  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.
