Análise e aplicações do algoritmo UMAP para classificação e redução de dimensionalidade de conjuntos de dados com múltiplas variáveis

Abstract

Through many real-life applications, gathering information through real instruments subject to noise and imperfections tends to generate datasets where the number of observed variables and components easily exceeds a number of dimensions where manipulation, clustering and classification of said data into distinct sets based on their similarities becomes either difficult or computationally expensive. An efficient way to preemptively prepare this data for further processing and meaningful representation is dimensionality reduction, a process that transforms a dataset from a high-dimensional space to a low-dimensional space such as the low-dimensional space still retains relevant properties from the original dataset. This work proposes to evaluate the current state-of-the-art and establish, using performance criteria, comparisons between the frequently used dimensionality reduction used today and historically, with the main focus on UMAP, a method that seeks to prioritize the classification of data locally close by means of their characteristics. Results were obtained using different datasets with different properties, in order to obtain relevant metrics on the impact that each characteristic of these datasets has on the final results.