  We propose a framework for descriptively analyzing sets of partial orders
based on the concept of depth functions. Despite intensive studies in linear
and metric spaces, there is very little discussion on depth functions for
non-standard data types such as partial orders. We introduce an adaptation of
the well-known simplicial depth to the set of all partial orders, the
union-free generic (ufg) depth. Moreover, we utilize our ufg depth for a
comparison of machine learning algorithms based on multidimensional performance
measures. Concretely, we provide two examples of classifier comparisons on
samples of standard benchmark data sets. Our results demonstrate promisingly
the wide variety of different analysis approaches based on ufg methods.
Furthermore, the examples outline that our approach differs substantially from
existing benchmarking approaches, and thus adds a new perspective to the vivid
debate on classifier comparison.
