  Supervised mapping methods project multi-dimensional labeled data onto a
2-dimensional space attempting to preserve both data similarities and topology
of classes. Supervised mappings are expected to help the user to understand the
underlying original class structure and to classify new data visually. Several
methods have been designed to achieve supervised mapping, but many of them
modify original distances prior to the mapping so that original data
similarities are corrupted and even overlapping classes tend to be separated
onto the map ignoring their original topology. We propose ClassiMap, an
alternative method for supervised mapping. Mappings come with distortions which
can be split between tears (close points mapped far apart) and false
neighborhoods (points far apart mapped as neighbors). Some mapping methods
favor the former while others favor the latter. ClassiMap switches between such
mapping methods so that tears tend to appear between classes and false
neighborhood within classes, better preserving classes' topology. We also
propose two new objective criteria instead of the usual subjective visual
inspection to perform fair comparisons of supervised mapping methods. ClassiMap
appears to be the best supervised mapping method according to these criteria in
our experiments on synthetic and real datasets.
