Abstract: Data objects are usually organized hierarchically, and
the relations between them are analyzed based on a corresponding
concept hierarchy. The relation between data objects, for example how
similar they are, are usually analyzed based on the conceptual distance
in the hierarchy. If a node is an ancestor of another node, it is enough
to analyze how close they are by calculating the distance vertically.
However, if there is not such relation between two nodes, the vertical
distance cannot express their relation explicitly. This paper tries to fill
this gap by improving the analysis method for data objects based on
hierarchy. The contributions of this paper include: (1) proposing an
improved method to evaluate the vertical distance between concepts;
(2) defining the concept horizontal distance and a method to calculate
the horizontal distance; and (3) discussing the methods to confine a
range by the horizontal distance and the vertical distance, and
evaluating the relation between concepts.