# Explainable Trajectory Representation through Dictionary Learning

arXiv: https://arxiv.org/abs/2312.08052 · HTML: https://mlsanity.com/paper/2312.08052/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 14 references that are in the map.
- First posted on arXiv 13 Dec 2023.

## Builds on (most cited first, 2 of 2)

- [NetTraj: A Network-based Vehicle Trajectory Prediction Model with Directional Representation and Spatiotemporal Attention Mechanisms](https://mlsanity.com/paper/2106.11175/) (2021)
- [(Blue) Taxi Destination and Trip Time Prediction from Partial Trajectories](https://mlsanity.com/paper/1509.05257/) (2015)

## Built on by (most cited first, 6 of 6)

- [A Unified Probabilistic Framework for Dictionary Learning with Parsimonious Activation](https://mlsanity.com/paper/2509.25690/) (2025)
- [Dy-mer: An Explainable DNA Sequence Representation Scheme using Dictionary Learning](https://mlsanity.com/paper/2407.12051/) (2024)
- [Modeling Musical Genre Trajectories through Pathlet Learning](https://mlsanity.com/paper/2505.03480/) (2025)
- [A Pretrained Probabilistic Transformer for City-Scale Traffic Volume Prediction](https://mlsanity.com/paper/2506.02654/) (2025)
- [Data-Efficient and Robust Trajectory Generation through Pathlet Dictionary Learning](https://mlsanity.com/paper/2511.16105/) (2025)
- [Sparse Compositional Flow Matching by geometric assembly from motion primitives](https://mlsanity.com/paper/2605.23341/) (2026)

## Abstract (arXiv)

Trajectory representation learning on a network enhances our understanding of vehicular traffic patterns and benefits numerous downstream applications. Existing approaches using classic machine learning or deep learning embed trajectories as dense vectors, which lack interpretability and are inefficient to store and analyze in downstream tasks. In this paper, an explainable trajectory representation learning framework through dictionary learning is proposed. Given a collection of trajectories on a network, it extracts a compact dictionary of commonly used subpaths called "pathlets", which optimally reconstruct each trajectory by simple concatenations. The resulting representation is naturally sparse and encodes strong spatial semantics. Theoretical analysis of our proposed algorithm is conducted to provide a probabilistic bound on the estimation error of the optimal dictionary. A hierarchical dictionary learning scheme is also proposed to ensure the algorithm's scalability on large networks, leading to a multi-scale trajectory representation. Our framework is evaluated on two large-scale real-world taxi datasets. Compared to previous work, the dictionary learned by our method is more compact and has better reconstruction rate for new trajectories. We also demonstrate the promising performance of this method in downstream tasks including trip time prediction task and data compression.