FYS-STK4155/doc/MathFoundationML/PythonCode_KernelPCA.ipynb

Nonlinear/Kernel PCA Example#

1. Half-Moon Data##

In [2]:

%matplotlib inline
import matplotlib.pyplot as plt

from sklearn.datasets import make_moons
X, y = make_moons(n_samples=100, random_state=123)

plt.figure(figsize=(8,6))

plt.scatter(X[y==0, 0], X[y==0, 1], color='red', alpha=0.5)
plt.scatter(X[y==1, 0], X[y==1, 1], color='blue', alpha=0.5)

plt.title('A nonlinear 2Ddataset')
plt.ylabel('y coordinate')
plt.xlabel('x coordinate')

plt.show()

2. Linear PCA with Two Principal Components##

In [5]:

from sklearn.decomposition import PCA

scikit_pca = PCA(n_components=2)
X_spca = scikit_pca.fit_transform(X)

plt.figure(figsize=(8,6))
plt.scatter(X_spca[y==0, 0], X_spca[y==0, 1], color='red', alpha=0.5)
plt.scatter(X_spca[y==1, 0], X_spca[y==1, 1], color='blue', alpha=0.5)

plt.title('First 2 principal components after Linear PCA')
plt.xlabel('PC1')
plt.ylabel('PC2')
plt.show()

3. Linear PCA with One Principal Component##

In [6]:

import numpy as np
scikit_pca = PCA(n_components=1)
X_spca = scikit_pca.fit_transform(X)

plt.figure(figsize=(8,6))
plt.scatter(X_spca[y==0, 0], np.zeros((50,1)), color='red', alpha=0.5)
plt.scatter(X_spca[y==1, 0], np.zeros((50,1)), color='blue', alpha=0.5)

plt.title('First principal component after Linear PCA')
plt.xlabel('PC1')

plt.show()

4. Kernel PCA with Radial Basis Function (RBF) Kernel and Two Principal Components##

The radial basis function kernel is

k(x,y) = \exp(-\gamma \|x-y\|^2).

In [7]:

from sklearn.decomposition import KernelPCA

scikit_kpca = KernelPCA(n_components=2, kernel='rbf', gamma=15)
X_skernpca = scikit_kpca.fit_transform(X)

plt.figure(figsize=(8,6))
plt.scatter(X_skernpca[y==0, 0], X_skernpca[y==0, 1], color='red', alpha=0.5)
plt.scatter(X_skernpca[y==1, 0], X_skernpca[y==1, 1], color='blue', alpha=0.5)

plt.text(-0.48, 0.35, 'gamma = 15', fontsize=12)
plt.title('First 2 principal components after RBF Kernel PCA via scikit-learn')
plt.xlabel('PC1')
plt.ylabel('PC2')
plt.show()

5. Kernel PCA with Radial Basis Function (RBF) Kernel and One Principal Components##

In [8]:

scikit_kpca = KernelPCA(n_components=1, kernel='rbf', gamma=15)
X_skernpca = scikit_kpca.fit_transform(X)

plt.figure(figsize=(8,6))
plt.scatter(X_skernpca[y==0, 0], np.zeros((50,1)), color='red', alpha=0.5)
plt.scatter(X_skernpca[y==1, 0], np.zeros((50,1)), color='blue', alpha=0.5)
plt.text(-0.48, 0.007, 'gamma = 15', fontsize=12)
plt.title('First principal component after RBF Kernel PCA')
plt.xlabel('PC1')
plt.show()

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