Pathlet Variational Auto-Encoder for Robust Trajectory Generation

TL;DR

This paper introduces Pathlet Variational Auto-Encoder (Pathlet-VAE), a robust trajectory generation framework that combines a learned pathlet dictionary with a Binary VAE and a linear decoder to produce realistic, noise-robust trajectories. By framing trajectory generation as x = D r + ε with r drawn from a Bernoulli distribution and jointly learning D and the VAE latent representation via an MDL-based objective, the approach achieves superior distributional fidelity under noise and enables efficient, interpretable downstream tasks like conditional generation and data denoising. Key contributions include the first integration of dictionary learning with trajectory generative modeling, a principled MDL regularization to control dictionary complexity and sparsity, and empirical evidence of improved JSD performance, along with substantial efficiency gains in training time and memory. The framework supports practical deployment in privacy-preserving urban mobility and location-based services, offering interpretable pathlets, conditional synthesis, and denoising capabilities with scalable computation.

Abstract

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.

Figures (6)

• Figure 1: Basic idea of trajectory generation using a pathlet dictionary learned from data. The framework supports both road network-based and grid-based trajectory representations, with inherent sparsity making the algorithm more robust and understandable.
• Figure 2: Illustration of the generative framework which describes the generative process of path.
• Figure 3: Illustration of the matrices $D,X,R$ (visualized in edge form): $X$ is the trajectory matrix generated from the dataset; $D$ refers to the pathlet dictionary matrix; $R$ is the representation matrix where each column corresponds to a representation vector.
• Figure 4: Architecture of Conditional Pathlet-VAE.
• Figure 5: (a) Visualization of conditionally generated trajectories. (b) Probability distribution of path selection over time.