Title: Inverse multiple correspondence analysis
Authors: Michel van de Velden - Erasmus University Rotterdam (Netherlands) [presenting]
Wilco van den Heuvel - Erasmus Universiteit Rotterdam (Netherlands)
Patrick Groenen - Erasmus University Rotterdam (Netherlands)
Abstract: In correspondence analysis (CA), the aim is to obtain a low-dimensional representation that optimally depicts associations in a two-way contingency table. An important and useful extension of CA is multiple correspondence analysis (MCA). MCA allows a simultaneous representation of the observations (subjects) and the categories of several categorical variables in a space of, user selected, low-dimensionality. For inverse MCA, this low-dimensional solution is given and the aim is to retrieve the original data or, if such is not possible, to identify possibly underlying data sets. In previous work on inverse methods for CA, it was shown that solutions can be found by taking convex combinations of a set of so-called vertices. Moreover, for problems where the original data matrix is of relatively small dimensionality, the complete set of such vertices can be obtained using complete enumeration procedures. However, the proposed methods cannot be applied to larger problems, and are therefore not suited for inverse MCA problems. We take a different approach to the inverse CA and MCA problems, by considering it from an integer programming perspective.