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

University Of Texas At Dallas, Richardson TX

Investigators

Abstract

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.