C-ANALYSIS OF C-STRUCTURES: REPRESENTATION AND EVALUATION OF RECONSTRUCTION HYPOTHESES BY INFORMATION MEASURES†‡

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Abstract
C-Analysis, or Constraint Analysis, is concerned with the study of the decomposability (reconstructability) of multidimensional relations upon which a probability distribution may or may not be defined. This paper deals with the former case, and the approach taken is based on concepts derived from general information theory. C-structures21 constitute a particular class of structures which can be viewed as one canonical representation of an equivalence class of so-called general structures based on a particular graph. A C-structure derives its importance from its uniqueness which is based on the set of all cliques of a graph. It plays a dominant role in the generation of meaningful structure hypotheses. This paper, after presenting a brief overview of the main concepts and theorems relevant to C-Analysis, focuses on the representation and evaluation aspects of the reconstructability problem as it is defined by Cavallo and Klir.21,22 The ultimate result of the paper is the closed-form representation of all 156 6-variable C-structures by information measures, on the basis of which some useful representation and evaluation algorithms have been constructed. The paper illustrates the use of a combined two-stage (global/local) search procedure, and also provides a heuristic method for relatively fast identification of a good starting reconstruction hypothesis. Various problems of estimation and testing are also discussed at some length.

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