  Nearest-neighbor methods have become popular in statistics and play a key
role in statistical learning. Important decisions in nearest-neighbor methods
concern the variables to use (when many potential candidates exist) and how to
measure the dissimilarity between units. The first decision depends on the
scope of the application while second depends mainly on the type of variables.
Unfortunately, relatively few options permit to handle mixed-type variables, a
situation frequently encountered in practical applications. The most popular
dissimilarity for mixed-type variables is derived as the complement to one of
the Gower's similarity coefficient. It is appealing because ranges between 0
and 1, being an average of the scaled dissimilarities calculated variable by
variable, handles missing values and allows for a user-defined weighting scheme
when averaging dissimilarities. The discussion on the weighting schemes is
sometimes misleading since it often ignores that the unweighted "standard"
setting hides an unbalanced contribution of the single variables to the overall
dissimilarity. We address this drawback following the recent idea of
introducing a weighting scheme that minimizes the differences in the
correlation between each contributing dissimilarity and the resulting weighted
Gower's dissimilarity. In particular, this note proposes different approaches
for measuring the correlation depending on the type of variables. The
performances of the proposed approaches are evaluated in simulation studies
related to classification and imputation of missing values.
