In 1961 Herbert Simon and Albert Ando published the theory behind the
long-term behavior of a dynamical system that can be described by a nearly
uncoupled matrix. Over the past fifty years this theory has been used in a
variety of contexts, including queueing theory, brain organization, and
ecology. In all these applications, the structure of the system is known and
the point of interest is the various stages the system passes through on its
way to some long-term equilibrium.
This paper looks at this problem from the other direction. That is, we
develop a technique for using the evolution of the system to tell us about its
initial structure, and we use this technique to develop a new algorithm for
data clustering.Comment: 23 page