Competitive learning methods can also be used for *density
estimation*, i.e. for the generation of an estimate for the
unknown probability density of the input signals.

Another possible goal is *clustering*, where a partition of the
data into subgroups or *clusters* is sought, such that the
distance of data items within the same cluster (intra-cluster
variance) is small and the distance of data items stemming from
different clusters (inter-cluster variance) is large. Many different
flavors of the clustering problem exist depending, e.g., on whether
the number of clusters is pre-defined or should be a result of the
clustering process. A comprehensive overview of clustering methods is
given by Jain and Dubes (1988).

Combinations of competitive learning methods with *supervised
learning* approaches are feasible, too. One possibility are radial basis
function networks (RBFN) where competitive learning is used to
position the radial centers (Fritzke, 1994b; Moody and Darken, 1989). Moreover,
*local linear maps* have been combined with competitive learning
methods (Fritzke, 1995b; Martinetz et al., 1989, 1993; Walter et al., 1990). In the
simplest case for each Voronoi region one linear model is used to
describe the input/output relationship of the data within the Voronoi
region.

Sat Apr 5 18:17:58 MET DST 1997