A new supervised non-linear mapping (1203.2021v1)

Abstract: 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.