Title:  PARTIAL MIXTURE ESTIMATION WITH APPLICATION TO CLUSTERING

Authors:  David W. Scott (*) and Chad A. Shaw

Abstract:

The use of density estimation to find clusters in
multivariate data can take several forms.  Nonparametric
approaches may form high-density regions or simply
locate sample modes, as in the mode tree.  A semiparametric
approach is to fit a mixture model and associate each
component with a different cluster.  Here we describe
a hybrid approach, in which we fit a mixture model
using a nonparametric criterion.  Use of the nonparametric
criterion permits local estimation of individual mixture
locations.  From these estimates, a tree of modes may
be formed and tested graphically for weight of evidence.

We use this approach to examine transcriptional patterns
in cDNA microarray experiments using laboratory
preparations of Dictyostelium discoideum, which is a
simple eukaryote that undergoes aggregation and celltype
differentiation when starved.  This organism is a model
system for studying chemotactic aggregation and multicellular
development.  The search for modes ranges from 5 to 13 dimensions.