Robust Alignment via Partial Gromov-Wasserstein Distances

The Gromov-Wasserstein (GW) problem provides a powerful framework for aligning heterogeneous datasets by matching their internal structures in a way that minimizes distortion. However, GW alignment is sensitive to data contamination by outliers, which can greatly distort the resulting matching scheme. To address this issue, we study robust GW alignment, where upon observing contaminated versions of the clean data distributions, our goal is to accurately estimate the GW alignment cost between the original (uncontaminated) measures. We propose an estimator based on the partial GW distance, which trims out a fraction of the mass from each distribution before optimally aligning the rest. The estimator is shown to be minimax optimal in the population setting and is near-optimal in the finite-sample regime, where the optimality gap originates only from the suboptimality of the plug-in estimator in the empirical estimation setting (i.e., without contamination). Towards the analysis, we derive new structural results pertaining to the approximate pseudo-metric structure of the partial GW distance. Overall, our results endow the partial GW distance with an operational meaning by posing it as a robust surrogate of the classical distance when the observed data may be contaminated.

Self-consistent Deep Geometric Learning for Heterogeneous Multi-source Spatial Point Data Prediction

Multi-source spatial point data prediction is crucial in fields like environmental monitoring and natural resource management, where integrating data from various sensors is the key to achieving a holistic environmental understanding. Existing models in this area often fall short due to their domain-specific nature and lack a strategy for integrating information from various sources in the absence of ground truth labels. Key challenges include evaluating the quality of different data sources and modeling spatial relationships among them effectively. Addressing these issues, we introduce an innovative multi-source spatial point data prediction framework that adeptly aligns information from varied sources without relying on ground truth labels. A unique aspect of our method is the 'fidelity score,' a quantitative measure for evaluating the reliability of each data source. Furthermore, we develop a geo-location-aware graph neural network tailored to accurately depict spatial relationships between data points. Our framework has been rigorously tested on two real-world datasets and one synthetic dataset. The results consistently demonstrate its superior performance over existing state-of-the-art methods.

Graph Neural Network for spatiotemporal data: methods and applications

In the era of big data, there has been a surge in the availability of data containing rich spatial and temporal information, offering valuable insights into dynamic systems and processes for applications such as weather forecasting, natural disaster management, intelligent transport systems, and precision agriculture. Graph neural networks (GNNs) have emerged as a powerful tool for modeling and understanding data with dependencies to each other such as spatial and temporal dependencies. There is a large amount of existing work that focuses on addressing the complex spatial and temporal dependencies in spatiotemporal data using GNNs. However, the strong interdisciplinary nature of spatiotemporal data has created numerous GNNs variants specifically designed for distinct application domains. Although the techniques are generally applicable across various domains, cross-referencing these methods remains essential yet challenging due to the absence of a comprehensive literature review on GNNs for spatiotemporal data. This article aims to provide a systematic and comprehensive overview of the technologies and applications of GNNs in the spatiotemporal domain. First, the ways of constructing graphs from spatiotemporal data are summarized to help domain experts understand how to generate graphs from various types of spatiotemporal data. Then, a systematic categorization and summary of existing spatiotemporal GNNs are presented to enable domain experts to identify suitable techniques and to support model developers in advancing their research. Moreover, a comprehensive overview of significant applications in the spatiotemporal domain is offered to introduce a broader range of applications to model developers and domain experts, assisting them in exploring potential research topics and enhancing the impact of their work. Finally, open challenges and future directions are discussed.