Kernel PCA in R
Introduction
Welcome, learners! Today, we embark on an exciting chapter on non-linear dimensionality reduction techniques, focusing on Kernel Principal Component Analysis (Kernel PCA), an extension of Principal Component Analysis (PCA). Kernel PCA enhances the capabilities of PCA by enabling it to handle non-linear relationships in data.
In this lesson, you will learn the theoretical foundations of Kernel PCA, the importance of kernel selection, and how to apply Kernel PCA in practice using R. We will use the kernlab package for Kernel PCA and ggplot2 for data visualization.
Theoretical Insight: Kernel PCA
Kernel PCA is a powerful variant of PCA that efficiently handles non-linear transformations through kernel methods. The "Kernel Trick" allows us to map input data into a higher-dimensional feature space, making it possible to separate data that is not linearly separable in the original space.
Kernels are essential for measuring similarity between observations. Choosing the right kernel — such as linear, polynomial, or radial basis function (RBF) — is crucial for the performance of Kernel PCA.
Creating a Non-Linearly Separable Dataset
