Active classification of structures is an example of wave interrogation of complex environments. An algorithmic architecture is suggested that decomposes global complexity into problem-dependent clusters which interact across interfaces. A cluster is treated either analytically (preferably based on good physics) or numerically, deterministically and/or stochastically, etc., and the interconnects between clusters map representations on one side into those on the other side, subject to the continuity requirements of the relevant field equations. Projecting the field problem onto the cluster boundaries gives rise to a network formulation that impacts the analytic as well as numerical strategies. This field-based approach is coupled to, and modified by, considerations of signal processing. The challenge in the implementation is to effect an ``optimal'' decomposition into tractable clusters, and to treat each cluster problem in a fashion that anticipates its role as part of a larger conglomerate, taking into account the limitations imposed by the intended pre- and post-processing. Example scenarios are presented to illustrate these concepts.