Proposta de algoritmos para aumento de dados via arquétipos

Abstract

In statistics, archetypes are the most representative extreme observations of a sample or population, from which all others can be written. The Archetypal Analysis (AA) is a multivariate technique that aims to reduce the dimensionality of data through convex combinations of data itself, providing to find and select their archetypes. There are applications of AA in several areas of knowledge, but its potential in sample data augmentation still has not been exploited. When our data set is characterized as missing data or does not have the size needed to make the desired error in statistical inference procedure, there is the idea or need to increase this sample. For this purpose, data augmentation technique consists to introduce non observed data or latent variables by iterative methods or sampling algorithms. Thus, as archetypes allow rewriting the sample elements with a minimum error, generating elements not observed, these could be used to augment data. So the aim of this work was to propose and evaluate the efficiency of data augmentation through archetypes. Three algorithms were programmed to augment sample data using the archetypes (Algorithms 1, 2 and 3 - A1, A2 and A3, respectively), and two simulation studies were conducted to assess and compare the algorithms about the efficacy; testing the random variable distribution, and the estimatives of its parameters, and also to check whether this augment can be run successive times. In addition, was made an application of the algorithms into a real sensory analysis data. All algorithms showed similar results, highlighting the A3, that present an appropriate performance in all scenarios. This algorithm allowed to augment 10% of the initial sample size, without changing the probability distribution, as well as estimatives of its parameters. The study about successive augments also indicated A3 as the most efficient, that was able to augment the sample up to 110% of their initial size by 11 successive augments of 10%. The study with real data allowed to augment the sample size and improve the precision in practiced inference. So it seems safe to perform data augmentation by archetypes suggesting the algorithm 3.