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TraveL: Transformer-based Multi-view Path Distributional Representation Learning
Fang He, Tao-yang Fu, Wang-chien Lee
TL;DR
PRL methods often omit varied traveler behaviors and regional correlations, limiting the information captured by path representations. TraveL learns a departure-time-conditioned distributional representation with multi-view regional attention and sampling-based decoding, and outperforms state-of-the-art methods across three downstream tasks.
Problem
Existing PRL methods typically learn vector representations from road-segment and path co-occurrences without modeling varied traveler behaviors or regional correlations.
Method
TraveL encodes a path and departure time into a distribution, uses multi-view regional attention, samples possible on-path sequences, and applies K-S-based evaluation.
Results
TraveL outperforms state-of-the-art methods across travel time distribution estimation, path similarity prediction, and destination prediction; travel time estimation improves by 14.7% in mean K-S distance.
Takeaways & Limitations
Distributional path representations capture varied traveler behaviors while multi-view regional attention captures complementary regional correlations for downstream PRL tasks.
Takeaways & Limitations
Real-world path-level OP-Seq sparsity can bias the observed travel-time distribution and make the direct K-S distance unreliable; the method regularizes using segment-level distributions.
Abstract
from arXiv · showhide
Path representation learning (PRL) for road networks has received increasing research attention, due to various path-related applications. Existing works on PRL typically exploit the co-occurrence relationship among road segments and paths to learn a vector as the path representation, without exploring the varied traveler behaviors and the regional correlation on the path. In this work, we propose to learn distributional representations, which provide valuable information for use in path-related applications, by capturing the varied traveler behaviors as well as the various dependencies within regions of road segments. We propose a novel Transformer-based Multi-view Distributional Representation Learning (TraveL) framework to encode a path along with a travel starting time to a distributional representation, which can be used to decode possible samples of on-path traveler behavior. Moreover, by analyzing the regional correlation which reveals various road segment relationships, we propose a regional attention to encode these correlations in a path. Also, we explore the idea of Kolmogorov-Smirnov (K-S) test to compare the sampled traveler behavior against the collected ground truth to facilitate training. Experimental results show that the proposed TraveL model outperforms the state-of-the-art methods on both synthetic and real-world datasets, by 14.7% in Mean K-S distance for travel time distribution estimation, 16.7% in Mean Absolute Error (MAE) for path similarity prediction, and 3.97% in MAE for destination prediction.
1 INTRODUCTION
Path representation learning supports path-related transportation applications, but existing methods do not capture varied traveler behaviors and regional correlations. TraveL addresses both gaps with distributional representations, regional attention, sampling-based decoding, and K-S-based evaluation.
- PRL encodes road-network paths for applications including travel-time estimation, path recommendation, and destination prediction.
- Varied traveler behaviors and regional correlations are identified as essential information beyond static path features.Traveler behavior is especially relevant to travel-time distribution and behavior-related path similarity estimation.
- Regional attention captures correlations among road segments within regions formed by road type or hop distance.These structures are treated as different views of the path.
- TraveL encodes a path and departure time into a distributional representation and decodes possible on-path traveler behaviors.Its framework combines a Path Encoder with an On-path Sequence Generator.
- 14.7% lower mean K-S distance was achieved for travel time distribution estimation against state-of-the-art PRL models.The experiments covered synthetic and real-world datasets and three downstream applications.
2 RELATED WORK
Prior work includes task-specific and general-purpose path representation methods, while distributional representation learning has mainly addressed other objects or goals. TraveL targets path distributional representations in road networks.
- Representation learning broadly converts raw data into general-purpose low-dimensional latent vectors for downstream methods.
- Existing path representation methods aggregate road-segment embeddings, with some designed for specific tasks and others for general-purpose path embeddings.
- VAE learns a generator matching the input distribution, rather than a distributional representation for each input.
- TraveL is presented as the first attempt to learn path distributional representations in road networks.
3 RESEARCH PROBLEM AND CHALLENGES
The paper defines road-network paths, on-path sequences, trajectories, and Gaussian path representations, then frames challenges in generating varied traveler behaviors from those representations. Departure time is part of the path definition because behavior may depend on it.
- A road network is a directed graph whose nodes represent intersections and edges represent feature-bearing road segments.
- A path is a connected sequence of road segments paired with a departure time classified as rush hour or normal hour.
- An on-path sequence augments each path road segment with its travel time, whereas a trajectory contains spatio-temporal sample points.
- PRL maps a path to a d-dimensional Gaussian distribution N_p(μ_p, Σ_p) for path-mining tasks.
- Traveler travel times may not follow known distributions, creating the challenge of generating and evaluating varied behaviors from the learned representation.
4 DESIGN OF TRAVEL
TraveL uses an encoder-decoder design to represent a path and departure time as a Gaussian distribution, sample possible traveler behaviors, and train generation and path recovery jointly. Its encoder combines multi-view regional attention, Transformer self-attention, and gated aggregation, while K-S-based losses address distribution matching and data sparsity.
- Framework Overview: TraveL encodes a road-segment path and departure time into a Gaussian distribution, then samples representations for generating possible on-path sequences.The framework includes a Path Encoder, an OP-Seq Generator, and an OP-Seq Evaluator.
- Framework Overview: The OP-Seq Generator uses sampled distribution points with an LSTM to jointly generate segment travel times and predict the next road segment.The generator also supports path recovery through sequential next-segment predictions.
- Path Encoder: Path Encoder combines road-segment, departure-time, and positional embeddings before applying a multi-view Path Transformer and aggregation to produce the path distributional representation.Road2Vec initializes segment embeddings, while departure time is represented with a two-dimensional one-hot embedding.
- Multi-view Path Transformer: Multi-view regional attention captures correlations within road-type or hop-based regions, while shifted hop views ensure correlated segment pairs can share a region in at least one view.Regional outputs are averaged before multi-head path self-attention captures longer-term dependencies.
- Multi-view Path Transformer: Stacked multi-view regional attention layers enhance segment representations, which self-gating aggregation weights to predict the Gaussian mean and variance parameters.The aggregation transforms segment embeddings into separate latent spaces for the distribution parameters before producing the final representation.
- Loss Design: K-S distance evaluates generated versus historical travel-time samples, while segment-level regularization addresses sparse historical OP-Seqs on individual paths.The regularizer compares generated segment travel-time distributions with historical distributions for the corresponding road segments.
5 PERFORMANCE EVALUATION
The evaluation compares TraveL with state-of-the-art path representation learning models on synthetic and real-world trajectory datasets across three downstream tasks.
- The evaluation covers travel time distribution estimation, path similarity prediction, and destination prediction for all datasets.
- The real-world datasets are Porto, containing 1.7 million taxi trajectories, and Tokyo, containing 78 million GPS sample points from 617K users.
- Porto and Tokyo trajectories are map-matched into on-path sequences after removing short trajectories and outlier road-segment travel times.
- Compared models include Node2Vec, RoadSegment, InfoGraph, BERT, and Path InfoMax, representing graph, recurrent, graph-level, language-model, and path-specific approaches.
5.3 Representation Learning Process
TraveL representations are trained and evaluated through sampling-based travel-time distribution prediction, with results reported across synthetic and real-world settings and varying path lengths.
- Representation Learning Process: Training uses a 90%/10% path split, Adam optimization, an initial learning rate of 0.0001, and validation loss for model selection.
- Travel Time Distribution Estimation: For TTDE, models generate travel-time samples from learned representations and train feed-forward networks by minimizing K-S distance to ground truth.
- Travel Time Distribution Estimation: Baseline vectors are mapped to 128-dimensional mean and standard-deviation vectors so they can participate in the same sampling-based K-S-loss procedure.
- Travel Time Distribution Estimation: On synthetic datasets, TraveL consistently outperforms baselines, reducing Mean K-S distance by 3.57% to 36.1% across reported path categories.
- Travel Time Distribution Estimation: All models perform worse on longer paths, while TraveL shows smaller or comparable deterioration and is attributed to capturing long-term dependencies and varied traveler behaviors.
- Travel Time Distribution Estimation: On Porto and Tokyo sub-paths of all evaluated lengths, TraveL outperforms the baselines; BERT performs worse despite also using Transformer structure.
5.5 Path Similarity Prediction (PSP)
The path similarity prediction experiment evaluates both length-based and speed-relevant similarity, with the latter requiring traveler-speed information. Results show that speed-relevant similarity is harder to predict and that models capturing same-type road relationships can perform better on it.
- Similarity Measures: Weighted Jaccard similarity (WJ) measures shared road-segment length relative to the total length of two paths.
- Evaluation: SWJ prediction is more challenging than WJ prediction because it requires speed-relevant information in addition to segment lengths.
- Dataset and Metrics: The experiment constructs path-pair datasets using same-origin, same-destination candidates for Syn-Porto and thresholded random pairs for Porto and Tokyo.For Porto and Tokyo, the final collection contains 1 million path pairs with WJ or SWJ above 0.5.
- Dataset and Metrics: Evaluation uses MAE and MAPE for similarity prediction, with Kendall and Spearman rank correlations additionally used on Syn-Porto.Higher Kendall τ and Spearman ρ indicate more accurate ranking consistency.
- Results: Trembr performs worse than PIM for WJ prediction but better for SWJ prediction, possibly because it captures same-type road relationships associated with speeds.
5.6 Destination Prediction (DP)
Destination prediction uses partial-path representations to estimate the path endpoint, with performance evaluated across varying observed path lengths. TraveL consistently outperforms the baselines on all three datasets, with larger partial paths making the task easier.
- Task Setup: Destination prediction estimates the endpoint coordinate from a partial path representation.The target is the final road-segment coordinate in the synthetic dataset or the final map-matched coordinate in real-world datasets.
- Task Setup: The partial path length is controlled by δ, tested at 0.5, 0.625, 0.75, and 0.875.
- Evaluation: Performance is measured by MAE of the geographic distance between the predicted and true destination coordinates in kilometers.
- Results: As δ increases, all models achieve lower MAE, indicating that destination prediction becomes less difficult with longer partial paths.
- Results: At δ = 0.75, TraveL reduces MAE relative to Trembr by 3.97% on Tokyo and 10.6% on Porto.The reported comparisons are 1.69 versus 1.76 on Tokyo and 0.67 versus 0.75 on Porto.
5.7 Ablation Study
The ablation study tests the contributions of multi-view attention, individual regional views, distributional representations, and on-path behavior generation. Complete TraveL performs best overall, while different components benefit different tasks.
- Variants: The ablations remove multi-view attention, individual highway, lane, or hop views, distributional representations, or travel-time generation.
- Results: Complete TraveL outperforms all variants on the path similarity prediction task.
- Results: Removing all views performs worst among the view ablations, indicating that highway, lane, and hop views provide complementary benefits.
- Task-Specific Effects: Traveler-behavior modeling contributes more than regional-correlation modeling to path similarity prediction in the comparison between OnlyPath and NoViews.
- Task-Specific Effects: Different regional views benefit different tasks: hop views help destination prediction, whereas highway and lane views help path similarity prediction.
- Results: The NoDistr variant performs worst for travel-time distribution estimation and destination prediction, and second worst for path similarity prediction.This supports the paper’s claim that distributional representations have greater capacity for capturing varied traveler behaviors than vector representations.
5.8 Details of Kolmogorov–Smirnov Test
The K-S test compares generated and ground-truth travel-time samples through their empirical distributions. Its K-S distance is the maximum absolute difference between the two empirical cumulative distribution functions.
- Test Definition: The Kolmogorov–Smirnov test assesses whether two continuous one-dimensional sample sets come from the same distribution.
- Empirical Distributions: The test transforms each sample set into an empirical distribution function.
- Distance Measure: The K-S distance is the supremum over x of the absolute difference between the two empirical distribution functions.The paper uses this distance to compare generated travel-time samples with ground-truth samples.
5.9 Hyper-parameter Settings
TraveL’s selected hyperparameters specify the architecture, representation dimensions, sampling budget, and dataset-specific loss weights.
- The Multi-view Path Transformer uses 6 multi-view regional attention layers.
- Hop-view uses 3 hops to model regional correlations.
- The distributional representation dimensions for μ_p and σ_p are both 128.
- TraveL samples 100 points from each distributional representation.
- For Syn-porto, λ_1, λ_2, λ_3, λ_4, and λ_5 are set to 0.3, 0.0, 0.7, 0.1, and 0.05, respectively.λ_2 is set to 0.0 because synthetic data does not face the data sparsity issue.
6 CONCLUSION
The conclusion presents TraveL as a distributional path-representation framework combining sampling-based behavior modeling with multi-view regional attention. It also identifies broader distributional representations as future work.
- TraveL uses distributional representations and an On-path Sequence Generator to capture varied traveler behaviors.
- Multi-view regional attention captures correlations within regions of road segments.
- K-S testing is explored to facilitate model training and evaluation.
- Experiments demonstrate TraveL’s superiority over state-of-the-art methods.
- Future work will explore other distributional-representation forms to capture additional traveler behaviors for PRL.