GTM uses the EM algorithm to fit adaptive parameters $\mathbf{W}$ and $\beta$ of a constrained mixture of Gaussian model to the data.

The constrained mixture of Gaussian model consists of a set $\{\mathbf{x}_i\}$ of points in latent space which are mapped via a general linear model $\mathbf{W}\phi(x)$ into data space, and the inverse variance $\beta$ of the Gaussian noise model.⇒