论文标题
在高维空间中的质心伏洛伊丝网的计算
Computation of Centroidal Voronoi Tessellations in High Dimensional spaces
论文作者
论文摘要
由于自然的解释和各种理想的数学特性，质心voronoi Tessellations（CVT）发现了广泛的应用，并且在文献中相应地发展了广泛的发展。但是，在更高维空间中CVT的计算仍然很困难。在本文中，我们利用CVT在较高维空间中进行计算的非唯一性。我们在一维空间中构建了CVT的高维镶嵌。然后，我们证明，在所考虑的一维空间的密度之间的独立性下，这种镶嵌是质心。各种数值评估备份理论结果，通过镶嵌的低能量。通过最小的计算时间有效地获得了所得的网格样镶嵌。
Owing to the natural interpretation and various desirable mathematical properties, centroidal Voronoi tessellations (CVT) have found a wide range of applications and correspondingly a vast development in their literature. However the computation of CVT in higher dimensional spaces still remains difficult. In this paper, we exploit the non-uniqueness of CVTs in higher dimensional spaces for their computation. We construct such high dimensional tessellations from CVTs in one-dimensional spaces. We then prove that such a tessellation is centroidal under the condition of independence among densities over the one-dimensional spaces considered. Various numerical evaluations backup the theoretical result through the low energy of the tessellations. The resulting grid-like tessellations are obtained efficiently with minimal computation time.
