Neural networks for convex hull computation
Neural networks for convex hull computation
复制标题
用于凸包计算的神经网络
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
Zongben Xu
中科院分区：
文献类型：
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作者：
Y. Leung;Jiangshe Zhang;Zongben Xu
计算凸壳是计算几何形状各种应用中的核心问题之一。在本文中，开发了凸船体计算神经网络（CHCNN）来解决N维空间中的相关问题。该算法基于一个两层神经网络，与艺术相似，新开发的自适应训练策略称为“兴奋学习”。 CHCNN提供了对数据的并行实时处理，在训练后，该处理产生了两个密切相关的近似值，一个来自所需的凸船体内部和一个来自外部的近似值。结果表明，获得的近似凸壳的精度在O [K（-1）（N-1/）]左右，其中K是CHCNN输出层中神经元的数量。当k被认为足够大时，CHCNN可以生成任何准确的近似凸壳。我们还表明，上限的存在使得CHCNN在K大于或等于该结合时会产生精确的凸壳。提供了一系列的模拟和应用，以证明所提出算法的可行性，有效性和高效率。
Computing convex hull is one of the central problems in various applications of computational geometry. In this paper, a convex hull computing neural network (CHCNN) is developed to solve the related problems in the N-dimensional spaces. The algorithm is based on a two-layered neural network, topologically similar to ART, with a newly developed adaptive training strategy called excited learning. The CHCNN provides a parallel online and real-time processing of data which, after training, yields two closely related approximations, one from within and one from outside, of the desired convex hull. It is shown that accuracy of the approximate convex hulls obtained is around O[K(-1)(N-1/)], where K is the number of neurons in the output layer of the CHCNN. When K is taken to be sufficiently large, the CHCNN can generate any accurate approximate convex hull. We also show that an upper bound exists such that the CHCNN will yield the precise convex hull when K is larger than or equal to this bound. A series of simulations and applications is provided to demonstrate the feasibility, effectiveness, and high efficiency of the proposed algorithm.