Many kinds of texts are now available in various types of databases,
and it has been requested to develop new methods to fully utilize them
in a wide range of applications.  In the field of information
retrieval of full text databases, the vector-space model has been
developed over 20 years (Salton et
al.~\cite{salton-cacm,salton-science}), and further the so-called
latent semantic indexing based on the singular value decomposition of
the corresponding matrix in the vector-space model has been
demonstrated to find latent semantics (e.g., see Berry and Dumais
\cite{berry-dumais}).  This kind of geometric model has also be used
in image databases (e.g., see Faloutsos et al \cite{faloutsos-al}).

This paper investigates the problem of
learning some useful classifications in these databases as an
unsupervised learning in such geometric setting.
We clarify underlying geometric structures
for them, and, based on the distances (similarity/dissimilarity
measures) in the above-mentioned existing research, propose
using geometric clustering algorithms for variance-based clustering
developed by our groups in a space normalized by the $L_2$ norm.
We also mention using the Kullback-Leibler divergence as a measure
when another normalization is used.