Data modeling in industry is often challenged by the complexity of massive, heterogeneous (mixed-type) data sets. Furthermore, categorical variables can potentially have hundreds (or even thousands) of levels (values). This work explores an efficient procedure for enriching an original data set (of practically any complexity) by assigning numerical scores to the levels of categorical variables. A novel-scoring objective attempts to preserve the mutual information between all the variables. A nontraditional clustering approach for mixed data (supervised-contrasting-independence clustering) is used. Although the preprocessing developed here was primarily motivated by the need for low-dimensional, exploratory visualization of complex, heterogeneous data, the proposed relatively simple preprocessing scheme can be useful in any distance-based learning problem. Two examples demonstrate this approach in instance-based, supervised applications.