Trajectory generation has recently drawn growing interest in privacy-preserving urban mobility studies and location-based service applications. Although many studies have used deep learning or generative AI methods to model trajectories and have achieved promising results, the robustness and interpretability of such models are largely unexplored. This limits the application of trajectory generation algorithms on noisy real-world data and their trustworthiness in downstream tasks. To address this issue, we exploit the regular structure in urban trajectories and propose a deep generative model based on the pathlet representation, which encode trajectories with binary vectors associated with a learned dictionary of trajectory segments. Specifically, we introduce a probabilistic graphical model to describe the trajectory generation process, which includes a Variational Autoencoder (VAE) component and a linear decoder component. During training, the model can simultaneously learn the latent embedding of pathlet representations and the pathlet dictionary that captures mobility patterns in the trajectory dataset. The conditional version of our model can also be used to generate customized trajectories based on temporal and spatial constraints. Our model can effectively learn data distribution even using noisy data, achieving relative improvements of $35.4\%$ and $26.3\%$ over strong baselines on two real-world trajectory datasets. Moreover, the generated trajectories can be conveniently utilized for multiple downstream tasks, including trajectory prediction and data denoising. Lastly, the framework design offers a significant efficiency advantage, saving $64.8\%$ of the time and $56.5\%$ of GPU memory compared to previous approaches.

Advances in tracking technologies have spurred the rapid growth of large-scale trajectory data. Building a compact collection of pathlets, referred to as a trajectory pathlet dictionary, is essential for supporting mobility-related applications. Existing methods typically adopt a top-down approach, generating numerous candidate pathlets and selecting a subset, leading to high memory usage and redundant storage from overlapping pathlets. To overcome these limitations, we propose a bottom-up strategy that incrementally merges basic pathlets to build the dictionary, reducing memory requirements by up to 24,000 times compared to baseline methods. The approach begins with unit-length pathlets and iteratively merges them while optimizing utility, which is defined using newly introduced metrics of trajectory loss and representability. We develop a deep reinforcement learning framework, PathletRL, which utilizes Deep Q-Networks (DQN) to approximate the utility function, resulting in a compact and efficient pathlet dictionary. Experiments on both synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art techniques, reducing the size of the constructed dictionary by up to 65.8%. Additionally, our results show that only half of the dictionary pathlets are needed to reconstruct 85% of the original trajectory data. Building on PathletRL, we introduce PathletRL++, which extends the original model by incorporating a richer state representation and an improved reward function to optimize decision-making during pathlet merging. These enhancements enable the agent to gain a more nuanced understanding of the environment, leading to higher-quality pathlet dictionaries. PathletRL++ achieves even greater dictionary size reduction, surpassing the performance of PathletRL, while maintaining high trajectory representability.

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.