PIECE-WISE MULTILINEAR PREDICTION FROM FCV DISJOINT PRINCIPAL COMPONENT MODELS∗

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Abstract
The fuzzy c-varieties (FCV) family of pattern recognition algorithms can be interpreted as furnishing a simultaneous fit of experimental multi-dimensional data with class substructure to a specified number of disjoint principal component models. A method is developed which uses these class models for multilinear orthogonal prediction of any of the measurement variables from known values of the remaining ones. This piece-wise multilinear regression technique effectively takes into account nonlinearities in the total data and also the presence of within-class measurement collinearities. The method allows useful and accurate regression results to be obtained where traditional single-class methods of multilinear regression do not.

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