Comparison between SOM and generative topographic mapping (GTM) in non-linear mapping

Abstract

Kohonen-type Self-organizing map (SOM) is widely used in clustering. When using SOM, you can have a trouble in choosing proper parameters. Generative topographic mapping (GTM) proposed by Bishop et al. seems to be superior to SOM, because in GTM there is a well-defined objective function given by the log likelihood. And the objective function convergence to a (local) maximum is guaranteed by the use of EM algorithm. In this paper, we made a comparison between these two mappings by the both artificial and real data, and also evaluated the mapping performance of both GTM and SOM by introducing the root mean square of midpoint (RMSM). RMSM is calculated as RMS of mapping error of all midpoints instead of the original data points. RMSM represents how the map complement between data points. Comparing RMSM, you can know which technique maps more smoothly onto the data space. We applied this barometer to the wine data. It indicated that GTM produces the smoother map than SOM, and the RMS of GTM is approximate to that of SOM. Thus GTM can be superior to SOM as mapping method.