论文标题
D维球面中随机点的线性和渔民可分离性
Linear and Fisher Separability of Random Points in the d-dimensional Spherical Layer
论文作者
论文摘要
随机分离定理在高维数据分析和机器学习中起重要作用。事实证明，在高尺寸中，即使尺寸的点数指数为指数，也可以通过超平面将一组随机点的任何点与其他点分开。这个事实和类似的事实可用于为人工智能系统构建校正器，以确定数据的内在维度和解释各种自然智力现象。在本文中，我们完善了点数数量和随机分离定理的概率的估计，从而加强了前面获得的一些结果。当从$ d $维球形层随机，独立和均匀地绘制点时，我们提出了线性和渔民可分离性的边界。这些结果使我们能够更好地概述应用中随机分离定理的适用性限制。
Stochastic separation theorems play important role in high-dimensional data analysis and machine learning. It turns out that in high dimension any point of a random set of points can be separated from other points by a hyperplane with high probability even if the number of points is exponential in terms of dimension. This and similar facts can be used for constructing correctors for artificial intelligent systems, for determining an intrinsic dimension of data and for explaining various natural intelligence phenomena. In this paper, we refine the estimations for the number of points and for the probability in stochastic separation theorems, thereby strengthening some results obtained earlier. We propose the boundaries for linear and Fisher separability, when the points are drawn randomly, independently and uniformly from a $d$-dimensional spherical layer. These results allow us to better outline the applicability limits of the stochastic separation theorems in applications.
