Developing Modern Spatial and Shape Analysis for New Heterogeneous High-dimensional Geospatial Data

现代数据科学涉及越来越多的异构地理空间数据，其中对象的特征作为离散变量进行测量。定性标记的空间相关性的量化一直是空间统计学中长期关注的焦点。它是人口林学和生态学理论的一个重要方面，但在生物医学领域却很少受到重视。深度学习和生物技术的最新发展极大地促进了产生具有空间信息的大量高维基因组序列计数数据。这就迫切需要创新来分析如此复杂的数据，从而推动空间统计方法的现代化和理论的发展。在这个项目中，研究者将开发一系列计算效率高的空间和形状方法，这些方法在理论上是合理的，在解决新的地理空间数据（例如，空间转录组学数据）中常见的异质性问题方面实际上是有用的。研究者还计划开发用户友好的开源软件。该项目将使本科生和研究生接触到先进的科学、技术、工程和数学技能。研究者将开发三种建模框架来分析不同空间分辨率下的异构地理空间数据。首先，将开发一个基于能量的框架，以表征网格和点数据的异构空间模式。与传统的基于核的方法相比，新方法对噪声的鲁棒性更强，计算效率更高。为此，研究者将在框架中引入一种新的特征选择机制，以共同识别高维地理空间数据的多种空间模式。然后，研究将探讨如何构建一个可解释的地理空间数据的低维表示。特别是，研究者将专注于整合多模态地理空间数据，以提高空间域划分的精度和分辨率。一旦空间域被分割，一个直接的任务是表征其复杂的形状。最后，将研究一个基于地标的框架来量化空间域的边界，以考虑异构边界粗糙度。所开发的方法将有助于贝叶斯空间和形状分析急需的理论和应用。研究者还将从理论和计算两个方面研究参数贝叶斯方法和非参数贝叶斯方法在这方面的潜在优点和缺点。研究结果将通过研讨会、出版物和新课程传播。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Modern data science involves more and more heterogeneous geospatial data where the features of objects are measured as discrete variables. The quantification of spatial correlation of qualitative marks has been a longstanding focus in spatial statistics. It is a key aspect of population forestry and ecology theory but receives little attention in biomedicine. Recent developments in deep learning and biotechnology have greatly facilitated generating massive high-dimensional genome sequence count data with spatial information. This creates an urgent need for innovation to analyze such complex data, driving the methodological modernization and theoretical developments in spatial statistics. In this project, the investigator will develop a series of computationally efficient spatial and shape methods that are theoretically sound and practically useful for addressing the heterogeneity issue commonly seen in the new geospatial data (e.g., spatial transcriptomics data). The investigator also plans to develop user-friendly and open-source software. The project will expose undergraduate and graduate students to advanced science, technology, engineering, and mathematical skillsets.The investigator will develop three modeling frameworks to analyze heterogeneous geospatial data at different spatial resolutions. First, an energy-based framework that characterizes heterogeneous spatial patterns for both grided and point data will be developed. Compared with the traditional kernel-based methods, the new method is more robust to noise and computationally more efficient. Towards the goal, the investigator will incorporate a novel feature selection mechanism into the framework to jointly identify multiple spatial patterns for the high-dimensional geospatial data. Then, the study will explore how to construct an interpretable low-dimensional representation of the geospatial data. In particular, the investigator will focus on integrating multi-modal geospatial data to improve the accuracy and resolution of spatial domain partition. Once the spatial domains have been segmented, an immediate task is to characterize their complex shapes. Finally, a landmark-based framework that quantifies a spatial domain’s boundary will be studied to account for heterogeneous boundary roughness. The developed methodologies will contribute to much-needed theories and applications in Bayesian spatial and shape analysis. The investigator will also study the potential benefits and shortcomings of parametric and nonparametric Bayesian methods in this context from both theoretical and computational aspects. Results will be disseminated through workshops, publications, and new courses.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.