtrees](https://mlsanity.com/paper/2207.04216/) (2022)
- [Fast block-coordinate Frank-Wolfe algorithm for semi-relaxed optimal transport](https://mlsanity.com/paper/2103.05857/) (2021)
- [CityGPT: Towards Urban IoT Learning, Analysis and Interaction with Multi-Agent System](https://mlsanity.com/paper/2405.14691/) (2024)
- [On the Convergence of Semi-Relaxed Sinkhorn with Marginal Constraint and OT Distance Gaps](https://mlsanity.com/paper/2205.13846/) (2022)
- [Longest Common Substring in Longest Common Subsequence's Solution Service: A Novel Hyper-Heuristic](https://mlsanity.com/paper/2212.03178/) (2022)
- [Anchor Space Optimal Transport as a Fast Solution to Multiple Optimal Transport Problems](https://mlsanity.com/paper/2310.16123/) (2023)

## Abstract (arXiv)

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 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.