  Parametric Embedding (PE) has recently been proposed as a general-purpose
algorithm for class visualisation. It takes class posteriors produced by a
mixture-based clustering algorithm and projects them in 2D for visualisation.
However, although this fully modularised combination of objectives (clustering
and projection) is attractive for its conceptual simplicity, in the case of
high dimensional data, we show that a more optimal combination of these
objectives can be achieved by integrating them both into a consistent
probabilistic model. In this way, the projection step will fulfil a role of
regularisation, guarding against the curse of dimensionality. As a result, the
tradeoff between clustering and visualisation turns out to enhance the
predictive abilities of the overall model. We present results on both synthetic
data and two real-world high-dimensional data sets: observed spectra of
early-type galaxies and gene expression arrays.
