Mathematical Sciences: Topics in Projection Pursuit, Neural Networks and Pattern Recognition

数学科学：投影寻踪、神经网络和模式识别主题

• 批准号: 9202161
• 负责人: Lee Jones
• 金额: --
• 依托单位: University of Massachusetts Lowell Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-09-15 至 1994-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9202161&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Projection; Pursuit

Problems in the interface of statistics, mathematics and computational science will be studied, focusing on Fourier approximation and ridge estimation of regression and density functions and, in a separate context, on filtered Dirichlet distributions for local smoothing. In particular, preference orders will be studied for the frequency weights in multiple Fourier expansions and for the connection weights in single hidden-layer neural networks. Properties will be derived and applications such as feature extraction and projection pursuit will be considered in detail. This research will aid in automated learning from large data sets such as those arising in robotics, medicine and artificial intelligence. One aspect of the work will develop sophisticated mathematical techniques for application to problems in statistics and electrical engineering. A second aspect of the work will develop statistical methods to utilize an expert's knowledge directly without restricting the form in which the expert must express this information.

在统计，数学和计算科学的接口问题将进行研究，重点是傅立叶近似和回归和密度函数的岭估计，并在一个单独的上下文中，过滤Dirichlet分布的局部平滑。特别是，偏好顺序将研究在多个傅立叶展开的频率权重和单隐层神经网络的连接权重。属性将被导出，并将详细考虑特征提取和投影寻踪等应用程序。这项研究将有助于从机器人、医学和人工智能等领域产生的大型数据集中进行自动学习。工作的一个方面将开发复杂的数学技术应用于统计和电气工程中的问题。这项工作的第二个方面将发展统计方法，以便直接利用专家的知识，而不限制专家必须表达这种信息的形式。