Correspondence analysis for symbolic contingency tables based on interval algebra

AbstractIn this paper, we propose interval algebraic correspondence analysis (IACA), a new correspondence analysis method for interval contingency tables based on interval algebra. The interval contingency table, which is made by counting up the observations measured by two multi-valued variables, is an extension of the classical contingency table. Correspondence analysis for the interval contingency table has been proposed by Rodŕiguez[8] (SymCA); this analysis is based on the centers method in principal component analysis for the interval variables (Cazes, et al.,[2]). However, his method has the disadvantage that when computing statistical indices, the internal variation of intervals is lost. To overcome this problem, we propose a new correspondence analysis through which the internal variation of the interval is retained. A numerical example using IACA is discussed and the usefulness is shown

A least squares approach to Principal Component Analysis for interval valued data

Principal Component Analysis (PCA) is a well known technique the aim of which is to synthesize huge amounts of numerical data by means of a low number of unobserved variables, called components. In this paper, an extension of PCA to deal with interval valued data is proposed. The method, called Midpoint Radius Principal Component Analysis (MR-PCA) recovers the underlying structure of interval valued data by using both the midpoints (or centers) and the radii (a measure of the interval width) information. In order to analyze how MR-PCA works, the results of a simulation study and two applications on chemical data are proposed.Principal Component Analysis, Least squares approach, Interval valued data, Chemical data