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Discriminant Correspondence Analysis

As the name indicates, discriminant correspondence analysis (DCA) is an extension of discriminant analysis (DA) and correspondence analysis (CA). Like discriminant analysis, the goal of DCA is to categorize observations in pre-defined groups, and like correspondence analysis, it is used with nominal variables. The main idea behind DCA is to represent each group by the sum of its observations and to perform a simple CA on the groups by variables matrix. The original observations are then projected as supplementary elements and each observation is assigned to the closest group. The comparison between the a priori and the a posteriori classifications can be used to assess the quality of the discrimination. A similar procedure can be used to assign new observations to categories. The stability of the analysis can be evaluated using cross-validation techniques such as jackknifing or bootstrapping.