  We develop an effective nonhierarchical data clustering method using an
analogy to the dynamic coarse graining of a stochastic system. Analyzing the
eigensystem of an interitem transition matrix identifies fuzzy clusters
corresponding to the metastable macroscopic states (macrostates) of a diffusive
system. A "minimum uncertainty criterion" determines the linear transformation
from eigenvectors to cluster-defining window functions. Eigenspectrum gap and
cluster certainty conditions identify the proper number of clusters. The
physically motivated fuzzy representation and associated uncertainty analysis
distinguishes macrostate clustering from spectral partitioning methods.
Macrostate data clustering solves a variety of test cases that challenge other
methods.
