High Dimensional Data Reduction using approximate Convex Hulls

这个项目是应用数学和航空航天工程的联合成果。它的目的是利用 减少材料结构稳定性测试所需数据点数量的数学方法。材料 必须在广泛的条件下进行测试(模拟)，每个条件都由一个高 多维数据点。然而，每一次测试都很耗时，计算密集。我们可以减少 仅使用数据点的极值进行测试的次数。在高维空间中，凸壳是 用来找出这些极值。然而，现有的求解凸包的算法都局限于较小的范围 尺寸。这项研究提出了一种更有效的方法来使用修改的凸集来约简数据 可以在更高维度进行有效计算的船体。

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.