RankVisu: Mapping from the neighborhood network

Abstract

Most multidimensional scaling methods focus on the preservation of dissimilarities to map high dimensional items in a low-dimensional space. However, the mapping function usually does not consider the preservation of small dissimilarities as important, since the cost is small with respect to the preservation of large dissimilarities. As a consequence, an item's neighborhoods may be sacrificed for the benefit of the overall mapping. We have subsequently designed a mapping method devoted to the preservation of neighborhood ranks rather than their dissimilarities: RankVisu. A mapping of data is obtained in which neighborhood ranks are as close as possible according to the original space. A comparison with both metric and non-metric MDS highlights the pros (in particular, cluster enhancement) and cons of RankVisu.