  Building on a specific formalization of analogical relationships of the form
"A relates to B as C relates to D", we establish a connection between two
important subfields of artificial intelligence, namely analogical reasoning and
kernel-based machine learning. More specifically, we show that so-called
analogical proportions are closely connected to kernel functions on pairs of
objects. Based on this result, we introduce the analogy kernel, which can be
seen as a measure of how strongly four objects are in analogical relationship.
As an application, we consider the problem of object ranking in the realm of
preference learning, for which we develop a new method based on support vector
machines trained with the analogy kernel. Our first experimental results for
data sets from different domains (sports, education, tourism, etc.) are
promising and suggest that our approach is competitive to state-of-the-art
algorithms in terms of predictive accuracy.
