Modelos de mistura normal/independente via processo pontual por determinante e seu uso para redução de dimensionalidade em variáveis categóricas

Abstract

With the increasing volume of data currently available, it is essential to have efficient methods to organize, explore and extract knowledge from this data. Cluster analysis is a powerful approach to dealing with this large amount of information and identifying beneficial patterns, which have gained more notoriety with the popularization of machine learning. This work provides a flexible unsupervised clustering method that incorporates the repulsion characteristic in the behavior of the location parameters, the clusters representing: a Finite Mixture Model of Normal/Independent Distributions developed considering the behavior of the location parameters as a realization of a Determinantal Point Process (DPP) probability distribution that avoids the creation of redundant groups through its natural characteristic of repulsion of points. The proposal extends a known model in the literature providing a priori an uncertainty structure to the PPD parameters, proposing an approach for its estimation. We introduce the proposal for density estimation with a simulation study that exalts the model's ability to correctly estimate the number of groups and the allocation of individuals in these groups, in addition to an application in agribusiness demand data in banana plantations. The model was also used in the linear regression context to deal with latent groups and dimensionality reduction, especially for categorical variables with many levels. The proposal offers an alternative to the use of LASSO-type penalties. The effects of specifying the model's parameters were evaluated on dimensionality reduction, comparing it with existing models in the literature for analyzing education data. The model allows robust grouping and proven parsimonious estimating of the number of groups compared to the other models. Furthermore, we developed a complete Markov Chain Monte Carlo (MCMC) algorithm to estimate the model parameters, following the Bayesian paradigm, and we available its implementation in R.