Estimating Low Dimensional Structure in Point Clouds

估计点云中的低维结构

• 批准号: 1208354
• 负责人: Isabella Verdinelli
• 金额: $ 23.22万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1208354&HistoricalAwards=false
• 关键词: Estimating; Low; Dimensional; Structure; Point

This project will develop computationally efficient estimation methods with accompanying theory for the problem of identifying low-dimensional structure in point-cloud data, both low and high dimensional. A canonical example is a noisy sample from a manifold. The investigators will develop minimax lower bounds for the estimation problem and construct estimators that achieve these lower bounds. They will then implement these methods in a practically useful form nd apply them to several important scientific problems.Datasets sometimes contain hidden, low-dimensional structure such as clusters, filaments and low dimensional surfaces. The goal of this project to develop rigorously justified, computationally efficient methods for extracting such structure from data. The developed methods will be applied to a diverse set of problems in astrophysics,seismology, biology, and neuroscience. The project will advance knowledge in several fields including computational geometry, machine learning, and statistics.

本计画将针对点云资料之低维结构辨识问题，发展计算效率高之估计方法，并辅以相关理论。 一个典型的例子是来自流形的噪声样本。研究人员将开发极小极大的估计问题的下限，并构建估计，实现这些下限。然后，他们将以实际有用的形式实现这些方法，并将其应用于几个重要的科学问题。数据集有时包含隐藏的低维结构，如簇，细丝和低维表面。该项目的目标是开发严格合理的，计算效率高的方法，从数据中提取这种结构。 开发的方法将应用于天体物理学，地震学，生物学和神经科学的各种问题。 该项目将推进几个领域的知识，包括计算几何，机器学习和统计。