Principal Ellipsoid Analysis
Résumé
In Applied Statistics 2007 Conference a formal approach of redundancy among multivariate data has been presented. This approach leads to information measures of multivariate tables different with those usually used and particularly with the trace criterion of Principal Components Analysis but rather consistent with some interesting proposals. A new dimensional reduction method consistent with the former formal approach is presented in order to provide a consistent way to analyse multivariate data and to get some valuable representations. It is called ``principal Ellipsoïd Analysis" because it is connected with the ``minimum spanning (or enclosing) ellipsoid". The comparison of this method with classical Principal Component Analysis is detailed and a real data set is worked on to appreciate the differences from an applied point of view. The link between the method and a new kind of ``robustness" is highlighted and some extensions are evocated.