Pairwise elastic self-organizing maps

Visualization is one of the most powerful means for understanding the structure of multidimensional data. One of the most popular visualization methods is the Self-Organizing Map (SOM) that maps high dimensional data into low dimensional space while preserving the data's topological structure. While the topographical visualization can reveal the intrinsic characteristics of the data, SOM often fails to correctly reflect the distances between the data on the low dimensional map, thus reducing the fidelity of the visualization. The limitation of SOM to mimic the data structure is partly due to its inflexible structure, where the reference vectors are fixed, usually in two dimensional grid. In this study, a variant of SOM, where the reference vector can flexibly move to reconstruct the distribution of high dimensional data and thus can provide more precise visualization, is proposed. The proposed Elastic Self-Organizing Maps (ESOM) can also be used as nearest neighbors classifiers. This brief paper explains the basic characteristics and evaluation of ESOM against some benchmark problems.