The problem of finding the number and location of
clusters is technically difficult because the
problem is reasonably ill-posed.  Hierarchical clustering methods
produce dendrograms which may be pruned to select one of
many different possible clusterings.
Dendrograms may also be derived from novel approaches such as
the mode tree (Minnotte and Scott, 1993), which records and plots the locations
of all of the modes of a multivariate kernel density estimator for
all bandwidths.
Alternative clustering approaches such as
$k$-means and mixture modeling give answers that
may depend strongly on initial guesses.  The purpose of this
paper is to introduce an algorithm that fits an individual component
of the mixture model, and
to illustrate the use of the resultant estimated
{\it probability density component} as a mechanism for
locating clusters and
generating a mode tree.  However, the new
{\it stochastic mode tree} does not simply find
all modes within the kernel family $\{{\hat f}(x|h),\,0<h<\infty\}$,
but rather performs local density estimation across the data domain.
The resulting figure
greatly reduces the number of plausible clustering configurations.
An interactive algorithm for pruning noisy features is derived
and illustrated with real data.
The results may be used to locate clusters
or to provide initial parameter values for fitting mixture models
in any dimension.
