  We propose a method to reduce the complexity of Generalized Linear Models in
the presence of categorical predictors. The traditional one-hot encoding, where
each category is represented by a dummy variable, can be wasteful, difficult to
interpret, and prone to overfitting, especially when dealing with
high-cardinality categorical predictors. This paper addresses these challenges
by finding a reduced representation of the categorical predictors by clustering
their categories. This is done through a numerical method which aims to
preserve (or even, improve) accuracy, while reducing the number of coefficients
to be estimated for the categorical predictors. Thanks to its design, we are
able to derive a proximity measure between categories of a categorical
predictor that can be easily visualized. We illustrate the performance of our
approach in real-world classification and count-data datasets where we see that
clustering the categorical predictors reduces complexity substantially without
harming accuracy.
