![8
METHODOLOGY
Point knowledge Graph Embedding
• Construct a road network trajectory knowledge graph 𝐺 = {𝑉, 𝐸, 𝑅}.
o Relation types 𝑅: road network edge 𝑟𝑛, trajectory virtual edge 𝑟𝑡, dual edge 𝑟𝑛𝑡.
o A triplet: 𝑢, 𝑟𝑛, 𝑣
• Apply TransH[1] to learn entity and relation embeddings.
o Score function:
[1] Wang, Z., Zhang, J., Feng, J., & Chen, Z. (2014, June). Knowledge graph embedding by translating on hyperplanes. In Proceedings of the AAAI conference on artificial intelligence (Vol. 28, No. 1).](https://image.slidesharecdn.com/20240614labseminarhuygrlstm-240704112414-fae85d52/85/20240614_LabSeminar_Huy-GRLSTM-Trajectory-Similarity-Computation-with-Graph-Based-Residual-LSTM-pptx-8-320.jpg)
![10
METHODOLOGY
Graph Embedding on Point
• To capture the topology in the fusion graph, apply Graph attention network (GAT)[1].
o points embedding 𝑃 = 𝑝1, 𝑝2, … , 𝑝|𝑉|
|| is represents concatenation, and 𝑁𝑖 is the neighbor set which can be
obtained from G
• Concatenate the output embeddings of multi-head GAT.
[1] Velickovic, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., & Bengio, Y. (2017). Graph attention networks. stat, 1050(20), 10-48550.
where H is the number of the heads, || is the concatenationoperation, and σ is the activation
function.](https://image.slidesharecdn.com/20240614labseminarhuygrlstm-240704112414-fae85d52/85/20240614_LabSeminar_Huy-GRLSTM-Trajectory-Similarity-Computation-with-Graph-Based-Residual-LSTM-pptx-10-320.jpg)
![11
METHODOLOGY
Multi-Layer LSTM with Residual Network
• Inspired by ResNet[1], integrate ResNet
into the multi-layer LSTM.
o residual block at each time step i:
[1] He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 770-778).
• take the last timestep hidden output of LSTM
as the final trajectory embeddings.
ℱ(·) is the residual function, which stands for the learned
residuals.
ℋ(·) represents the identity connection: ℋ(𝑝𝑖
𝑙−1
) = 𝑝𝑖
𝑙−1](https://image.slidesharecdn.com/20240614labseminarhuygrlstm-240704112414-fae85d52/85/20240614_LabSeminar_Huy-GRLSTM-Trajectory-Similarity-Computation-with-Graph-Based-Residual-LSTM-pptx-11-320.jpg)
![14
EXPERIMENT AND RESULT
EXPERIMENT SETTINGs
• Measurement:
o top-k hitting ratio (HR@k): HR@1, HR@5, HR@10, HR@20,
and HR@50.
o overlap between there turned top-k results and the
ground truth
• Dataset – taxi trajectories network:
o Beijing and New York: GPS coordinates and timestamp.
• Baselines:
o Traj2vec[1], Siamese [2], NeuTraj [3], Traj2SimVec [4], and GTS[5].
[1] Yao, D., Zhang, C., Zhu, Z., Hu, Q., Wang, Z., Huang, J., & Bi, J. (2018). Learning deep representation for trajectory clustering. Expert Systems, 35(2), e12252.
[2] Pei, W., Tax, D. M., & van der Maaten, L. (2016). Modeling time series similarity with siamese recurrent networks. arXiv preprint arXiv:1603.04713.
[3] Yao, D., Cong, G., Zhang, C., & Bi, J. (2019, April). Computing trajectory similarity in linear time: A generic seed-guided neural metric learning approach. In 2019 IEEE 35th international conference on data engineering (ICDE) (pp. 1358-1369). IEEE.
[4] Zhang, H., Zhang, X., Jiang, Q., Zheng, B., Sun, Z., Sun, W., & Wang, C. (2020). Trajectory similarity learning with auxiliary supervision and optimal matching.
[5] Han, P., Wang, J., Yao, D., Shang, S., & Zhang, X. (2021, August). A graph-based approach for trajectory similarity computation in spatial networks. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining (pp. 556-564).](https://image.slidesharecdn.com/20240614labseminarhuygrlstm-240704112414-fae85d52/85/20240614_LabSeminar_Huy-GRLSTM-Trajectory-Similarity-Computation-with-Graph-Based-Residual-LSTM-pptx-14-320.jpg)
![[20240614_LabSeminar_Huy]GRLSTM: Trajectory Similarity Computation with Graph-Based Residual LSTM.pptx](https://image.slidesharecdn.com/20240614labseminarhuygrlstm-240704112414-fae85d52/85/20240614_LabSeminar_Huy-GRLSTM-Trajectory-Similarity-Computation-with-Graph-Based-Residual-LSTM-pptx-18-320.jpg)
![[20240614_LabSeminar_Huy]GRLSTM: Trajectory Similarity Computation with Graph-Based Residual LSTM.pptx](https://image.slidesharecdn.com/20240614labseminarhuygrlstm-240704112414-fae85d52/85/20240614_LabSeminar_Huy-GRLSTM-Trajectory-Similarity-Computation-with-Graph-Based-Residual-LSTM-pptx-19-320.jpg)
[20240614_LabSeminar_Huy]GRLSTM: Trajectory Similarity Computation with Graph-Based Residual LSTM.pptx
- 1. Quang-Huy Tran Network Science Lab Dept. of Artificial Intelligence The Catholic University of Korea E-mail: huytran1126@gmail.com 2024-06-14 GRLSTM: Trajectory Similarity Computation with Graph-Based Residual LSTM Silin Zhou et al. AAAI-2023: Proceedings of the Thirty-Seventh Conference on Artificial Intelligence
- 2. 2 OUTLINE • MOTIVATION • INTRODUCTION • METHODOLOGY • EXPERIMENT & RESULT • CONCLUSION
- 3. 3 MOTIVATION • With the ubiquitousness of GPS-enabled devices, massive trajectory data is being collected at an unprecedented rate. Overview • One of main way for trajectory similarity computation: o Each trajectory is encoded as a latent vector in Euclidean space with deep learning methods. • Trajectory similarity computation is an essential function in many real-world applications: o trajectory clustering, anomaly trajectory detection, route planning, transportation optimization, and trajectory matching.
- 4. 4 MOTIVATION Overview: Limitation • No considering directly on the road network. • Existing work on applying GNN into road network only considered road network. o ignores the trajectory information during the graph processing. o Adjacent points in a trajectory are not necessarily adjacent on the road.
- 5. 5 INTRODUCTION • Propose a novel trajectory similarity computation framework on road networks GRLSTM: o Modeling multi-relation of points with knowledge graph. o Introduce the residual network into multi-layer LSTM to learn trajectory embeddings • Design two new neighbor-based point-aware loss functions: o graph-based point loss and trajectory-based point loss.
- 6. 6 METHODOLOGY Problem Definition • A road network graph 𝐺 = {𝑉, 𝐸} o Each node 𝑣 ∈ 𝑉 is a point featured with a geographic coordinate, representing an endpoint of a road segment or a road intersection. o Each edge e = 𝑢, 𝑣 ∈ 𝐸 represents a road segment connecting 2 nodes. • A trajectory set 𝑇 = {𝜏1, 𝜏2, … , 𝜏𝑚} o A length n trajectory 𝜏 = 𝑣1, 𝑣2, . . , 𝑣𝑛 in the road network graph 𝐺 consists of an ordered sequence of n point coordinates. • The trajectory similarity computation problem: o Find 𝜏𝑎, 𝜏𝑏 ∈ T, 𝑎 ≠ 𝑏 such that 𝜏𝑏 is most similar to 𝜏𝑎.
- 7. 7 METHODOLOGY Main Architecture - LSTF • 3 main components: o Point knowledge graph embedding. o Fusion graph embedding. o Residual-LSTM.
- 8. 8 METHODOLOGY Point knowledge Graph Embedding • Construct a road network trajectory knowledge graph 𝐺 = {𝑉, 𝐸, 𝑅}. o Relation types 𝑅: road network edge 𝑟𝑛, trajectory virtual edge 𝑟𝑡, dual edge 𝑟𝑛𝑡. o A triplet: 𝑢, 𝑟𝑛, 𝑣 • Apply TransH[1] to learn entity and relation embeddings. o Score function: [1] Wang, Z., Zhang, J., Feng, J., & Chen, Z. (2014, June). Knowledge graph embedding by translating on hyperplanes. In Proceedings of the AAAI conference on artificial intelligence (Vol. 28, No. 1).
- 9. 9 METHODOLOGY Point knowledge Graph Embedding • To capture the correlation of points within different relations: o design entity-relation similarity function • Construct a point fusion graph by using k-nearest selection to obtain point 𝑣𝑖 neighbor set 𝑁𝑠(𝑣𝑖) o based on similarity to keep sparsity on graph and decrease noisy. • To show higher similarity for the closer distance, compute similarity between u and v. where 𝑒𝑢, 𝑒𝑣 denote the learned embeddings of point u and point v, respectively, 𝑒𝑟 is the learned relation embedding between u and v and ||. || represents L2-norm.
- 10. 10 METHODOLOGY Graph Embedding on Point • To capture the topology in the fusion graph, apply Graph attention network (GAT)[1]. o points embedding 𝑃 = 𝑝1, 𝑝2, … , 𝑝|𝑉| || is represents concatenation, and 𝑁𝑖 is the neighbor set which can be obtained from G • Concatenate the output embeddings of multi-head GAT. [1] Velickovic, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., & Bengio, Y. (2017). Graph attention networks. stat, 1050(20), 10-48550. where H is the number of the heads, || is the concatenationoperation, and σ is the activation function.
- 11. 11 METHODOLOGY Multi-Layer LSTM with Residual Network • Inspired by ResNet[1], integrate ResNet into the multi-layer LSTM. o residual block at each time step i: [1] He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 770-778). • take the last timestep hidden output of LSTM as the final trajectory embeddings. ℱ(·) is the residual function, which stands for the learned residuals. ℋ(·) represents the identity connection: ℋ(𝑝𝑖 𝑙−1 ) = 𝑝𝑖 𝑙−1
- 12. 12 METHODOLOGY Objective Functions • Embedding Similarity Measurement: after training, calculate similarity scores. o Trajectory embedding similarity score between 2 trajectories 𝜏𝑖, 𝜏𝑗: o Point embedding similarity score between 2 nodes points 𝑣𝑖, 𝑣𝑗: • Point-Aware Loss Function: define two neighbor-based point-aware loss functions – graph-based and trajectory-based. o Graph-based point neighbors: first-order neighbors 𝑁𝑔𝑝 on the fusion graph
- 13. 13 METHODOLOGY Objective Functions • Trajectory-Based Point Neighbors: each point in trajectory has previous and next point. o denote trajectory-based point neighbors as 𝑁𝑡𝑝 and 𝑁𝑡𝑝 ∈ {1,2}. • Trajectory-Aware Loss Function: . o define trajectory loss function for finding most similarity trajectories: o Final objective function:
- 14. 14 EXPERIMENT AND RESULT EXPERIMENT SETTINGs • Measurement: o top-k hitting ratio (HR@k): HR@1, HR@5, HR@10, HR@20, and HR@50. o overlap between there turned top-k results and the ground truth • Dataset – taxi trajectories network: o Beijing and New York: GPS coordinates and timestamp. • Baselines: o Traj2vec[1], Siamese [2], NeuTraj [3], Traj2SimVec [4], and GTS[5]. [1] Yao, D., Zhang, C., Zhu, Z., Hu, Q., Wang, Z., Huang, J., & Bi, J. (2018). Learning deep representation for trajectory clustering. Expert Systems, 35(2), e12252. [2] Pei, W., Tax, D. M., & van der Maaten, L. (2016). Modeling time series similarity with siamese recurrent networks. arXiv preprint arXiv:1603.04713. [3] Yao, D., Cong, G., Zhang, C., & Bi, J. (2019, April). Computing trajectory similarity in linear time: A generic seed-guided neural metric learning approach. In 2019 IEEE 35th international conference on data engineering (ICDE) (pp. 1358-1369). IEEE. [4] Zhang, H., Zhang, X., Jiang, Q., Zheng, B., Sun, Z., Sun, W., & Wang, C. (2020). Trajectory similarity learning with auxiliary supervision and optimal matching. [5] Han, P., Wang, J., Yao, D., Shang, S., & Zhang, X. (2021, August). A graph-based approach for trajectory similarity computation in spatial networks. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining (pp. 556-564).
- 15. 15 EXPERIMENT AND RESULT RESULT – Overall Performance
- 16. 16 EXPERIMENT AND RESULT RESULT – Residual-LSTM Layers Experiment
- 17. 17 CONCLUSION • proposed a novel trajectory similarity computation framework named GRLSTM on road networks. o multi-relation of points on road networks and construct a point knowledge graph. o utilize the knowledge graph embedding method to learn entity (point) and relation embeddings. • Constructed the point fusion graph to integrate trajectory and road network: o k-nearest selection. • To capture topology and trajectory embedding at each time: o multi-head GAT and Residual-LSTM. • Design two new neighbor-based point-aware loss function from graph and trajectory- based.