Given a set of historical vehicle trajectories and their descriptive attributes, the goal is to train a generative model that produces synthetic trajectories with high physical fidelity. Here, physical fidelity is defined as fidelity to both geometric and dynamic properties of trajectories. The problem is important since trajectory generation can contribute to data augmentation for many traffic-related applications, such as popular route discovery and traffic light control. The key challenge of this problem lies in achieving high physical fidelity under coarse geospatial attributes (e.g., origin-destination pairs) that lack fine-grained details. Current methods, which mostly focus on geometric properties, have limited utility in domain-specific scenarios due to their neglect of trajectory dynamics. To address these limitations, we propose GCDM, a novel Geo-Lucid Conditional Diffusion Model framework that integrates road map attributes into the generative process through spatially hierarchical generation and map-informed latent variables. Experiments on real-world vehicle trajectory datasets show that GCDM outperforms state-of-the-art methods in geo-distribution similarity and dynamics fidelity.

Given multi-type point maps from different place-types (e.g., tumor regions), our objective is to develop a classifier trained on the source place-type to accurately distinguish between two classes of the target place-type based on their point arrangements. This problem is societally important for many applications, such as generating clinical hypotheses for designing new immunotherapies for cancer treatment. The challenge lies in the spatial variability, the inherent heterogeneity and variation observed in spatial properties or arrangements across different locations (i.e., place-types). Previous techniques focus on self-supervised tasks to learn domain-invariant features and mitigate domain differences; however, they often neglect the underlying spatial arrangements among data points, leading to significant discrepancies across different place-types. We explore a novel multi-task self-learning framework that targets spatial arrangements, such as spatial mix-up masking and spatial contrastive predictive coding, for spatially-delineated domain-adapted AI classification. Experimental results on real-world datasets (e.g., oncology data) show that the proposed framework provides higher prediction accuracy than baseline methods.

Given a collection of Boolean spatial features, Super-Colocation Pattern Discovery identifies subsets of features that are not only frequently located together but also have dense interactions.For example, the presence of multiple immune cells around cancer cells is more interesting to oncologists than a simple colocation between immune and cancer cells.This problem is important due to its societal applications, including oncology, transportation, and economic analysis.The problem is challenging due to the need to model interaction density among a subset of Boolean spatial features.Related work on colocation pattern mining is limited due to a lack of conceptual, logical, and physical models that accurately represent interaction density.Traditional interest measures (e.g., participation index) largely focus on the mere presence of another spatial feature type and overlook the number or density of neighboring instances.We propose a novel interest measure, termed Super-Colocation Density, which utilizes a matrix or tensor along with a utility-based index to quantify the interaction density among subsets of spatial features.We also introduce novel Super-Colocation Mining algorithms and evaluate the proposed methods through both theoretical analysis and experiments with real and synthetic data.

Given coarser-resolution projections from global climate models or satellite data, the downscaling problem aims to estimate finer-resolution regional climate data, capturing fine-scale spatial patterns and variability. Downscaling is any method to derive high-resolution data from low-resolution variables, often to provide more detailed and local predictions and analyses. This problem is societally crucial for effective adaptation, mitigation, and resilience against significant risks from climate change. The challenge arises from spatial heterogeneity and the need to recover finer-scale features while ensuring model generalization. Most downscaling methods [21] fail to capture the spatial dependencies at finer scales and underperform on real-world climate datasets, such as sea-level rise. We propose a novel Kriging-informed Conditional Diffusion Probabilistic Model (Ki-CDPM) to capture spatial variability while preserving fine-scale features. Experimental results on climate data show that our proposed method is more accurate than state-of-the-art downscaling techniques.

Given multi-category point sets from different place-types, our goal is to develop a spatially-lucid classifier that can distinguish between two classes based on the arrangements of their points. This problem is important for many applications, such as oncology, for analyzing immune-tumor relationships and designing new immunotherapies. It is challenging due to spatial variability and interpretability needs. Previously proposed techniques require dense training data or have limited ability to handle significant spatial variability within a single place-type. Most importantly, these deep neural network (DNN) approaches are not designed to work in non-Euclidean space, particularly point sets. Existing non-Euclidean DNN methods are limited to one-size-fits-all approaches. We explore a spatial ensemble framework that explicitly uses different training strategies, including weighted-distance learning rate and spatial domain adaptation, on various place-types for spatially-lucid classification. Experimental results on real-world datasets (e.g., MxIF oncology data) show that the proposed framework provides higher prediction accuracy than baseline methods.

Given trajectories with gaps (i.e., missing data), we investigate algorithms to identify abnormal gaps in trajectories which occur when a given moving object did not report its location, but other moving objects in the same geographic region periodically did. The problem is important due to its societal applications, such as improving maritime safety and regulatory enforcement for global security concerns, such as illegal fishing, illegal oil transfers, and trans-shipments. The problem is challenging due to the difficulty of bounding the possible locations of the moving object during a trajectory gap, and the very high computational cost of detecting gaps in such a large volume of location data. The current literature on anomalous trajectory detection assumes linear interpolation within gaps, which may not be able to detect abnormal gaps since objects within a given region may have traveled away from their shortest path. In preliminary work, we introduced an abnormal gap measure that uses a classical space-time prism model to bound an object's possible movement during the trajectory gap and provided a scalable memoized gap detection algorithm (Memo-AGD). In this article, we propose a space time-aware gap detection (STAGD) approach to leverage space-time indexing and merging of trajectory gaps. We also incorporate a dynamic region merge-based (DRM) approach to efficiently compute gap abnormality scores. We provide theoretical proofs that both algorithms are correct and complete and also provide analysis of asymptotic time complexity. Experimental results on synthetic and real-world maritime trajectory data show that the proposed approach substantially improves computation time over the baseline technique.

Given a collection of Boolean spatial feature-types, their instances, a neighborhood relation (e.g., proximity), and a hierarchical taxonomy on the feature-types, taxonomy-aware colocation pattern discovery finds the subsets of feature-types or their parents frequently located together. Taxonomy-aware colocations are important due to their use in taxonomy-reliant societal applications in ecology (e.g., finding new symbiotic relationships across food-chain), spatial pathology (e.g., immunotherapy for cancer), etc. Due to the taxonomy, the number of candidate patterns increases considerably (i.e., exponential in the number of colocated instances, where a subset of instances have a parent-child relation). Existing algorithms for mining general colocations are not designed to use taxonomy and will incur redundant computations across the hierarchy. We propose a taxonomy-aware colocation miner (TCM) algorithm which uses a user-defined taxonomy to find taxonomy-aware colocation patterns. We also propose TCM-Prune algorithm that prunes duplicate colocations instances having a parent-child relation. Experiments with synthetic and real data sets show that TCM and TCM-Prune can find colocation patterns missed by the traditional approach (i.e., the ones which do not take hierarchy into account), and TCM-Prune can remove duplicate colocation instances.

Given trajectories with gaps, we investigate methods to tighten spatial bounds on areas (e.g., nodes in a spatial network) where possible rendezvous activity could have occurred. The problem is important for reducing manual effort to post-process possible rendezvous areas using satellite imagery and has many societal applications to improve public safety, security, and health. The problem of rendezvous detection is challenging due to the difficulty of interpreting missing data within a trajectory gap and the very high cost of detecting gaps in such a large volume of location data. Most recent literature presents formal models, namely space-time prism, to track an object's rendezvous patterns within trajectory gaps on a spatial network. However, the bounds derived from the space-time prism are rather loose, resulting in unnecessarily extensive postprocessing manual effort. To address these limitations, we propose a Time Slicing-based Gap-Aware Rendezvous Detection (TGARD) algorithm to tighten the spatial bounds in spatial networks. We propose a Dual Convergence TGARD (DC-TGARD) algorithm to improve computational efficiency using a bi-directional pruning approach. Theoretical results show the proposed spatial bounds on the area of possible rendezvous are tighter than that from related work (space-time prism). Experimental results on synthetic and real-world spatial networks (e.g., road networks) show that the proposed DC-TGARD is more scalable than the TGARD algorithm.

Given trajectory data with gaps, we investigate methods to identify possible rendezvous regions. The problem has societal applications such as improving maritime safety and regulatory enforcement. The challenges come from two aspects. First, gaps in trajectory data make it difficult to identify regions where moving objects may have rendezvoused for nefarious reasons. Hence, traditional linear or shortest path interpolation methods may not be able to detect such activities, since objects in a rendezvous may have traveled away from their usual routes to meet. Second, user detecting a rendezvous regions involve a large number of gaps and associated trajectories, making the task computationally very expensive. In preliminary work, we proposed a more effective way of handling gaps and provided examples to illustrate potential rendezvous regions. In this article, we are providing detailed experiments with both synthetic and real-world data. Experiments on synthetic data show that the accuracy improved by 50 percent, which is substantial as compared to the baseline approach. In this article, we propose a refined algorithm Temporal Selection Search for finding a potential rendezvous region and finding an optimal temporal range to improve computational efficiency. We also incorporate two novel spatial filters: (i) a Static Ellipse Intersection Filter and (ii) a Dynamic Circle Intersection Spatial Filter. Both the baseline and proposed approaches account for every possible rendezvous pattern. We provide a theoretical evaluation of the algorithms correctness and completeness along with a time complexity analysis. Experimental results on synthetic and real-world maritime trajectory data show that the proposed approach substantially improves the area pruning effectiveness and computation time over the baseline technique. We also performed experiments based on accuracy and precision on synthetic dataset on both proposed and baseline techniques.