The Radial Basis Function (RBF) kernel is one of the most powerful, useful, and popular kernels in the Support Vector Machine (SVM) family of classifiers. In this article, we’ll discuss what exactly makes this kernel so powerful, look at its working, and study examples of it in action. We’ll also provide code samples for implementing the RBF kernel from scratch in Python that illustrates how to use the RBF kernel on your own data sets. Let’s dive in!...
What are Kernels in SVM?
SVM is an algorithm that has shown great success in the field of classification. It separates the data into different categories by finding the best hyperplane and maximizing the distance between points. To this end, a kernel function will be introduced to demonstrate how it works with support vector machines. Kernel functions are a very powerful tool for exploring high-dimensional spaces. They allow us to do linear discriminants on nonlinear manifolds, which can lead to higher accuracies and robustness than traditional linear models alone.
If you want to have a quick overview of SVM kernels, check this article: SVM Kernels: Polynomial Kernel - From Scratch Using Python.
The kernel function is just a mathematical function that converts a low-dimensional input space into a higher-dimensional space. This is done by mapping the data into a new feature space. In this space, the data will be linearly separable. This means that a support vector machine can be used to find a hyperplane that separates the data.
For example, if the input 𝑥 is two-dimensional, the kernel function will map it into a three-dimensional space. In this space, the data will be linearly separable.
In addition, they provide more features than those of other algorithms such as neural networks or tree ensembles in some kinds of problems involving handwritten recognition, face detection, etc because they extract intrinsic properties of data points through a kernel function.