  We introduce a method that uses low-rank approximations of cross-correlation
matrices in mixed continuous and categorical Gaussian Process models. This new
method -- called Low-Rank Correlation (LRC) -- offers the ability to flexibly
adapt the number of parameters to the problem at hand by choosing an
appropriate rank of the approximation. Furthermore, we present a systematic
approach of defining test functions that can be used for assessing the accuracy
of models or optimization methods that are concerned with both continuous and
categorical inputs. We compare LRC to existing approaches of modeling the
cross-correlation matrix. It turns out that the new approach performs well in
terms of estimation of cross-correlations and response surface prediction.
Therefore, LRC is a flexible and useful addition to existing methods,
especially for increasing numbers of combinations of levels of the categorical
inputs.
