  Clustering methods must be tailored to the dataset it operates on, as there
is no objective or universal definition of ``cluster,'' but nevertheless
arbitrariness in the clustering method must be minimized. This paper develops a
quantitative ``stability'' method of determining clusters, where stable or
persistent clustering signals are used to indicate real structures have been
identified in the underlying dataset. This method is based on modulating
clustering methods by controlling a parameter -- through a thermodynamic
analogy, the modulation parameter is considered ``time'' and the evolving
clustering methodologies can be considered a ``heat flow.'' When the
information entropy of the heat flow is stable over a wide range of times --
either globally or in the local sense which we define -- we interpret this
stability as an indication that essential features of the data have been found,
and create clusters on this basis.
