Dimensionality reduction methods for contingency tables with ordinal variables

Several extensions of correspondence analysis have been introduced in literature coping with the possible ordinal structure of the variables. They usually obtain a graphical representation of the interdependence between the rows and columns of a contingency table, by using several tools for the dimensionality reduction of the involved spaces. These tools are able to enrich the interpretation of the graphical planes, providing also additional information, with respect to the usual singular value decomposition. The main aim of this paper is to suggest an unified theoretical framework of several methods of correspondence analysis coping with ordinal variables.