  We present a fast and transparent multi-variate event classification
technique, called PDE-RS, which is based on sampling the signal and background
densities in a multi-dimensional phase space using range-searching. The
employed algorithm is presented in detail and its behaviour is studied with
simple toy examples representing basic patterns of problems often encountered
in High Energy Physics data analyses. In addition an example relevant for the
search for instanton-induced processes in deep-inelastic scattering at HERA is
discussed. For all studied examples, the new presented method performs as good
as artificial Neural Networks and has furthermore the advantage to need less
computation time. This allows to carefully select the best combination of
observables which optimally separate the signal and background and for which
the simulations describe the data best. Moreover, the systematic and
statistical uncertainties can be easily evaluated. The method is therefore a
powerful tool to find a small number of signal events in the large data samples
expected at future particle colliders.
