Visual displays: analytical study and applications to graphs and real data

Principal axis methods such as principal component analysis (PCA) and correspondence analysis (CA) are useful for identifying structures in data through interesting planar graphic displays. However, some kinds of data sets can be dealt alternatively with PCA or CA. This paper focuses on methods, such as PCA and CA, and on visual displays. Our aim is to illustrate the implications for a potential user of selecting either method, and its advantages and disadvantages, from an applied point of view. This is a matter covered broadly in textbooks and elsewhere considering theoretical arguments. Our purpose is to contribute to the comparison between these methods, over the same data set, in order to illustrate them for the practitioner. In the first part of this paper we present a novel analytical study of a binary matrix associated with a non-oriented axis-symmetric graph and show that CA outperforms standardized PCA for the reconstitution and visualization of such kind of graphs. In the second part we present a case using real data dealing with the distribution of employees in different economic sectors for the countries of the European Union, analyzed by means of standardized PCA and two-way CA, in order to see the differences between the two methods in practice.