kpca.py

import numpy as np
import matplotlib.pyplot as plt

from sklearn.decomposition import PCA, KernelPCA
from sklearn.datasets import make_circles

# Set the seed for random number generator
np.random.seed(7)

# Generate samples
X, y = make_circles(n_samples=500, factor=0.2, noise=0.04)

# Perform PCA
pca = PCA()
X_pca = pca.fit_transform(X)

# Perform Kernel PCA
kernel_pca = KernelPCA(kernel="rbf", fit_inverse_transform=True, gamma=10)
X_kernel_pca = kernel_pca.fit_transform(X)
X_inverse = kernel_pca.inverse_transform(X_kernel_pca)

# Plot original data
class_0 = np.where(y == 0)
class_1 = np.where(y == 1)
plt.figure()
plt.title("Original data")
plt.plot(X[class_0, 0], X[class_0, 1], "ko", mfc='none')
plt.plot(X[class_1, 0], X[class_1, 1], "kx")
plt.xlabel("1st dimension")
plt.ylabel("2nd dimension")

# Plot PCA projection of the data
plt.figure()
plt.plot(X_pca[class_0, 0], X_pca[class_0, 1], "ko", mfc='none')
plt.plot(X_pca[class_1, 0], X_pca[class_1, 1], "kx")
plt.title("Data transformed using PCA")
plt.xlabel("1st principal component")
plt.ylabel("2nd principal component")

# Plot Kernel PCA projection of the data
plt.figure()
plt.plot(X_kernel_pca[class_0, 0], X_kernel_pca[class_0, 1], "ko", mfc='none')
plt.plot(X_kernel_pca[class_1, 0], X_kernel_pca[class_1, 1], "kx")
plt.title("Data transformed using Kernel PCA")
plt.xlabel("1st principal component")
plt.ylabel("2nd principal component")

# Transform the data back to original space
plt.figure()
plt.plot(X_inverse[class_0, 0], X_inverse[class_0, 1], "ko", mfc='none')
plt.plot(X_inverse[class_1, 0], X_inverse[class_1, 1], "kx")
plt.title("Inverse transform")
plt.xlabel("1st dimension")
plt.ylabel("2nd dimension")

plt.show()