Uma abordagem geométrica para o estudo do problema de classificação binária

Abstract

Binary Classification is an essential task in the field of Machine Learning, where finding a classifier with high accuracy and generalization performance is one of its central problems. This research studies the binary classification problem from a geometric perspective, producing new insights through two main approaches. The first approach is related to the development of evolutionary algorithms and the use of the spherical coordinate system. This part of the research resulted in two evolutionary algorithms: the first, a large-margin classifier, and the second, a classifier that approximates the analytical center. The second approach, based on Computational Geometry, produced an efficient method, which requires finite time, to analyze the relevance of instances in a binary classification problem. This is achieved by reducing the problem to determining if a point is an extreme point of a convex cloud. As a consequence of this reduction, an efficient technique, also capable of being executed in finite time, was developed to determine if a binary classification problem is linearly separable in the input or feature space for a chosen kernel function. It is important to highlight that both the primal and dual representation spaces were considered during the development of these methods, enabling the use of an implicit mapping. The obtained results are competitive with other methods that represent the current state of the art for binary classification.