Trajectory similarity is a cornerstone of trajectory data management and analysis. Traditional similarity functions often suffer from high computational complexity and a reliance on specific distance metrics, prompting a shift towards deep representation learning in Euclidean space. However, existing Euclidean-based trajectory embeddings often face challenges due to the triangle inequality constraints that do not universally hold for trajectory data. To address this issue, this paper introduces a novel approach by incorporating non-Euclidean geometry, specifically hyperbolic space, into trajectory representation learning. We present the first-ever integration of hyperbolic space to resolve the inherent limitations of the triangle inequality in Euclidean embeddings. In particular, we achieve it by designing a Lorentz distance measure, which is proven to overcome triangle inequality constraints. Additionally, we design a model-agnostic framework LH-plugin to seamlessly integrate hyperbolic embeddings into existing representation learning pipelines. This includes a novel projection method optimized with the Cosh function to prevent the diminishment of distances, supported by a theoretical foundation. Furthermore, we propose a dynamic fusion distance that intelligently adapts to variations in triangle inequality constraints across different trajectory pairs, blending Lorentzian and Euclidean distances for more robust similarity calculations. Comprehensive experimental evaluations demonstrate that our approach effectively enhances the accuracy of trajectory similarity measures in state-of-the-art models across multiple real-world datasets. The LH-plugin not only addresses the triangle inequality issues but also significantly refines the precision of trajectory similarity computations, marking a substantial advancement in the field of trajectory representation learning.

Trajectory similarity measure is a fundamental component in trajectory databases, supporting many down-stream trajectory tasks. Existing similarity functions often exhibit unacceptable time complexities, hampering their efficiency for real-world scenarios. To address this limitation, learning-based approximation techniques utilizing trajectory embeddings have been proposed. However, creating a robust embedding model presents challenges, including the lack of direct involvement in the computational similarity process, adherence to non-metric similarity spaces, and the integration of precise similarity computation alignments. To address these challenges, we introduce DTisT, a novel embedding framework that enhances trajectory embeddings by pairwise learning from dual-trajectory input models. DTisT not only captures the dynamics of trajectory similarity computation through a dual-trajectory learning model but also integrates a learnable virtual trajectory to align the embedding space with non-metric similarity spaces effectively. Additionally, we incorporate aligned information from actual similarity computations into our embedding process using an attention mask mechanism. To ensure effective learning, we adopt a pre-train and fine-tune strategy, utilizing contrastive learning during the pre-training stage. Extensive experiments conducted on two real datasets demonstrate that DTisT surpasses state-of-the-art methods, showcasing its effectiveness in trajectory similarity embedding.

Data imputation (DI) is a common means of enhancing data quality. To adapt to the flourishing field of machine learning (ML), an innovative class of imputation methods that consider downstream models in the imputation process has been proposed, denoted as DI for ML. A critical challenge within this context is establishing the optimal order for imputing a set of incomplete samples. To address this, we propose an iterative approach that strategically determines the imputation order based on the potential impact on model performance. At first, we design the impact score in a what-if manner to evaluate the significance of each incomplete data point for downstream ML models. In addition, to tackle the challenge of insufficient reliable complete data in real-world scenarios, we ingeniously leverage meta-learning mechanisms to enhance the robustness of the impact score computation. Finally, to avoid the risk of converging to local optima and non-diverse data selection during iterative imputation, we introduce a real-time feedback strategy using the Multi-Armed Bandit mechanism. By balancing immediate rewards with long-term strategic gains, our approach effectively navigates the complex optimization landscape, leading to globally optimal imputation orders. We experimentally validated our method on eight real-world datasets and five types of ML models, with the results indicating that the imputation order optimized by our method outperforms the current state-of-the-art methods.

The next point-of-interest (POI) prediction is a significant task in location-based services, yet its complexity arises from the consolidation of spatial and semantic intent. This fusion is subject to the influences of historical preferences, prevailing location, and environmental factors, thereby posing significant challenges. In addition, the uneven POI distribution further complicates the next POI prediction procedure. To address these challenges, we enrich input features and propose an effective deep-learning method within a two-step prediction framework. Our method first incorporates remote sensing data, capturing pivotal environmental context to enhance input features regarding both location and semantics. Subsequently, we employ a region quad-tree structure to integrate urban remote sensing, road network, and POI distribution spaces, aiming to devise a more coherent graph representation method for urban spatial. Leveraging this method, we construct the QR-P graph for the user's historical trajectories to encapsulate historical travel knowledge, thereby augmenting input features with comprehensive spatial and semantic insights. We devise distinct embedding modules to encode these features and employ an attention mechanism to fuse diverse encodings. In the two-step prediction procedure, we initially identify potential spatial zones by predicting user-preferred tiles, followed by pinpointing specific POls of a designated type within the projected tiles. Empirical findings from four real-world location-based social network datasets underscore the remarkable superiority of our proposed approach over competitive baseline methods.

Edge computing serves as a critical solution for latency-sensitive services on mobile and IoT devices. However, the high cost and limited edge resources present significant challenges for service and infrastructure providers in establishing efficient collaborations, particularly with conflicting profit objectives. Inspired by the pseudo elbow formation of octopuses, we propose a multi-participant double auction for resource allocation and pricing between service and infrastructure providers. We introduce a neutral third-party auctioneer to eliminate direct bargaining among participants, leading to an improved amount of allocated resources and matching efficiency. The presence of heterogeneous participants, many-to-many mapping and an advisable payment strategy that satisfies economic properties exacerbate the difficulty. To address these challenges, we propose a Matching and Pricing Resource Allocation algorithm for a long-term steady market, and a Truthful Resource Allocation algorithm for a short-term market. Simulation results demonstrate that the proposed algorithms exhibit superior performance not only in maximizing social welfare and utility of both service and infrastructure providers, but also in improving resource utilization.