Cluster Analysis and Lumpability of Large Linear Systems

We consider the use of clustering algorithms for sorting the states of a large linear system into a small number of lumped states which serve as the basis for a low order model. Cluster analysis facilitates identification of a hierarchy of reduced order models which represent nearly or exactly lumpable partitions of the underlying state set. Critera for exact and approximate lumpability will be examined in the context of particular examples of large systems.