Joint Mathematics Junior Colloquium
Foundations of support vector machines. The role of kernels
Speaker: Diego Serrano Ortega (Universidad Autónoma de Madrid)Date: Wednesday, 22 May 2024 - 17:00 (coffe break a las 16:30)Place: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Abstract:
Support vector machines (commonly known as SVMs) are one of the most widely used supervised statistical learning algorithms for data analysis, particularly in classification problems. In this talk, we will explain the mathematical foundations of SVMs, analyzing the optimization problem of hard margin and soft margin classifiers. One of the key parts of SVMs is the use of kernels, which allow working with nonlinear data through a mapping to higher dimensions where the data is separable. We will study the theory of kernels from an analytical point of view and provide a perspective of these functions as similarity measures, which facilitates and allows a new interpretation of the role of kernels within SVMs. We will also review and analyze the most relevant examples, with special attention to kernels of orthogonal polynomials.
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