Extending the SOM Algorithm to Non-Euclidean Distances via the Kernel Trick

The Self Organizing Map is a nonlinear projection technique that allows to visualize the underlying structure of high dimensional data. However, the original algorithm relies on the use of Euclidean distances which often becomes a serious drawback for a number of real problems. In this paper, we present a new kernel version of the SOM algorithm that incorporates non-Euclidean dissimilarities keeping the simplicity of the classical version. To achieve this goal, the data are nonlinearly transformed to a feature space taking advantage of Mercer kernels, while the overall data structure is preserved. The new SOM algorithm has been applied to the challenging problem of word relation visualization. We report that the kernel SOM improves the map generated by other alternatives for certain classes of kernels.