Aplicações da álgebra linear à análise fatorial de correspondências

Abstract

Multidimensional Data Analysis has received considerable development in recent decades, especially since the 1970s. The reasons for this are, in particular: 1) the availability of high-capacity and high-capacity data storage which allowed the "mise-au-point" (in operational terms) of methods whose interest was only of theoretical order, until then, besides the stimulus for the formulation and the test of new methods, more and more perfected; 2) the need to have efficient procedures for the simultaneous analysis of possible mutual relationships between the various variables involved in the formulation of technical-scientific problems or resulting from the systematic application of socio-economic surveys, etc. By multidimensional data analysis it is understood in principle the application of such methods, along with its computational counterpart (corresponding to the development and implementation of respective software), for the analysis of large data tables. In fact, Data Analysis groups many methods from which we can distinguish two main branches: Automatic Classification, which consists of classifying statistical units with the help of previously established algorithms, and Factorial Analysis, which uses properties of Euclidean vector spaces of which the Correspondence Analysis is part, subject of this monograph. Factorial Correspondence Analysis is a recent technique, developed in particular by the research team of Professor J.P BENZÉCRI, at the University of Paris VI. Initially limited to the study of contingency tables, that is, to study the dependence between qualitative characters; such study is performed through flat graphical representations and parameters that allow interpreting them. There are several ways to introduce Match Analysis. The one discussed here is based on Principal Component Analysis, which in turn consists of describing a set of individuals and a set of quantitative characters. Correspondence Analysis will be presented as a Double Principal Component Analysis. Basically, we will study here: Principal Component Analysis, Correspondence Analysis and Multiple Correspondence Analysis.