Análise de Arquétipos: introdução a teoria e aplicações

Abstract

There are several techniques that aid in the interpretation and analysis of multivariate data. One of the most widespread techniques used and is the Principal Component Analysis, which aims to reduce the dimensionality of the data in order to facilitate interpretation. The Archetypal Analysis is also a multivariate technique that seeks to reduce the dimensionality of the data, but through convex combinations of the data itself. Archetypes are selected by minimizing the residual sum of squares that is the mistake to reconstruct the original data using the archetypes. This work aimed to explore in more detail the Archetypal Analysis and trace its history, and to identify capabilities of existing and future applications in various areas of knowledge. More specifically it aimed to: describe in detail the Archetypal analysis, identify similarities and differences between the Archetypal Analysis and Principal Component Analysis, conduct simulation studies to assess how best metric for measuring the lack of fit of the data recomposed by archetypes, apply the Archetypal Analysis on data of the movement of soccer players, perform Monte Carlo simulations to assess whether there is some gain in performing Archetypal Analysis in conjunction with the Principal Component Analysis, and apply this to experimental sensory data of burgers. The methodologies used were an extensive literature review and Monte Carlo simulations. The results showed that the Archetypal Analysis is a technique with wide applicability and excellent practical results. The study of metrics concluded that the residual sum of squares should be used because it is the simplest, and that there is no harm in using this metric compared to the others tha was studied. In the context of the soccer, Archetypal Analysis was able to verify that the player or group of players are in their designated space, the offensive or defensive behavior among others, being a new approach to be used in conjunction with other techniques for this purpose. About the study of simulation designed to implement both techniques, was evidenced a improvement of reconstruction capacity and in the interpretability.