Fuzzy crisp complete disjunctive coding system

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The SGCA of symbolic data (Verde 1997, 1999) is based on an extension of classic generalized canonical analysis (Volle, 1985). The decomposition criterion in the analysis is the squared multiple correlation index computed on coded symbolic variables. The analysis is performed on a coding matrix of the SO descriptions where each row identifies the coordinates of the vertices of the hypercubes associated with each SO in the representation space.

Similarly to the other factor methods (principal component analysis, factor discriminant analysis) employed in SDA, SGCA is a multi-step symbolic–numerical–symbolic procedure. This means it is based on an intermediate coding phase in order to homogenize different kinds of descriptors using, for instance, a fuzzy or a crisp (complete disjunctive) coding system. Therefore, the symbolic nature of the input data is retrieved in a symbolic interpretation of the output.