Data visualization for asymmetric relations

Abstract

Most 2D visualization methods based on multidimensional scaling (MDS) and self-organizing maps (SOMs) use a symmetric distance matrix to represent and visualize object relationships in a data set. In many real-world applications, however, raw data such as a world-trade data are best captured as an asymmetric proximity matrix. Such asymmetric matrices cannot be perfectly represented by most previous methods. To handle such an intrinsic limitation, in this paper, we propose a dynamic learning for metric representations of asymmetric proximity data to better understand the data. The proposed learning generates two representations (maps) with the row vectors (sending or exporting) and column vectors (receiving or importing) of the matrix, respectively. To better present the patterns, we supplement the maps with two analysis tools: cluster analysis and distance analysis, which connect and compare the different patterns from the different maps. Experiment results using three real world data sets confirm that the proposed learning method is useful to understand asymmetric proximity data.