Experimental Analysis of GTM

Not linear methods for statistical data analysis have become more and more popular thanks to the rapid development of computers. The fields in which they are applied to are as various as the methods them self. Generative topographic mapping (GTM) has been developed by [Bishop et al. 1997] as a principal alternative to the self-organizing map (SOM) algorithm [Kohonen 1982] in which a set of unlabelled data vectors is summarized in terms of a set to reference vectors having a spatial organization corresponding to a (generally) two-dimensional sheet. While the SOM algorithm has achieved many successes in practical applications, it also suffers from the significant deficiencies, many of which highlighted in [Kohonen 1995]. They include: the absence of a cost function, the lack of theoretical basis for choosing learning rate parameter schedules and neighborhood parameters to ensure topographic ordering, the absence of any general proofs of convergence, and the fact that the model does not define a probability density. These Problems can all be traced to the heuristic origins of the SOM algorithm. The GTM algorithm overcomes most of the limitations of the SOM while introducing no significant disadvantages. The datasets used to analyze the strengths and weaknesses of GTM range from low dimensional with few vectors to very high dimensional with many vectors. In Section 2 I give an overview of related work. I summarize the method in Section 3. In Section 4 I describe the experiments I made and discuss the similarities to the SOM. Conclusions are presented in Section 5.