Simple Non Symmetrical Correspondence Analysis Antonello D’Ambra 1 , Pietro Amenta 1 and Valentin Rousson 2 1 University of Sannio, Benevento, Italy. andambra@unisannio.it, amenta@unisannio.it. 2 Department of Biostatistics, University of Z¨ urich, Switzerland. rousson@ifspm.unizh.ch. Abstract. Simple Component Analysis (SCA) was introduced by Rousson and Gasser (2004) as an alternative to Principal Component Analysis (PCA). The goal of SCA was to find the ”optimal simple system” of components for a given data set, which are slightly correlated but easier to interpret. Aim of this paper is to consider an extension of SCA to categorical data. In particular, we consider a simple version of the Non Symmetrical Correspondence Analysis (D’Ambra and Lauro, 1989). This last approach can be seen as a centered PCA on the column profile matrix with suit- able metrics enabling the study of a two way contingency table when the behaviour of one variable is supposed to be dependent with respect to the other one. Keywords: Principal components, simple components, interpretability of components, contingency table. 1 Introduction It is well known that principal components are optimal in at least two ways: principal components extract a maximum of the variability of the original variables and they are uncorrelated. The former ensures that a minimum of ”total information” will be missed when looking at the first few principal components. The latter warrants that the extracted information will be orga- nized in an optimal way: we may look at one principal component after the other, separately, without taking into account the rest. Unfortunately, princi- pal components often lack interpretability. They define some abstract scores which often are not meaningful, or not well interpretable in practice. As con- sequence of this aspect all the methods which are PCA based could have the same remark. Simple Component Analysis was introduced by Rousson and Gasser (2004) as an alternative to Principal Component Analysis. The goal of SCA was to