# Kernel PCA

Published on: January 2, 2022

Kernel PCA is an extension of PCA that allows for the separability of nonlinear data by making use of kernels. The basic idea behind it is to project the linearly inseparable data onto a higher dimensional space where it becomes linearly separable.

Kernel PCA can be summarized as a 4 step process [1]:

1. Construct the kernel matrix from the training dataset

1. If the projected dataset doesn’t have zero mean use the Gram matrix to substitute the kernel matrix .

1. Use to solve for the vector .

2. Compute the kernel principal components