PCA is good at reducing the number of dimensions, but it works in a linear manner. If the data is not organized in a linear fashion, PCA fails to do the required job. This is where Kernel PCA comes into the picture. You can learn more about it at http://www.ics.uci.edu/~welling/classnotes/papers_class/Kernel-PCA.pdf. Let's see how to perform Kernel PCA on the input data and compare it to how PCA performs on the same data.

- Create a new Python file, and import the following packages:
import numpy as np import matplotlib.pyplot as plt from sklearn.decomposition import PCA, KernelPCA from sklearn.datasets import make_circles

- Define the seed value for the random number generator. This is needed ...

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