# Unsupervised Path Representation Learning with Curriculum Negative Sampling

arXiv: https://arxiv.org/abs/2106.09373 · HTML: https://mlsanity.com/paper/2106.09373/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 28 references that are in the map.
- First posted on arXiv 17 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [DeepCas: an End-to-end Predictor of Information Cascades](https://mlsanity.com/paper/1611.05373/) (2016)
- [Simplify and Robustify Negative Sampling for Implicit Collaborative Filtering](https://mlsanity.com/paper/2009.03376/) (2020)
- [Incorporating GAN for Negative Sampling in Knowledge Representation Learning](https://mlsanity.com/paper/1809.11017/) (2018)
- [Learning to Route with Sparse Trajectory Sets---Extended Version](https://mlsanity.com/paper/1802.07980/) (2018)

## Built on by (most cited first, 30 of 42)

- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [DUET: Dual Clustering Enhanced Multivariate Time Series Forecasting](https://mlsanity.com/paper/2412.10859/) (2024)
- [CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patching](https://mlsanity.com/paper/2410.12261/) (2024)
- [Towards Spatio-Temporal Aware Traffic Time Series Forecasting--Full Version](https://mlsanity.com/paper/2203.15737/) (2022)
- [Triformer: Triangular, Variable-Specific Attentions for Long Sequence Multivariate Time Series Forecasting--Full Version](https://mlsanity.com/paper/2204.13767/) (2022)
- [Self-supervised Trajectory Representation Learning with Temporal Regularities and Travel Semantics](https://mlsanity.com/paper/2211.09510/) (2022)
- [AutoCTS: Automated Correlated Time Series Forecasting -- Extended Version](https://mlsanity.com/paper/2112.11174/) (2021)
- [Unsupervised Time Series Outlier Detection with Diversity-Driven Convolutional Ensembles -- Extended Version](https://mlsanity.com/paper/2111.11108/) (2021)
- [Jointly Contrastive Representation Learning on Road Network and Trajectory](https://mlsanity.com/paper/2209.06389/) (2022)
- [LightPath: Lightweight and Scalable Path Representation Learning](https://mlsanity.com/paper/2307.10171/) (2023)
- [Towards Urban General Intelligence: A Review and Outlook of Urban Foundation Models](https://mlsanity.com/paper/2402.01749/) (2024)
- [Trajectory Data Management and Mining: A Survey from Deep Learning to the LLM Era](https://mlsanity.com/paper/2403.14151/) (2024)
- [More Than Routing: Joint GPS and Route Modeling for Refine Trajectory Representation Learning](https://mlsanity.com/paper/2402.16915/) (2024)
- [Robust and Explainable Autoencoders for Unsupervised Time Series Outlier Detection---Extended Version](https://mlsanity.com/paper/2204.03341/) (2022)
- [BIGCity: A Universal Spatiotemporal Model for Unified Trajectory and Traffic State Data Analysis](https://mlsanity.com/paper/2412.00953/) (2024)
- [Weakly-supervised Temporal Path Representation Learning with Contrastive Curriculum Learning -- Extended Version](https://mlsanity.com/paper/2203.16110/) (2022)
- [Bridging Traffic State and Trajectory for Dynamic Road Network and Trajectory Representation Learning](https://mlsanity.com/paper/2502.06870/) (2025)
- [Self-Supervised Representation Learning for Geospatial Objects: A Survey](https://mlsanity.com/paper/2408.12133/) (2024)
- [RED: Effective Trajectory Representation Learning with Comprehensive Information](https://mlsanity.com/paper/2411.15096/) (2024)
- [K2VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.23017/) (2025)
- [Blurred Encoding for Trajectory Representation Learning](https://mlsanity.com/paper/2511.13741/) (2025)
- [Grid and Road Expressions Are Complementary for Trajectory Representation Learning](https://mlsanity.com/paper/2411.14768/) (2024)
- [Fine-Grained Trajectory-based Travel Time Estimation for Multi-city Scenarios Based on Deep Meta-Learning](https://mlsanity.com/paper/2201.08017/) (2022)
- [A Critical Perceptual Pre-trained Model for Complex Trajectory Recovery](https://mlsanity.com/paper/2311.02631/) (2023)
- [TrajCogn: Leveraging LLMs for Cognizing Movement Patterns and Travel Purposes from Trajectories](https://mlsanity.com/paper/2405.12459/) (2024)
- [RCRank: Multimodal Ranking of Root Causes of Slow Queries in Cloud Database Systems](https://mlsanity.com/paper/2503.04252/) (2025)
- [Taxonomy of the Retrieval System Framework: Pitfalls and Paradigms](https://mlsanity.com/paper/2601.20131/) (2026)
- [VisionTraj: A Noise-Robust Trajectory Recovery Framework based on Large-scale Camera Network](https://mlsanity.com/paper/2312.06428/) (2023)
- [Towards Lightweight Time Series Forecasting: a Patch-wise Transformer with Weak Data Enriching](https://mlsanity.com/paper/2501.10448/) (2025)
- [Spatio-Temporal Trajectory Foundation Model - Recent Advances and Future Directions](https://mlsanity.com/paper/2511.20729/) (2025)

## Abstract (arXiv)

Path representations are critical in a variety of transportation applications, such as estimating path ranking in path recommendation systems and estimating path travel time in navigation systems. Existing studies often learn task-specific path representations in a supervised manner, which require a large amount of labeled training data and generalize poorly to other tasks. We propose an unsupervised learning framework Path InfoMax (PIM) to learn generic path representations that work for different downstream tasks. We first propose a curriculum negative sampling method, for each input path, to generate a small amount of negative paths, by following the principles of curriculum learning. Next, PIM employs mutual information maximization to learn path representations from both a global and a local view. In the global view, PIM distinguishes the representations of the input paths from those of the negative paths. In the local view, PIM distinguishes the input path representations from the representations of the nodes that appear only in the negative paths. This enables the learned path representations to encode both global and local information at different scales. Extensive experiments on two downstream tasks, ranking score estimation and travel time estimation, using two road network datasets suggest that PIM significantly outperforms other unsupervised methods and is also able to be used as a pre-training method to enhance supervised path representation learning.