# Deep Spatially and Temporally Aware Similarity Computation for Road Network Constrained Trajectories

arXiv: https://arxiv.org/abs/2112.09339 · HTML: https://mlsanity.com/paper/2112.09339/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 17 Dec 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Deep Metric Learning with Hierarchical Triplet Loss](https://mlsanity.com/paper/1810.06951/) (2018)
- [Norm-Based Curriculum Learning for Neural Machine Translation](https://mlsanity.com/paper/2006.02014/) (2020)
- [DarkRank: Accelerating Deep Metric Learning via Cross Sample Similarities Transfer](https://mlsanity.com/paper/1707.01220/) (2017)
- [ViSiL: Fine-grained Spatio-Temporal Video Similarity Learning](https://mlsanity.com/paper/1908.07410/) (2019)
- [Curriculum Self-Paced Learning for Cross-Domain Object Detection](https://mlsanity.com/paper/1911.06849/) (2019)
- [Does the Order of Training Samples Matter? Improving Neural Data-to-Text Generation with Curriculum Learning](https://mlsanity.com/paper/2102.03554/) (2021)
- [Zone pAth Construction (ZAC) based Approaches for Effective Real-Time Ridesharing](https://mlsanity.com/paper/2009.06051/) (2020)
- [Fast Subtrajectory Similarity Search in Road Networks under Weighted Edit Distance Constraints](https://mlsanity.com/paper/2006.05564/) (2020)

## Built on by (most cited first, 29 of 29)

- [Contrastive Trajectory Similarity Learning with Dual-Feature Attention](https://mlsanity.com/paper/2210.05155/) (2022)
- [Trajectory Data Management and Mining: A Survey from Deep Learning to the LLM Era](https://mlsanity.com/paper/2403.14151/) (2024)
- [RNTrajRec: Road Network Enhanced Trajectory Recovery with Spatial-Temporal Transformer](https://mlsanity.com/paper/2211.13234/) (2022)
- [More Than Routing: Joint GPS and Route Modeling for Refine Trajectory Representation Learning](https://mlsanity.com/paper/2402.16915/) (2024)
- [TrajFM: A Vehicle Trajectory Foundation Model for Region and Task Transferability](https://mlsanity.com/paper/2408.15251/) (2024)
- [Robust Spatiotemporal Traffic Forecasting with Reinforced Dynamic Adversarial Training](https://mlsanity.com/paper/2306.14126/) (2023)
- [Micro-Macro Spatial-Temporal Graph-based Encoder-Decoder for Map-Constrained Trajectory Recovery](https://mlsanity.com/paper/2404.19141/) (2024)
- [Self-Supervised Representation Learning for Geospatial Objects: A Survey](https://mlsanity.com/paper/2408.12133/) (2024)
- [Grid and Road Expressions Are Complementary for Trajectory Representation Learning](https://mlsanity.com/paper/2411.14768/) (2024)
- [A Data-driven Region Generation Framework for Spatiotemporal Transportation Service Management](https://mlsanity.com/paper/2306.02806/) (2023)
- [SIMformer: Single-Layer Vanilla Transformer Can Learn Free-Space Trajectory Similarity](https://mlsanity.com/paper/2410.14629/) (2024)
- [TrajCogn: Leveraging LLMs for Cognizing Movement Patterns and Travel Purposes from Trajectories](https://mlsanity.com/paper/2405.12459/) (2024)
- [Revisiting CNNs for Trajectory Similarity Learning](https://mlsanity.com/paper/2405.19761/) (2024)
- [TransferTraj: A Vehicle Trajectory Learning Model for Region and Task Transferability](https://mlsanity.com/paper/2505.12672/) (2025)
- [PTrajM: Efficient and Semantic-rich Trajectory Learning with Pretrained Trajectory-Mamba](https://mlsanity.com/paper/2408.04916/) (2024)
- [Spatio-Temporal Trajectory Foundation Model - Recent Advances and Future Directions](https://mlsanity.com/paper/2511.20729/) (2025)
- [Clustering Human Mobility with Multiple Spaces](https://mlsanity.com/paper/2301.08524/) (2023)
- [Jointly spatial-temporal representation learning for individual trajectories](https://mlsanity.com/paper/2312.04055/) (2023)
- [TSMini: A Simple Yet Highly Effective Trajectory Similarity Learning Model](https://mlsanity.com/paper/2502.00285/) (2025)
- [PathletRL++: Optimizing Trajectory Pathlet Extraction and Dictionary Formation via Reinforcement Learning](https://mlsanity.com/paper/2412.03715/) (2024)
- [Learning Spatio-Temporal Dynamics for Trajectory Recovery via Time-Aware Transformer](https://mlsanity.com/paper/2505.13857/) (2025)
- [Learning Generalized and Flexible Trajectory Models from Omni-Semantic Supervision](https://mlsanity.com/paper/2505.17437/) (2025)
- [REFINE: Trajectory Representation Learning via Closed-Loop Transcription -- Extended Version](https://mlsanity.com/paper/2609.07206/) (2026)
- [A principled distributional approach to trajectory similarity measurement](https://mlsanity.com/paper/2301.00393/) (2023)
- [Efficient Methods for Accurate Sparse Trajectory Recovery and Map Matching](https://mlsanity.com/paper/2508.10460/) (2025)
- [GeoPTH: A Lightweight Approach to Category-Based Trajectory Retrieval via Geometric Prototype Trajectory Hashing](https://mlsanity.com/paper/2511.16258/) (2025)
- [DiSGMM: A Method for Time-varying Microscopic Weight Completion on Road Networks](https://mlsanity.com/paper/2603.29837/) (2026)
- [Using Lower-Bound Representations for Trajectory Similarity Learning](https://mlsanity.com/paper/2608.01039/) (2026)
- [SceneGTMM: A Conformal Mapping-based Scene-Aware Transferable GNN-Transformer Dual-Graph Interaction Framework for Map Matching](https://mlsanity.com/paper/2608.19298/) (2026)

## Abstract (arXiv)

Trajectory similarity computation has drawn massive attention, as it is core functionality in a wide range of applications such as ride-sharing, traffic analysis, and social recommendation. Motivated by the recent success of deep learning technologies, researchers start devoting efforts to learning-based similarity analyses to overcome the limitations (i.e., high cost and poor adaptability) of traditional methods. Specifically, deep trajectory similarity computation aims to learn a distance function that can evaluate how similar two trajectories are via neural networks. However, existing learning-based methods focus on spatial similarity but ignore the time dimension of trajectories, which is suboptimal for time-aware applications. Besides, they tend to disregard the embedding of trajectories into road networks, restricting their applicability in real scenarios. In this paper, we propose an effective learning-based framework, called ST2Vec, to perform efficient spatially and temporally aware trajectory similarity computation in road networks. Finally, extensive experimental evaluation using three real trajectory data sets shows that ST2Vec outperforms all the state-of-the-art approaches substantially.