论文标题
高维散射数据的内核插值
Kernel Interpolation of High Dimensional Scattered Data
论文作者
论文摘要
从建模高维问题中选择的数据站点通常以非制定方式散布。除了在某些地方进行零星聚类外，随着环境空间的增长，它们变得相对较远。这些特征无视任何需要局部或全局准统一性数据位点分布的理论处理。我们在机器学习中结合了整体操作者理论的最近开发的应用，我们在当前文章中提出和研究了一个新框架，以分析高维数据的内核插值，该框架以基础内核矩阵的频谱为具有边界的随机近似误差。理论分析和数值模拟都表明，内核矩阵的光谱是可靠且稳定的气压计，用于测量用于高维数据的内核交互方法的性能。
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These features defy any theoretical treatment that requires local or global quasi-uniformity of distribution of data sites. Incorporating a recently-developed application of integral operator theory in machine learning, we propose and study in the current article a new framework to analyze kernel interpolation of high dimensional data, which features bounding stochastic approximation error by the spectrum of the underlying kernel matrix. Both theoretical analysis and numerical simulations show that spectra of kernel matrices are reliable and stable barometers for gauging the performance of kernel-interpolation methods for high dimensional data.
