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

现代数据科学涉及到越来越多的异质地理空间数据，其中对象的特征被作为离散变量来度量。定性标志空间相关性的量化一直是空间统计学研究的热点。它是种群、林业和生态学理论的一个重要方面，但在生物医学中却鲜有人关注。深度学习和生物技术的最新发展极大地促进了利用空间信息生成海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，推动空间统计方法的现代化和理论的发展。在这个项目中，研究人员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可靠的，在实际中对解决新的地理空间数据(例如，空间转录数据)中常见的异质性问题是有用的。调查人员还计划开发用户友好的开源软件。该项目将向本科生和研究生展示先进的科学、技术、工程和数学技能。研究人员将开发三个建模框架，以分析不同空间分辨率的不同地理空间数据。首先，将开发一个基于能量的框架，该框架将表征网格数据和点数据的不同空间模式。与传统的基于核的方法相比，新方法对噪声具有更强的鲁棒性，计算效率更高。为了实现这一目标，研究人员将在框架中加入一种新的特征选择机制，以联合识别高维地理空间数据的多个空间模式。然后，研究将探索如何构建可解释的地理空间数据的低维表示。特别是，研究人员将专注于集成多模式地理空间数据，以提高空间域划分的精度和分辨率。一旦空间域被分割，当务之急就是描述它们复杂的形状。最后，将研究一个基于地标的框架来量化空间域的边界，以解释不同种类的边界粗糙度。所开发的方法将有助于贝叶斯空间和形状分析中急需的理论和应用。研究人员还将从理论和计算两个方面研究参数和非参数贝叶斯方法在这方面的潜在优势和不足。结果将通过研讨会、出版物和新课程传播。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.