Imputing missing values in spatial-temporal traffic data is essential for intelligent transportation systems. Among advanced imputation methods, score-based diffusion models have demonstrated competitive performance. These models generate data by reversing a noising process, using observed values as conditional guidance. However, existing diffusion models typically apply a uniform guidance scale across both spatial and temporal dimensions, which is inadequate for nodes with high missing data rates. Sparse observations provide insufficient conditional guidance, causing the generative process to drift toward the learned prior distribution rather than closely following the conditional observations, resulting in suboptimal imputation performance. To address this, we propose FENCE, a spatial-temporal feedback diffusion guidance method designed to adaptively control guidance scales during imputation. First, FENCE introduces a dynamic feedback mechanism that adjusts the guidance scale based on the posterior likelihood approximations. The guidance scale is increased when generated values diverge from observations and reduced when alignment improves, preventing overcorrection. Second, because alignment to observations varies across nodes and denoising steps, a global guidance scale for all nodes is suboptimal. FENCE computes guidance scales at the cluster level by grouping nodes based on their attention scores, leveraging spatial-temporal correlations to provide more accurate guidance. Experimental results on real-world traffic datasets show that FENCE significantly enhances imputation accuracy.

Structure-Based Drug Design (SBDD) has emerged as a popular approach in drug discovery, leveraging three-dimensional protein structures to generate drug ligands. However, existing generative models encounter several key challenges: (1) Incorporating boundary condition constraints, (2) Integrating hierarchical structural conditions and (3) Ensuring spatial modeling fidelity. To overcome these limitations, we propose SculptDrug, a spatial condition-aware generative model based on Bayesian Flow Networks (BFNs). First, SculptDrug follows a BFNs-based framework and employs a progressive denoising strategy to ensure spatial modeling fidelity, iteratively refining atom positions while enhancing local interactions for precise spatial alignment. Second, we introduce the Boundary Awareness Block, which incorporates protein surface constraints into the generative process to ensure that the generated ligands are geometrically compatible with the target protein. Finally, we design a Hierarchical Encoder that captures global structural context while preserving fine-grained molecular interactions, ensuring overall consistency and accurate ligand-protein conformations. We evaluate SculptDrug on the CrossDocked dataset, and experimental results demonstrate that SculptDrug outperforms state-of-the-art baselines, proving the efficacy of spatial condition-aware modeling.

Building a general model capable of analyzing human trajectories across different geographic regions and different tasks becomes an emergent yet important problem for various applications. However, existing works suffer from the generalization problem, i.e., they are either restricted to train for specific regions or only suitable for a few tasks. Given the recent advances of multimodal large language models (MLLMs), we raise the question: can MLLMs reform current trajectory data mining and solve the problem? Nevertheless, due to the modality gap of trajectory, how to generate task-independent multimodal trajectory representations and how to adapt flexibly to different tasks remain the foundational challenges. In this paper, we propose Traj-MLLM, which is the first general framework using MLLMs for trajectory data mining. By integrating multiview contexts, Traj-MLLM transforms raw trajectories into interleaved image-text sequences while preserving key spatial-temporal characteristics, and directly utilizes the reasoning ability of MLLMs for trajectory analysis. Additionally, a prompt optimization method is proposed to finalize data-invariant prompts for task adaptation. Extensive experiments on four publicly available datasets show that Traj-MLLM outperforms state-of-the-art baselines by 48.05%, 15.52%, 51.52%, 1.83% on travel time estimation, mobility prediction, anomaly detection and transportation mode identification, respectively. Traj-MLLM achieves these superior performances without requiring any training data or fine-tuning the MLLM backbones.

Uncertainty quantification in travel time estimation (TTE) aims to estimate the confidence interval for travel time, given the origin (O), destination (D), and departure time (T). Accurately quantifying this uncertainty requires generating the most likely path and assessing travel time uncertainty along the path. This involves two main challenges: 1) Predicting a path that aligns with the ground truth, and 2) modeling the impact of travel time in each segment on overall uncertainty under varying conditions. We propose DutyTTE to address these challenges. For the first challenge, we introduce a deep reinforcement learning method to improve alignment between the predicted path and the ground truth, providing more accurate travel time information from road segments to improve TTE. For the second challenge, we propose a mixture of experts guided uncertainty quantification mechanism to better capture travel time uncertainty for each segment under varying contexts. Extensive experiments on two real-world datasets demonstrate the superiority of our proposed method.

Spatio-temporal trajectories are crucial for data mining tasks, requiring versatile learning methods that can accurately extract movement patterns and travel purposes. While large language models (LLMs) have shown remarkable versatility through training on extensive datasets, and trajectories share similarities with natural language, standard LLMs cannot directly handle spatio-temporal features or extract trajectory-specific information. We propose TrajCogn, a model that effectively adapts LLMs for trajectory learning. TrajCogn incorporates a novel trajectory semantic embedder to process spatio-temporal features and extract movement patterns and travel purposes, along with a trajectory prompt that integrates this information into LLMs for various downstream tasks. Experiments on three real-world datasets and four representative tasks demonstrate TrajCogn's effectiveness.

Multivariate time series forecasting is crucial for various applications, such as financial investment, energy management, weather forecasting, and traffic optimization. However, accurate forecasting is challenging due to two main factors. First, real-world time series often show heterogeneous temporal patterns caused by distribution shifts over time. Second, correlations among channels are complex and intertwined, making it hard to model the interactions among channels precisely and flexibly.

Vehicle GPS trajectories record how vehicles move over time, storing valuable travel semantics, including movement patterns and travel purposes. Learning travel semantics effectively and efficiently is crucial for real-world applications of trajectory data, which is hindered by two major challenges. First, travel purposes are tied to the functions of the roads and points-of-interest (POIs) involved in a trip. Such information is encoded in textual addresses and descriptions and introduces heavy computational burden to modeling. Second, real-world trajectories often contain redundant points, which harm both computational efficiency and trajectory embedding quality. To address these challenges, we propose TrajMamba, a novel approach for efficient and semantically rich vehicle trajectory learning. TrajMamba introduces a Traj-Mamba Encoder that captures movement patterns by jointly modeling both GPS and road perspectives of trajectories, enabling robust representations of continuous travel behaviors. It also incorporates a Travel Purpose-aware Pre-training procedure to integrate travel purposes into the learned embeddings without introducing extra overhead to embedding calculation. To reduce redundancy in trajectories, TrajMamba features a Knowledge Distillation Pre-training scheme to identify key trajectory points through a learnable mask generator and obtain effective compressed trajectory embeddings. Extensive experiments on two real-world datasets and three downstream tasks show that TrajMamba outperforms state-of-the-art baselines in both efficiency and accuracy.

Spatiotemporal trajectory data is crucial for various traffic-related applications. However, issues such as device malfunctions and network instability often result in sparse trajectories that lose detailed movement information compared to their dense counterparts. Recovering missing points in sparse trajectories is thus essential. Despite recent progress, three challenges remain. First, the lack of large-scale dense trajectory datasets hinders the training of a trajectory recovery model. Second, the varying spatiotemporal correlations in sparse trajectories make it hard to generalize across different sampling intervals. Third, extracting road conditions for missing points is non-trivial. To address these challenges, we propose $\textit{PLMTrajRec}$, a novel trajectory recovery model. It leverages the scalability of a pre-trained language model (PLM) and can effectively recover trajectories by fine-tuning with small-scale dense trajectory datasets. To handle different sampling intervals in sparse trajectories, we first convert sampling intervals and movement features into prompts for the PLM to understand. We then introduce a trajectory encoder to unify trajectories of varying intervals into a single interval. To extract road conditions for missing points, we propose an area flow-guided implicit trajectory prompt that represents traffic conditions in each region, and a road condition passing mechanism that infers the road conditions of missing points using the observed ones. Experiments on four public trajectory datasets with three sampling intervals demonstrate the effectiveness, scalability, and generalization ability of PLMTrajRec. Code is available at https://github.com/wtl52656/PLMTrajRec.

Vehicle GPS trajectories provide valuable movement information that supports various downstream tasks and applications. A desirable trajectory learning model should be able to transfer across regions and tasks without retraining, avoiding the need to maintain multiple specialized models and subpar performance with limited training data. However, each region has its unique spatial features and contexts, which are reflected in vehicle movement patterns and are difficult to generalize. Additionally, transferring across different tasks faces technical challenges due to the varying input-output structures required for each task. Existing efforts towards transferability primarily involve learning embedding vectors for trajectories, which perform poorly in region transfer and require retraining of prediction modules for task transfer. To address these challenges, we propose $\textit{TransferTraj}$, a vehicle GPS trajectory learning model that excels in both region and task transferability. For region transferability, we introduce RTTE as the main learnable module within TransferTraj. It integrates spatial, temporal, POI, and road network modalities of trajectories to effectively manage variations in spatial context distribution across regions. It also introduces a TRIE module for incorporating relative information of spatial features and a spatial context MoE module for handling movement patterns in diverse contexts. For task transferability, we propose a task-transferable input-output scheme that unifies the input-output structure of different tasks into the masking and recovery of modalities and trajectory points. This approach allows TransferTraj to be pre-trained once and transferred to different tasks without retraining. We conduct extensive experiments on three real-world vehicle trajectory datasets under various transfer settings, including task transfer, zero-shot region transfer, and few-shot region transfer. Experimental results demonstrate that TransferTraj significantly outperforms state-of-the-art baselines in different scenarios, validating its effectiveness in region and task transfer. Code is available at https://github.com/wtl52656/TransferTraj.

The advancement of intelligent transportation systems has led to a growing demand for accurate path representations, which are essential for tasks such as travel time estimation, path ranking, and trajectory analysis. However, traditional path representation learning (PRL) methods often focus solely on single-modal road network data, overlooking important physical and regional factors that influence real-world traffic dynamics. To overcome this limitation, we introduce Path-LLM, a multi-modal path representation learning model that integrates large language models (LLMs) into PRL. Our approach leverages LLMs to interpret both topological and textual data, enabling robust multi-modal path representations. To effectively align and merge these modalities, we propose TPalign, a contrastive learning-based pretraining strategy that ensures alignment within the embedding space. We then present TPfusion, a multimodal fusion module that dynamically adjusts the weight of each modality before integration. To further optimize LLM training, we introduce a Two-stage Overlapping Curriculum Learning (TOCL) approach, which progressively increases the complexity of the training data. Finally, we evaluate Path-LLM on three real-world datasets across traditional PRL downstream tasks, achieving up to a 61.84% improvement in path ranking performance on the Xi'an dataset. Additionally, Path-LLM demonstrates superior performance in both few-shot and zero-shot learning scenarios. Our code is available at: https://github.com/decisionintelligence/Path-LLM.

Analyzing and comprehending check-in sequences is crucial for various applications in smart cities. However, publicly available check-in datasets are often limited in scale due to privacy concerns. This poses a significant obstacle to academic research and downstream applications. Thus, it is urgent to generate realistic check-in datasets. The denoising diffusion probabilistic model (DDPM) as one of the most capable generation methods is a good choice to achieve this goal. However, generating check-in sequences using DDPM is not an easy feat. The difficulties lie in handling check-in sequences of variable lengths and capturing the correlation from check-in sequences' distinct characteristics. This paper addresses the challenges by proposing a Spatio-Temporal Contrastive Diffusion Model (STCDM). This model introduces a novel spatio-temporal lossless encoding method that effectively encodes check-in sequences into a suitable format with equal length. Furthermore, we capture the spatio-temporal correlations with two disentangled diffusion modules to reduce the impact of the difference between spatial and temporal characteristics. Finally, we incorporate contrastive learning to enhance the relationship between diffusion modules. We generate four realistic datasets in different scenarios using STCDM and design four metrics for comparison. Experiments demonstrate that our generated datasets are more realistic and free of privacy leakage.

Vehicle movement is frequently captured in the form of GPS trajectories, i.e., sequences of timestamped GPS locations. Such data is widely used for various tasks such as travel-time estimation, trajectory recovery, and trajectory prediction. A universal vehicle trajectory model could be applied to different tasks, removing the need to maintain multiple specialized models, thereby reducing computational and storage costs. However, creating such a model is challenging when the integrity of trajectory features is compromised, i.e., in scenarios where only partial features are available or the trajectories are sparse. To address these challenges, we propose the Universal Vehicle Trajectory Model (UVTM), which can effectively adapt to different tasks without excessive retraining. UVTM incorporates two specialized designs. First, it divides trajectory features into three distinct domains. Each domain can be masked and generated independently to accommodate tasks with only partially available features. Second, UVTM is pre-trained by reconstructing dense, feature-complete trajectories from sparse, feature-incomplete counterparts, enabling strong performance even when the integrity of trajectory features is compromised. Experiments involving four representative trajectory-related tasks on three real-world vehicle trajectory datasets provide insight into the performance of UVTM and offer evidence that it is capable of meeting its objectives.

Spatiotemporal trajectories are sequences of timestamped locations, which enable a variety of analyses that in turn enable important real-world applications. It is common to map trajectories to vectors, called embeddings, before subsequent analyses. Thus, the qualities of embeddings are very important. Methods for pre-training embeddings, which leverage unlabeled trajectories for training universal embeddings, have shown promising applicability across different tasks, thus attracting considerable interest. However, research progress on this topic faces two key challenges: a lack of a comprehensive overview of existing methods, resulting in several related methods not being well-recognized, and the absence of a unified pipeline, complicating the development of new methods and the analysis of methods. We present UniTE, a survey and a unified pipeline for this domain. In doing so, we present a comprehensive list of existing methods for pre-training trajectory embeddings, which includes methods that either explicitly or implicitly employ pre-training techniques. Further, we present a unified and modular pipeline with publicly available underlying code, simplifying the process of constructing and evaluating methods for pre-training trajectory embeddings. Additionally, we contribute a selection of experimental results using the proposed pipeline on real-world datasets.

Location-based services (LBS) have accumulated extensive human mobility data on diverse behaviors through check-in sequences. These sequences offer valuable insights into users’ intentions and preferences. Yet, existing models analyzing check-in sequences fail to consider the semantics contained in these sequences, which closely reflect human visiting intentions and travel preferences, leading to an incomplete comprehension. Drawing inspiration from the exceptional semantic understanding and contextual information processing capabilities of large language models (LLMs) across various domains, we present Mobility-LLM, a novel framework that leverages LLMs to analyze check-in sequences for multiple tasks. Since LLMs cannot directly interpret check-ins, we reprogram these sequences to help LLMs comprehensively understand the semantics of human visiting intentions and travel preferences. Specifically, we introduce a visiting intention memory network (VIMN) to capture the visiting intentions at each record, along with a shared pool of human travel preference prompts (HTPP) to guide the LLM in understanding users’ travel preferences. These components enhance the model’s ability to extract and leverage semantic information from human mobility data effectively. Extensive experiments on four benchmark datasets and three downstream tasks demonstrate that our approach significantly outperforms existing models, underscoring the effectiveness of Mobility-LLM in advancing our understanding of human mobility data within LBS contexts.

The rapid growth of location-based services (LBS) has yielded massive amounts of data on human mobility. Effectively extracting meaningful representations for user-generated check-in sequences is pivotal for facilitating various downstream services. However, the user-generated check-in data are simultaneously influenced by the surrounding objective circumstances and the user's subjective intention. Specifically, the temporal uncertainty and spatial diversity exhibited in check-in data make it difficult to capture the macroscopic spatial-temporal patterns of users and to understand the semantics of user mobility activities. Furthermore, the distinct characteristics of the temporal and spatial information in check-in sequences call for an effective fusion method to incorporate these two types of information. In this paper, we propose a novel Spatial-Temporal Cross-view Contrastive Representation (STCCR) framework for check-in sequence representation learning. Specifically, STCCR addresses the above challenges by employing self-supervision from “spatial topic” and “temporal intention” views, facilitating effective fusion of spatial and temporal information at the semantic level. Besides, STCCR leverages contrastive clustering to uncover users’ shared spatial topics from diverse mobility activities, while employing angular momentum contrast to mitigate the impact of temporal uncertainty and noise. We extensively evaluate STCCR on three real-world datasets and demonstrate its superior performance across three downstream tasks.

Spatio-temporal trajectories provide valuable information about movement and travel behavior, enabling various downstream tasks that in turn power real-world applications. Learning trajectory embeddings can improve task performance but may incur high computational costs and face limited training data availability. Pre-training learns generic embeddings by means of specially constructed pretext tasks that enable learning from unlabeled data. Existing pre-training methods face (i) difficulties in learning general embeddings due to biases towards certain downstream tasks incurred by the pretext tasks, (ii) limitations in capturing both travel semantics and spatio-temporal correlations, and (iii) the complexity of long, irregularly sampled trajectories. To tackle these challenges, we propose Maximum Multi-view Trajectory Entropy Coding (MMTEC) for learning general and comprehensive trajectory embeddings. We introduce a pretext task that reduces biases in pre-trained trajectory embeddings, yielding embeddings that are useful for a wide variety of downstream tasks. We also propose an attention-based discrete encoder and a NeuralCDE-based continuous encoder that extract and represent travel behavior and continuous spatio-temporal correlations from trajectories in embeddings, respectively. Extensive experiments on two real-world datasets and three downstream tasks offer insight into the design properties of our proposal and indicate that it is capable of outperforming existing trajectory embedding methods.

Trajectory data is essential for various applications. However, publicly available trajectory datasets remain limited in scale due to privacy concerns, which hinders the development of trajectory mining and applications. Although some trajectory generation methods have been proposed to expand dataset scale, they generate trajectories in the geographical coordinate system, posing two limitations for practical applications: 1) failing to ensure that the generated trajectories are road-constrained. 2) lacking road-related information. In this paper, we propose a new problem, road network-constrained trajectory (RNTraj) generation, which can directly generate trajectories on the road network with road-related information. Specifically, RNTraj is a hybrid type of data, in which each point is represented by a discrete road segment and a continuous moving rate. To generate RNTraj, we design a diffusion model called Diff-RNTraj, which can effectively handle the hybrid RNTraj using a continuous diffusion framework by incorporating a pre-training strategy to embed hybrid RNTraj into continuous representations. During the sampling stage, a RNTraj decoder is designed to map the continuous representation generated by the diffusion model back to the hybrid RNTraj format. Furthermore, Diff-RNTraj introduces a novel loss function to enhance trajectory’s spatial validity. Extensive experiments conducted on two datasets demonstrate the effectiveness of Diff-RNTraj.

Recovering intermediate missing GPS points in a sparse trajectory, while adhering to the constraints of the road network, could offer deep insights into users' moving behaviors in intelligent transportation systems. Although recent studies have demonstrated the advantages of achieving map-constrained trajectory recovery via an end-to-end manner, they still face two significant challenges. Firstly, existing methods are mostly sequence-based models. It is extremely hard for them to comprehensively capture the micro-semantics of individual trajectory, including the information of each GPS point and the movement between two GPS points. Secondly, existing approaches ignore the impact of the macro-semantics,i.e., the road conditions and the people's shared travel preferences reflected by a group of trajectories. To address the above challenges, we propose a Micro-Macro Spatial-Temporal Graph-based Encoder-Decoder (MM-STGED). Specifically, we model each trajectory as a graph to efficiently describe the micro-semantics of trajectory and design a novel message-passing mechanism to learn trajectory representations. Additionally, we extract the macro-semantics of trajectories and further incorporate them into a well-designed graph-based decoder to guide trajectory recovery. Extensive experiments conducted on sparse trajectories with three different sampling intervals that are respectively constructed from two real-world trajectory datasets demonstrate the superiority of our proposed model.

A core step of mining human mobility data is to learn accurate representations for user-generated check-in sequences. The learned representations should be able to fully describe the spatial-temporal mobility patterns of users and the high-level semantics of traveling. However, existing check-in sequence representation learning is usually implicitly achieved by end-to-end models designed for specific downstream tasks, resulting in unsatisfactory generalizable abilities and poor performance. Besides, although the sequence representation learning models that follow the contrastive learning pre-training paradigm have achieved breakthroughs in many fields like NLP, they fail to simultaneously consider the unique spatial-temporal characteristics of check-in sequences and need manual adjustments on the data augmentation strategies. So, directly applying them to check-in sequences cannot yield a meaningful pretext task. To this end, in this paper we propose a contrastive pre-training model with adversarial perturbations for check-in sequence representation learning (CACSR). Firstly, we design a novel spatial-temporal augmentation block for disturbing the spatial-temporal features of check-in sequences in the latent space to relieve the stress of designing manual data augmentation strategies. Secondly, to construct an effective contrastive pretext task, we generate “hard” positive and negative pairs for the check-in sequence by adversarial training. These two designs encourage the model to capture the high-level spatial-temporal patterns and semantics of check-in sequences while ignoring the noisy and unimportant details. We demonstrate the effectiveness and versatility of CACSR on two kinds of downstream tasks using three real-world datasets. The results show that our model outperforms both the state-of-the-art pre-training methods and the end-to-end models.

Capturing semantic information is crucial for accurate long-range time series forecasting, which involves modeling global and local correlations, as well as discovering long- and short-term repetitive patterns. Previous works have partially addressed these issues separately, but have not been able to address all of them simultaneously. Meanwhile, their time and memory complexities are still not sufficiently low for long-range forecasting. To address the challenge of capturing different types of semantic information, we propose a novel Water-wave Information Transmission (WIT) framework. This framework captures both long- and short-term repetitive patterns through bi-granular information transmission. It also models global and local correlations by recursively fusing and selecting information using Horizontal Vertical Gated Selective Unit (HVGSU). In addition, to improve the computing efficiency, we propose a generic Recurrent Acceleration Network (RAN) which reduces the time complexity to $\mathcal{O}(\sqrt{L})$ while maintaining the memory complexity at $\mathcal{O}(L)$. Our proposed method, called Water-wave Information Transmission and Recurrent Acceleration Network (WITRAN), outperforms the state-of-the-art methods by 5.80% and 14.28% on long-range and ultra-long-range time series forecasting tasks respectively, as demonstrated by experiments on four benchmark datasets. The code is available at: https://github.com/Water2sea/WITRAN.

Accurate forecasting of time series mitigates the uncertainty of future outlooks and is a great help in reducing errors in decisions. Despite years of researches, there are still some challenges to accurate forecasting of time series, including the difficulty of dynamic modeling, the problem of capturing short-term correlations, and the conundrum of long-term forecasting. This paper offers an A dversarial Truncated Cauchy S elf- A ttentive T ime- V ariant Neural N etwork (ASATVN) for multi-step ahead time series forecasting. Specifically, the proposed model builds on Generative Adversarial Networks, in which the generator is composed of a novel time-variant model. The time-variant model contributes to learning dynamic time-series changes with its time-variant architecture and employs a newly proposed Truncated Cauchy Self-Attention block to capture the local sequential dependencies better. For the discriminator , two self-attentive discriminators are presented to regularize predictions with fidelity and continuity, which is beneficial to predicting sequence over longer time horizons. Our proposed ASATVN model outperforms the state-of-the-art predictive models on eleven real-world benchmark datasets, demonstrating its effectiveness.

Given an origin (O), a destination (D), and a departure time (T), an Origin-Destination (OD) travel time oracle~(ODT-Oracle) returns an estimate of the time it takes to travel from O to D when departing at T. ODT-Oracles serve important purposes in map-based services. To enable the construction of such oracles, we provide a travel-time estimation (TTE) solution that leverages historical trajectories to estimate time-varying travel times for OD pairs. The problem is complicated by the fact that multiple historical trajectories with different travel times may connect an OD pair, while trajectories may vary from one another. To solve the problem, it is crucial to remove outlier trajectories when doing travel time estimation for future queries. We propose a novel, two-stage framework called Diffusion-based Origin-destination Travel Time Estimation (DOT), that solves the problem. First, DOT employs a conditioned Pixelated Trajectories (PiT) denoiser that enables building a diffusion-based PiT inference process by learning correlations between OD pairs and historical trajectories. Specifically, given an OD pair and a departure time, we aim to infer a PiT. Next, DOT encompasses a Masked Vision Transformer~(MViT) that effectively and efficiently estimates a travel time based on the inferred PiT. We report on extensive experiments on two real-world datasets that offer evidence that DOT is capable of outperforming baseline methods in terms of accuracy, scalability, and explainability.

With the increasing accumulation of spatial-temporal trajectory data, location-based data mining has recently been extensively studied. A fundamental research topic in this field is learning the embedding vectors of locations through self-supervised pre-training. Pre-trained embedding vectors can utilize the highly available unlabeled trajectory data, and benefit downstream tasks in multiple aspects. However, most existing methods ignore the temporal information hidden in the visited time of locations in trajectories. Considering that human activities are highly regulated by specific periods of a day, temporal information can reflect some intrinsic characteristics of locations, so it is necessary to fuse them into location embedding vectors. In this paper, we propose a Time-Aware Location Embedding (TALE) pre-training method based on the CBOW framework, which is able to incorporate temporal information into the learned embedding vectors of locations. A novel temporal tree structure is designed to extract temporal information during the calculation of Hierarchical Softmax. In order to verify the effectiveness of TALE, we apply the learned embedding vectors into three downstream location-based prediction tasks, i.e., location classification, location visitor flow prediction and user next location prediction. Experiments are conducted on four real-world user trajectory datasets, and the experimental results demonstrate that our TALE model can obviously help downstream tasks gain better performance.

Pre-training location embeddings from spatial-temporal trajectories is a fundamental procedure and very beneficial for user next location prediction. In the real world, a location usually has variable functionalities under different contextual environments. If the exact functions of a location in the trajectory can be reflected in its embedding, the accuracy of user next location prediction should be improved. Yet, existing location embeddings pre-trained on trajectories are mostly based on distributed word representations, which mix a location's various functionalities into one latent representation vector. To address this problem, we propose a Context and Time aware Location Embedding (CTLE) model, which calculates a location's representation vector with consideration of its specific contextual neighbors in trajectories. In this way, the multi-functional properties of locations can be properly tackled. Furthermore, in order to incorporate temporal information in trajectories into location embeddings, we propose a subtle temporal encoding module and a novel pre-training objective, which further improve the quality of location embeddings. We evaluate our proposed model on two real-world mobile user trajectory datasets. The experimental results demonstrate that, compared with the existing embedding methods, our CTLE model can pre-train higher quality location embeddings and significantly improve the performance of downstream user location prediction models.