论文标题
维度独立数据集近似和分类应用程序
Dimension Independent Data Sets Approximation and Applications to Classification
论文作者
论文摘要
我们在非常具体的上下文中重新审视了经典的近似/插值理论的经典内核方法，该方法是由渴望获得强大的程序以通过（Super）级别级别函数集近似离散数据集的愿望而促成的，这些函数集集仅在数据集参数上是连续的，否则是顺畅的。为任何给定的数据集定义了特殊功能，称为数据信号，并用于以坚固的方式成功地解决监督分类问题，该问题不断取决于数据集。该方法的功效通过一系列低维示例，并将其应用于标准基准的高维高度问题。
We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely continuous at the data set arguments but are otherwise smooth. Special functions, called data signals, are defined for any given data set and are used to succesfully solve supervised classification problems in a robust way that depends continuously on the data set. The efficacy of the method is illustrated with a series of low dimensional examples and by its application to the standard benchmark high dimensional problem of MNIST digit classification.
