一、Kernel PCA(将线性不可分转化为线性可分)

1. 原理

   

2. 代码实现

   数据：

    User ID  Gender   Age  EstimatedSalary  Purchased
   15624510    Male  19.0          19000.0          0
   15810944    Male  35.0          20000.0          0
   15668575  Female  26.0          43000.0          0
   ...
   对于不同用户信息，是否会对投放广告进行点击
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   代码：

   from sklearn.model_selection import train_test_split
   from sklearn.linear_model import LogisticRegression
   from sklearn.preprocessing import StandardScaler
   from sklearn.metrics import confusion_matrix
   from matplotlib.colors import ListedColormap
   from sklearn.decomposition import KernelPCA
   import matplotlib.pyplot as plt
   import pandas as pd
   import numpy as np
   
   # Importing the dataset
   dataset = pd.read_csv('Social_Network_Ads.csv')
   X = dataset.iloc[:, [2, 3]].values
   y = dataset.iloc[:, 4].values
   
   # Splitting the dataset into the Training set and Test set
   X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=0)
   
   # Feature Scaling
   sc_X = StandardScaler()
   X_train = sc_X.fit_transform(X_train)
   X_test = sc_X.transform(X_test)
   
   
   # 构建kernel PCA
   kpca = KernelPCA(n_components=2, kernel="rbf")  # kernel="rbf": 高斯核函数
   X_train = kpca.fit_transform(X_train)
   X_test = kpca.transform(X_test)
   
   
   # 逻辑回归拟合数据
   classifier = LogisticRegression(random_state=0)
   classifier.fit(X_train, y_train)
   
   # 预测测试集
   y_pred = classifier.predict(X_test)
   
   # 构建混淆矩阵
   cm = confusion_matrix(y_test, y_pred)
   
   # 画图
   X_set, y_set = X_train, y_train
   X1, X2 = np.meshgrid(np.arange(start=X_set[:, 0].min() - 1, stop=X_set[:, 0].max() + 1, step=0.01),
                        np.arange(start=X_set[:, 1].min() - 1, stop=X_set[:, 1].max() + 1, step=0.01))
   plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),
                alpha=0.75, cmap=ListedColormap(('red', 'green', 'black')))
   plt.xlim(X1.min(), X1.max())
   plt.ylim(X2.min(), X2.max())
   for i, j in enumerate(np.unique(y_set)):
       plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
                   c=ListedColormap(('orange', 'blue', 'grey'))(i), label=j)
   plt.title('Logistic Regression (Training set)')
   plt.xlabel('pc1')
   plt.ylabel('pc2')
   plt.legend()
   plt.show()
   
   
   X_set, y_set = X_test, y_test
   X1, X2 = np.meshgrid(np.arange(start=X_set[:, 0].min() - 1, stop=X_set[:, 0].max() + 1, step=0.01),
                        np.arange(start=X_set[:, 1].min() - 1, stop=X_set[:, 1].max() + 1, step=0.01))
   plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),
                alpha=0.75, cmap=ListedColormap(('red', 'green', 'black')))
   plt.xlim(X1.min(), X1.max())
   plt.ylim(X2.min(), X2.max())
   for i, j in enumerate(np.unique(y_set)):
       plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
                   c=ListedColormap(('orange', 'blue', 'grey'))(i), label=j)
   plt.title('Logistic Regression (Test set)')
   plt.xlabel('pc1')
   plt.ylabel('pc2')
   plt.legend()
   plt.show()
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   输出结果：
   训练结果：
   
   测试结果：