High Dimensional Data Reduction using approximate Convex Hulls

使用近似凸包进行高维数据缩减

• 批准号: 486596-2015
• 负责人: Oberman, Adam
• 金额: $ 1.82万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Engage Grants Program
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=585692
• 关键词: Dimensional; Data; Reduction; using; approximate

This project is a joint effort between applied mathematics and aerospace engineering. It aims to use mathematics to reduce the number of data points required for structural stability testing of materials. Materials must be tested (simulated) under a wide range of conditions, each of which is represented by a high dimensional data point. However each test is time consuming and computationally intensive. We can reduce the number of tests by using only extreme values of the data points. In high dimensions, the convex hull is used to find these extreme values. However existing algorithms for the convex hull are limited to small dimensions. This research proposes to find a more efficient way to reduce the data using a modified convex hull which can be computed effectively in higher dimensions.

该项目是应用数学和航空工程之间的共同努力。它的目的是使用 数学以减少材料结构稳定性测试所需的数据点数量。材料 必须在各种条件下进行测试（模拟），每种条件都由高度表示 维数据点。但是，每个测试都是耗时和计算密集型的。我们可以减少 仅使用数据点的极值测试数量。在高尺寸中，凸壳为 用于找到这些极端值。但是，凸壳的现有算法仅限于小 方面。这项研究建议使用修改后的凸面找到一种更有效的方法来减少数据 可以在更高维度中有效计算的船体。