RUI: Multiscale and Modeling of Scattered Data

RUI：分散数据的多尺度和建模

• 批准号: 0605209
• 负责人: Hrushikesh Mhaskar
• 金额: $ 13.19万
• 依托单位: California State L A University Auxiliary Services Inc.
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-10-01 至 2010-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0605209&HistoricalAwards=false
• 关键词: RUI; Multiscale; Modeling; Scattered; Data

In many practical applications, one needs to study modeling and analysis of data based on smooth manifolds such as a sphere, and more generally, metric measure spaces. Examples include document analysis, face recognition, semi-supervised learning, image processing, cataloguing of galaxies, pattern analysis of brain potentials, and the study of brain tumors. The proposer will continue his work on approximation by analogues of neural and radial basis function (RBF) networks, sometimes redefined to take advantage of the geometry of the data, for modeling such data. He will also continue his work on multiscales for the analysis of the data. He will develop theoretical results as well as efficient algorithms based on these theories. The findings of the research will be disseminated, as usual, through articles in refereed journals and conference proceedings, as well as presentations in colloquia and conferences.While classical techniques from approximation theory require a judicious choice of the sites where the data is collected, many practical applications do not allow such a choice. One of the novelties of the research is to deal with data collected at arbitrary sites. Another novelty is to utilize global data, such as coefficients in an orthogonal expansion, to study local features of the functional relationship underlying the data.

在许多实际应用中，人们需要研究基于光滑流形（如球面）的数据建模和分析，更一般地，度量测度空间。 例子包括文件分析、人脸识别、半监督学习、图像处理、星系编目、脑电位模式分析和脑肿瘤研究。 提议者将继续他的工作近似神经和径向基函数（RBF）网络的模拟，有时重新定义，以利用数据的几何形状，为这些数据建模。 他还将继续进行多尺度数据分析工作。 他将开发理论结果以及基于这些理论的高效算法。 研究的结果将被传播，像往常一样，通过文章在参考期刊和会议记录，以及在座谈会和会议的介绍。虽然从近似理论的经典技术需要一个明智的选择的网站，收集数据，许多实际应用不允许这样的选择。 这项研究的新颖之处之一是处理在任意地点收集的数据。 另一个新奇是利用全局数据，如正交展开中的系数，来研究数据背后的函数关系的局部特征。