Chapter 17: Nonlinear Support Vector Machines
Many classification problems warrant nonlinear decision boundaries. This chapter introduces nonlinear support vector machines as a crucial extension to the linear variant.
-
Chapter 17.01: Feature Generation for Nonlinear Separation
We show how nonlinear feature maps project the input data to transformed spaces, where they become linearly separable.
-
Chapter 17.02: The Kernel Trick
In this section, we show how nonlinear SVMs work their magic by introducing nonlinearity efficiently via the kernel trick.
-
Chapter 17.03: The Polynomial Kernel
In this section, we introduce the polynomial kernel in the context of SVMs and demonstrate how different polynomial degrees affect decision boundaries.
-
Chapter 17.04: Reproducing Kernel Hilbert Space and Representer Theorem
In this section, we introduce important theoretical background on nonlinear SVMs that essentially allows us to express them as a weighted sum of basis functions.
-
Chapter 17.05: The Gaussian RBF Kernel
In this section, we introduce the popular Gaussian RBF kernel and discuss its properties.
-
Chapter 17.06: SVM Model Selection
In this section, we discuss the importance of SVM hyperparameters for adequate solutions.