Metric representations of data via the Kernel-based Sammon Mapping

In this paper we present a novel generalization of Sammon's Mapping (SM), which is a popular, metric multi-dimensional scaling technique used in data analysis and visualization. The new approach, namely the Kernel-based Sammon Mapping (KSM), yields the classic SM and other much related techniques as special cases. Apart from being able to approximate distance-preserving projections, it can also learn to metrically represent arbitrarily-defined dissimilarities or similarities between samples. Moreover, it can handle equally well numeric, categorical or mixed-type data. It is able to accomplish all this by modeling its projections as linear combinations of appropriate kernel functions. We report experimental results, which showcase KSM's capabilities in visually representing several meaningful relationships between samples of selected datasets.