  The outlying property detection problem is the problem of discovering the
properties distinguishing a given object, known in advance to be an outlier in
a database, from the other database objects. In this paper, we analyze the
problem within a context where numerical attributes are taken into account,
which represents a relevant case left open in the literature. We introduce a
measure to quantify the degree the outlierness of an object, which is
associated with the relative likelihood of the value, compared to the to the
relative likelihood of other objects in the database. As a major contribution,
we present an efficient algorithm to compute the outlierness relative to
significant subsets of the data. The latter subsets are characterized in a
"rule-based" fashion, and hence the basis for the underlying explanation of the
outlierness.
