Dynamic learning for visual representation of asymmetric proximity

While many methods like multidimensional scaling (MDS) are exploited to represent and visualize symmetric distance matrices on 2-dimensional spaces, asymmetric proximity matrices such as an importing/exporting matrix from/to countries cannot be perfectly represented on metric spaces, since the methods assume a symmetric distance matrix. To overcome 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 column vectors (importing) and row vectors (exporting) of the matrix, respectively. To better present the patterns, we supplement the maps with two analysis tools: cluster analysis and flow analysis, which connect and compare the different patterns from the different maps. Experimental results using cola-brand-switching data and world-trade data confirm that the proposed learning method is useful to understand asymmetric proximity data.