Stochastic Data Clustering

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.