Generative Topographic Map - Uses

Uses

In data analysis, GTMs are like a nonlinear version of principal components analysis, which allows high dimensional data to be modelled as resulting from Gaussian noise added to sources in lower-dimensional latent space. For example, to locate stocks in plottable 2D space based on their hi-D time-series shapes. Other applications may want to have fewer sources than data points, for example mixture models.

In generative deformational modelling, the latent and data spaces have the same dimensions, for example, 2D images or 1 audio sound waves. Extra 'empty' dimensions are added to the source (known as the 'template' in this form of modelling), for example locating the 1D sound wave in 2D space. Further nonlinear dimensions are then added, produced by combining the original dimensions. The enlarged latent space is then projected back into the 1D data space. The probability of a given projection is, as before, given by the product of the likelihood of the data under the Gaussian noise model with the prior on the deformation parameter. Unlike conventional spring-based deformation modelling, this has the advantage of being analytically optimizable. The disadvantage is that it is a 'data-mining' approach, i.e. the shape of the deformation prior is unlikely to be meaningful as an explanation of the possible deformations, as it is based on a very high, artificial- and arbitrarily constructed nonlinear latent space. For this reason the prior is learned from data rather than created by a human expert, as is possible for spring-based models.