In GTM the smoothness is governed by the widths of certain basis functions that are used in generating the probability distribution in the input space. One possible way of defining topology preservation is to require that the mapping from the lower-dimensional output space to the input space is smooth and continuous. According to this definition at least a continuous version of GTM can be interpreted to be topology preserving. Measures that help in choosing basis functions that provide suitably regular mappings would probably be useful in the case of the GTM, as well. It is probably useful in practical applications that different mappings generated with the GTM algorithm can be compared by comparing their likelihoods.
Likelihoods have a straightforward interpretation.
These methods enable, however, selecting the best mapping from among a set of candidate mappings, which is the main goal in most applications. It remains to be seen how important the advantages of the GTM are in practical applications.