Collaborative Research: Advances in the Theory and Practice of Non-Euclidean Statistics

合作研究：非欧几里得统计理论与实践的进展

• 批准号: 2311058
• 负责人: Robert Paige
• 金额: $ 10万
• 依托单位: Missouri University of Science and Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-15 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2311058&HistoricalAwards=false
• 关键词: Collaborative; Research; Advances; Theory; Practice

Shape, image, and RNA data types have had an important impact in many areas of Medicine, Science, Technology, etc. These modern data types contain different kinds of information that typically do not belong to a Euclidean space. As such, the analysis of these data types depends upon the development of statistical methodology that is adapted to address the topology and geometry of non-Euclidean metric object spaces. The project considers geometric-topologically informed statistical methods for the analysis of data lying on such object spaces. The methods to develop can find applications for new kinds of image analyses that are more likely to detect important features, identify new measures of location for shape, image, and RNA data, and improve the quality of peripheral computer vision and 3D image data. The developed methods for RNA sequencing data may apply to the investigation of viral diseases and cancer at the genomic level. The project also provided research training opportunities for graduate students.The project develops statistical parameters and their inference in object spaces that underlie projective shape data, digital image data, and RNA sequence analyses. The development relies upon two key features - nonlinearity and compactness. Information extracted from these data types is often represented as points on a stratified space. This project extends classical statistical methods to colored images via RGB correlations and 3D scene reconstructions and considers the processed images to be points on an object space, which is embeddable in a Hilbert space. Moreover, this project expands upon existing approaches with the aim of increasing the computational speed of algorithms required for real-world applications and introducing distribution-free methodologies for these data types.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.

形状，图像和RNA数据类型对医学，科学，技术等许多领域都有重要影响。这些现代数据类型包含通常不属于欧几里得空间的不同类型的信息。因此，对这些数据类型的分析取决于统计方法的发展，该方法适用于解决非欧几里得公制对象空间的拓扑和几何形状。该项目认为几何学知情的统计方法用于分析该对象空间上的数据。开发的方法可以找到新型图像分析的应用程序，这些分析更有可能检测重要特征，确定形状，图像和RNA数据的新位置度量，并提高外围计算机视觉和3D图像数据的质量。开发的RNA测序数据的方法可能适用于基因组水平的病毒疾病和癌症的研究。该项目还为研究生提供了研究培训机会。该项目开发了统计参数及其在基于投影形状数据，数字图像数据和RNA序列分析的对象空间中的推断。该发展依赖于两个关键特征 - 非线性和紧凑性。从这些数据类型中提取的信息通常表示为分层空间上的点。该项目通过RGB相关和3D场景重建将经典的统计方法扩展到彩色图像，并认为处理后的图像是对象空间上的点，该对象空间可嵌入希尔伯特空间中。此外，该项目扩展了现有方法，目的是提高现实世界应用所需的算法的计算速度，并为这些数据类型引入无分配方法。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力和更广泛影响的评估来通过评估来获得支持的值得支持的。