ch5-PCA1.py

import pandas as pd
df_wine = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data', header=None)

# Split and Normalize dataset
from sklearn.cross_validation import train_test_split
from sklearn.preprocessing import StandardScaler
X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values
X_train, X_test, y_train, y_test = train_test_split(X, y,test_size=0.3, random_state=0)
sc = StandardScaler()
X_train_std = sc.fit_transform(X_train)
X_test_std = sc.transform(X_test)


# Calculate Covariance Matrix and Eigen Vectors/Values
import numpy as np
cov_mat = np.cov(X_train_std.T)
eigen_vals, eigen_vecs = np.linalg.eig(cov_mat)
print('\nEigenvalues \n%s' % eigen_vals)

# Plot graph
tot = sum(eigen_vals)
var_exp = [(i / tot) for i in sorted(eigen_vals, reverse=True)]
cum_var_exp = np.cumsum(var_exp)
import matplotlib.pyplot as plt
plt.bar(range(1,14), var_exp, alpha=0.5, align='center', label='individual explained variance')
plt.step(range(1,14), cum_var_exp, where='mid',label='cumulative explained variance')
plt.ylabel('Explained variance ratio')
plt.xlabel('Principal components')
plt.legend(loc='best')
plt.show()

# Sort the eigenpairs by decreasing order of the eigenvalues:
eigen_pairs =[(np.abs(eigen_vals[i]),eigen_vecs[:,i]) for i in range(len(eigen_vals))]
eigen_pairs.sort(reverse=True)

# Pick k eigenvectors (k=2 here)
w= np.hstack((eigen_pairs[0][1][:, np.newaxis],eigen_pairs[1][1][:, np.newaxis]))

# Perform PCA
X_train_pca = X_train_std.dot(w)


# PLot PCAed data
colors = ['r', 'b', 'g']
markers = ['s', 'x', 'o']
for l, c, m in zip(np.unique(y_train), colors, markers):
    plt.scatter(X_train_pca[y_train==l, 0], X_train_pca[y_train==l, 1],  c=c, label=l, marker=m)
    plt.xlabel('PC 1')
    plt.ylabel('PC 2')
    plt.legend(loc='lower left')
    plt.show()