h-plots for displaying nonmetric dissimilarity matrices

Abstract

Nonmetric pairwise data with violations of symmetry, reflexivity, or triangle inequality appear in fields such as image matching, web mining, or cognitive psychology. When data are inherently nonmetric, we should not enforce metricity as real information could be lost. The multidimensional scaling problem is addressed from a new perspective. I propose a method based on the h-plot, which naturally handles asymmetric proximity data. Pairwise proximities between the objects are defined, though I do not embed these objects, but rather the variables that give the proximity to or from each object. The method is very simple to implement. The representation goodness can be easily assessed. The methodology is illustrated through several small examples and applied to the analysis of digital images of human corneal endothelia. Comparisons with well-known methods show its good behavior, especially with nonmetric pairwise data, which motivate my methodology. Other databases and methods are analyzed in the supporting information.