Visualizing asymmetric proximities with SOM and MDS models

Multidimensional scaling (MDS) and self organizing maps (SOM) algorithms are useful to visualize object relationships in a data set. These algorithms rely on the use of symmetric distances or similarity measures; for instance the Euclidean distance. There are a number of relevant applications, such as text mining and DNA microarray processing for which it is worth considering non symmetric similarity measures, that allow us to properly represent hierarchical relationships. In this paper we present asymmetric versions of SOM and MDS algorithms able to deal with asymmetric proximity matrices. We also compare these approaches to the corresponding symmetric versions. Experimental work on text databases and gene expression data sets show that the asymmetric proposed algorithms outperform their symmetric counterparts.