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Intuitively, Akaike's information criterion between one-component and two-component distribution models (AID) tests whether a one model or another describes the data better, with a penalty for model complexity.

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.