加载红酒数据



In [108]:

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

数据处理

转换到ndarray
分成train和test两部分数据
标准化



In [109]:

    
from sklearn.model_selection 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.fit_transform(X_test)

计算协方差矩阵和特征值



In [110]:

    
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)









    



Eigenvalues 
[ 4.8923083   2.46635032  1.42809973  1.01233462  0.84906459  0.60181514
  0.52251546  0.08414846  0.33051429  0.29595018  0.16831254  0.21432212
  0.2399553 ]

可视化主成分



In [111]:

    
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
%matplotlib inline

plt.bar(range(1, 14), var_exp, align='center', label='var')
plt.step(range(1, 14), cum_var_exp, where='mid', label='cum_var')
plt.ylabel('cov')
plt.xlabel('components')
plt.legend(loc='best')
plt.show()

特征映射



In [112]:

    
eigen_pairs = [(np.abs(eigen_vals[i]), eigen_vecs[:, i]) for i in range(len(eigen_vals))]
eigen_pairs.sort(reverse=True)

w = np.hstack((eigen_pairs[0][1][:, np.newaxis], eigen_pairs[1][1][:, np.newaxis]))
X_train_pca = X_train_std.dot(w)

colors = ['r', 'b', 'g']
markers = ['s', 'x', 'o']

# zip [a, b, c] [1, 2, 3] = [(a, 1), (b, 2), (c, 3)]
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('lower left')
plt.show()

使用scikit-learn分析PCA



In [113]:

    
from matplotlib.colors import ListedColormap

def plot_decision_regions(X, y, classifier, resolution=0.02):
    """ 工具方法：分类并画出决策区域图 """
    markers = ('s', 'x', 'o', '^', 'v')
    colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')
    cmap = ListedColormap(colors[:len(np.unique(y))])
    
    # plot the decision surface using contour 
    x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1
    x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1
    xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution), np.arange(x2_min, x2_max, resolution))
    Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)
    Z = Z.reshape(xx1.shape)
    plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap)
    plt.xlim(xx1.min(), xx1.max())
    plt.ylim(xx2.min(), xx2.max())
    
    # plot class sample
    for idx, cl in enumerate(np.unique(y)):
        plt.scatter(x=X[y == cl, 0], y=X[y == cl, 1], c=cmap(idx), marker=markers[idx], label=cl)
        
# 使用sklearn库提供的PCA
from sklearn.linear_model import LogisticRegression
from sklearn.decomposition import PCA

pca = PCA(n_components=2)
lr = LogisticRegression()

X_train_pca = pca.fit_transform(X_train_std)
X_test_pca = pca.fit_transform(X_test_std)

# 输出方差贡献率
print('方差和方差贡献率')
print(pca.explained_variance_)
print(pca.explained_variance_ratio_)

lr.fit(X_train_pca, y_train)
plot_decision_regions(X_train_pca, y_train, classifier=lr)
plt.xlabel('PC1')
plt.ylabel('PC2')
plt.legend(loc='lower left')
plt.show()









    



方差和方差贡献率
[ 4.48463954  2.72639812]
[ 0.34497227  0.20972293]

查看测试集的表现



In [114]:

    
# 测试集合*-1翻转数据
plot_decision_regions(X_test_pca * -1, y_test, classifier=lr)
plt.xlabel('PC1')
plt.ylabel('PC2')
plt.legend(loc='lower left')
plt.show()