以下ではまずscikit-learnの機能を使わずに主成分分析を行う。
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# データの取得と前処理（標準化）
import pandas as pd
df_wine = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data', header=None)
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)
In [3]:
import numpy as np
cov_mat = np.cov(X_train_std.T)
eigen_vals, eigen_vecs = np.linalg.eig(cov_mat)
print(eigen_vals)
print(eigen_vecs)
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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 exp var')
plt.step(range(1,14), cum_var_exp, where='mid', label='cum exp var')
plt.ylabel('ex')
plt.xlabel('prin')
plt.legend(loc='best')
plt.show()
In [9]:
# 固有値の大きいものから固有対を並び替える
eigen_pairs = [(np.abs(eigen_vals[i]), eigen_vecs[:,i]) for i in range(len(eigen_vals))]
eigen_pairs.sort(key=lambda k: k[0], reverse=True)
# 最も大きい２つの固有値に対応する固有ベクトルを集める
w = np.hstack((eigen_pairs[0][1][:, np.newaxis], eigen_pairs[1][1][:, np.newaxis]))
print('Matrix W:\n',w)
In [13]:
# 124 x 13 の特徴量を124 x 2 に変換
X_train_pca = X_train_std.dot(w)
print(X_train_std.shape)
print(w.shape)
print(X_train_pca.shape)
In [16]:
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.xlabel('PC 2')
plt.legend(loc='lower left')
plt.show()
In [17]:
# scikit-learnのPCAクラスを使用した場合
from matplotlib.colors import ListedColormap
def plot_decision_regions(X, y, classifier, resolution=0.02):
# setup marker generator and color map
markers = ('s', 'x', 'o', '^', 'v')
colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')
cmap = ListedColormap(colors[:len(np.unique(y))])
# plot the decision surface
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 samples
for idx, cl in enumerate(np.unique(y)):
plt.scatter(x=X[y == cl, 0], y=X[y == cl, 1],
alpha=0.8, c=cmap(idx),
edgecolor='black',
marker=markers[idx],
label=cl)
In [19]:
from sklearn.linear_model import LogisticRegression
from sklearn.decomposition import PCA
# 主成分数2で初期化
pca = PCA(n_components=2)
lr=LogisticRegression()
X_train_pca = pca.fit_transform(X_train_std)
X_test_pca = pca.transform(X_test_std)
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()
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