Análise comparativa entre os métodos decomposição em valores singulares e análise de componentes principais envolvendo matrizes esparsas de grande porte

Abstract

The Singular Value Decomposition and Principal Component Analysis techniques are from different areas and have different purposes. Nevertheless, they are often confused. Moreover, apart from more theoretical works, few studies know which technique to use. Questions such as: can a less elaborate choice between the techniques degrade the quality of a task? and when to use each one? are neglected in the literature. In addition, the eficient manipulation and analysis of large volumes of data has become a computational challenge due to the high dimensionality and sparsity of data, which makes it important to use techniques that benefit both the performance and the quality of analysis. However, current studies do not compare the use of those techniques, especially in sparse matrices of high order. So our goal is to compare and find differences between the two techniques on data classification task.