  The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear
probabilistic method of embedding a high dimensional dataset in terms low
dimensional `latent' variables. In this paper we illustrate that maximum a
posteriori (MAP) estimation of the latent variables and hyperparameters can be
used for model selection and hence we can determine the optimal number or
latent variables and the most appropriate model. This is an alternative to the
variational approaches developed recently and may be useful when we want to use
a non-Gaussian prior or kernel functions that don't have automatic relevance
determination (ARD) parameters. Using a second order expansion of the latent
variable posterior we can marginalise the latent variables and obtain an
estimate for the hyperparameter posterior. Secondly, we use the GP-LVM to
integrate multiple data sources by simultaneously embedding them in terms of
common latent variables. We present results from synthetic data to illustrate
the successful detection and retrieval of low dimensional structure from high
dimensional data. We demonstrate that the integration of multiple data sources
leads to more robust performance. Finally, we show that when the data are used
for binary classification tasks we can attain a significant gain in prediction
accuracy when the low dimensional representation is used.
