预处理--python实现用scikit-learn实现的线性判别分析（LDA）

python实现用scikit-learn实现的线性判别分析（LDA）

线性判别分析（LDA）可用于特征提取以提高计算效率和减少在非正则化过程中因维数过高而造成的过拟合。
LDA背后的基本概念与PCA非常类似。PCA试图找到数据集中最大方差的正交成分轴，而LDA的目标是寻找和优化具有可分性的特征子空间。

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()

# 是观察测试集上的结果
# 逻辑回归分类器能够用一个二维特征子空间代替原来的13个葡萄酒特征，从而在测试集中对样本进行精确分类
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()

运行结果图：