  Tagging items with descriptive annotations or keywords is a very natural way
to compress and highlight information about the properties of the given entity.
Over the years several methods have been proposed for extracting a hierarchy
between the tags for systems with a "flat", egalitarian organization of the
tags, which is very common when the tags correspond to free words given by
numerous independent people. Here we present a complete framework for automated
tag hierarchy extraction based on tag occurrence statistics. Along with
proposing new algorithms, we are also introducing different quality measures
enabling the detailed comparison of competing approaches from different
aspects. Furthermore, we set up a synthetic, computer generated benchmark
providing a versatile tool for testing, with a couple of tunable parameters
capable of generating a wide range of test beds. Beside the computer generated
input we also use real data in our studies, including a biological example with
a pre-defined hierarchy between the tags. The encouraging similarity between
the pre-defined and reconstructed hierarchy, as well as the seemingly
meaningful hierarchies obtained for other real systems indicate that tag
hierarchy extraction is a very promising direction for further research with a
great potential for practical applications.
