Variational Data Analysis Versus Classical Data Analysis

Summary In (1) and (2) we have proposed a new theory of classification called the S theory. This theory contains the family of the Scaldiscal classification criteria which can handle both quantitative and categorical data as a generalization of the new Condorcet classification criterion which can only handle categorical data. This Scaldiscal classification criteria family is itself a particular case of the variational criteria family we are going to see now in the general framework of Variational Analysis. Compared to the classical classification criteria, the variational classification criteria have two important advantages detailed in the S theory. They can be optimized in an order n (in terms of memory space and elementary operations), n being the number of elements to classify. They can be used for truly automatic classification since their optimization leads to a non-obvious partition when the optimization of classical classification criteria, like the within class inertia criterion, leads to an obvious and uninteresting partition. For these reasons variational classification criteria seem to be a nice substitute to classical classification criteria.