  We employ random geometric digraphs to construct semi-parametric classifiers.
These data-random digraphs are from parametrized random digraph families called
proximity catch digraphs (PCDs). A related geometric digraph family, class
cover catch digraph (CCCD), has been used to solve the class cover problem by
using its approximate minimum dominating set. CCCDs showed relatively good
performance in the classification of imbalanced data sets, and although CCCDs
have a convenient construction in $\mathbb{R}^d$, finding minimum dominating
sets is NP-hard and its probabilistic behaviour is not mathematically tractable
except for $d=1$. On the other hand, a particular family of PCDs, called
\emph{proportional-edge} PCDs (PE-PCDs), has mathematical tractable minimum
dominating sets in $\mathbb{R}^d$; however their construction in higher
dimensions may be computationally demanding. More specifically, we show that
the classifiers based on PE-PCDs are prototype-based classifiers such that the
exact minimum number of prototypes (equivalent to minimum dominating sets) are
found in polynomial time on the number of observations. We construct two types
of classifiers based on PE-PCDs. One is a family of hybrid classifiers depend
on the location of the points of the training data set, and another type is a
family of classifiers solely based on class covers. We assess the
classification performance of our PE-PCD based classifiers by extensive Monte
Carlo simulations, and compare them with that of other commonly used
classifiers. We also show that, similar to CCCD classifiers, our classifiers
are relatively better in classification in the presence of class imbalance.
