  The two most extended density-based approaches to clustering are surely
mixture model clustering and modal clustering. In the mixture model approach,
the density is represented as a mixture and clusters are associated to the
different mixture components. In modal clustering, clusters are understood as
regions of high density separated from each other by zones of lower density, so
that they are closely related to certain regions around the density modes. If
the true density is indeed in the assumed class of mixture densities, then
mixture model clustering allows to scrutinize more subtle situations than modal
clustering. However, when mixture modeling is used in a nonparametric way,
taking advantage of the denseness of the sieve of mixture densities to
approximate any density, then the correspondence between clusters and mixture
components may become questionable. In this paper we introduce two methods to
adopt a modal clustering point of view after a mixture model fit. Numerous
examples are provided to illustrate that mixture modeling can also be used for
clustering in a nonparametric sense, as long as clusters are understood as the
domains of attraction of the density modes.
