Self-organising maps (SOM) [5] and generative topographic mapping (GTM) [2] define a nonlinear coordinate system by stating the coordinates of lattice points called model vectors. The methods are in wide use, particularly the computationally efficient SOM, but the dimension of the latent space is normally quite small. Two-dimensional latent space is the most typical one because it allows an easy visualisation for human users.
The disadvantage of SOM and GTM is that the number of parameters required to describe the mapping from latent variables to observations grows exponentially with the dimension of the latent space. Our main motivation for using MLP network as the nonlinear mapping is that its parametrisation scales linearly with the dimension of the latent space. In this respect the mapping of MLP network is much closer to a linear mapping which has been proven to be applicable for very high dimensional latent spaces. SOM and GTM would probably be better models for the helical data set in Sect. 5.2, but the rest of the experiments have latent spaces whose dimensions are so large that SOM or GTM models would need very many parameters.