預處理（3）：python實現用scikit-learn實現的線性判別分析（LDA）

線性判別分析（LDA）可用於特徵提取以提高計算效率和減少在非正則化過程中因維數過高而造成的過擬合。
LDA背後的基本概念與PCA非常類似。PCA試圖找到資料集中最大方差的正交成分軸，而LDA的目標是尋找和優化具有可分性的特徵子空間。

import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
import numpy as np
import matplotlib.pyplot as plt
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA
from matplotlib.colors import ListedColormap
from sklearn.linear_model import LogisticRegression

df_wine = pd.read_csv('xxx\wine.data',
                      header=None)

df_wine.columns = ['Class label', 'Alcohol', 'Malic acid', 'Ash',
                   'Alcalinity of ash', 'Magnesium', 'Total phenols',
                   'Flavanoids', 'Nonflavanoid phenols', 'Proanthocyanins',
                   'Color intensity', 'Hue',
                   'OD280/OD315 of diluted wines', 'Proline']

df_wine.head()

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,
                     stratify=y,
                     random_state=0)

sc = StandardScaler()
X_train_std = sc.fit_transform(X_train)
X_test_std = sc.transform(X_test)

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=0.6,
                    c=cmap(idx),
                    edgecolor='black',
                    marker=markers[idx],
                    label=cl)

lda = LDA(n_components=2)
X_train_lda = lda.fit_transform(X_train_std, y_train)
lr = LogisticRegression()
lr = lr.fit(X_train_lda, y_train)

plot_decision_regions(X_train_lda, y_train, classifier=lr)
plt.xlabel('LD 1')
plt.ylabel('LD 2')
plt.legend(loc='lower left')
plt.tight_layout()
# plt.savefig('images/05_09.png', dpi=300)
plt.show()

# 是觀察測試集上的結果
# 邏輯迴歸分類器能夠用一個二維特徵子空間代替原來的13個葡萄酒特徵，從而在測試集中對樣本進行精確分類
X_test_lda = lda.transform(X_test_std)

plot_decision_regions(X_test_lda, y_test, classifier=lr)
plt.xlabel('LD 1')
plt.ylabel('LD 2')
plt.legend(loc='lower left')
plt.tight_layout()
# plt.savefig('images/05_10.png', dpi=300)
plt.show()

執行結果圖：

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