Otimizando funções de Kernel racionais para máquinas de vetores de suporte

Abstract

Machine learning, a subset of artificial intelligence, focuses on the development of mathe matical models that allow computers to learn and make decisions from data. Instead of being explicitly programmed to perform a task, these models employ statistical methods to identify patterns from data and make predictions. At the heart of this paradigm is the development of algorithms capable of modeling non-linear relationships through data. One of these prominent models is the Support Vector Machines, with roots in statistical learning theory, which are supervised learning models that excel in classification tasks by finding the best hyperplane that separates the distinct classes of a labeled dataset. Support Vector Machines have notable popularity in various scenarios due to their generalization ability and handling non-linear decision functions. One of the critical factors influencing its decision function to deal with non-linear problems is the choice of the kernel function, which represents the outcome of the inner product in the high-dimensional space where data is implicitly transformed so that linear models can find non-linear decision functions. While the Radial Basis Function kernel has been a traditional choice and widely used, this work explores the feasibility of rational functions, which are functions defined by the quotient between two polynomials, as kernel functions, optimized by the use of Differen tial Evolution. Thus, the main objective of this work is to build an automated learning methodology for rational functions as kernel functions to investigate the feasibility of achi eving comparable performance to the Radial Basis Function kernel, one of the most used kernel functions, while possibly offering advantages in terms of convergence, complexity and generalization ability. Experiments were conducted using the Pima dataset, and the results show that the rational kernel functions were able to achieve balanced accuracy statistically equal to the Radial Basis Function kernel. This outcome demonstrates the potential of rational functions, with coefficients optimized by Differential Evolution, as a viable alternative for the Support Vector Machines kernel. Moreover, rational functions as a kernel used fewer iterations to converge (84.14% lower) and fewer support vectors (3.84% lower), indicating a less complex model. The results were compared through statistical tests with a confidence level equal to 95%, and they indicate that there is still room in the literature to explore improvements in the use of kernel functions in Support Vector Machines.