Quimiometria III - Revisitando a análise exploratória dos dados multivariados

In this work, three methods for pattern recognition, used as exploratory data analysis, are revisited. A brief review of principal component analysis, PCA, an unsupervised method, is provided. Next, the Mahalanobis distance and the confidence ellipses usually drawn around the scores samples are discussed. Fisher’s canonical variate analysis (a supervised methodology) is the second method revisited in this work. The third exploratory data analysis methodology addressed is ANOVA-PCA, which uses the analysis of variance to separate variations into main effects, interaction and noise followed by principal component analysis. Unlike the other two, ANOVA-PCA was proposed recently and is still not yet explored in all its capabilities. One advantage of this method is the possibility to calculate the variance of each of the effects involved in the experimental design. The mathematical bases of the three methods are discussed as well as examples are presented.

Keywords:
principal component analysis; Mahalanobis distance; canonical variate analysis; CVA; ANOVA-PCA.