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.

翻译：我们在一个非常具体的背景下重新审视典型的近似/内插法理论,其动机是希望获得一种强有力的程序,通过(超)级功能组合离散数据集,这些功能在数据集参数上只是连续的,但在其他方面是顺利的。特殊功能,即所谓的数据信号,是为任何特定数据集所定义的,用于以持续依赖数据集的稳健方式全面解决受监督的分类问题。该方法的功效通过一系列低维实例及其应用于MNIMT数字分类的标准基准高维问题来说明。