A geometrically motivated classi er is presented and applied, with both training and testing stages, to 3 real datasets.Our results compared to those from 23 other classi ers have the least error.The algorithm is based on parallel coordinates and : ~has worst-case computational complexity O(N 2 jPj 2 ) in the number of variables N and dataset size jPj, ~provides comprehensible and explicit rules, ~does dimensionality selection { where the minimal set of original variables (not transformed new variables as in Principal Component Analysis) required to state the rule is found, and ~orders these variables so as to optimize the clarity o f separation between the designated set and its complement.