一、主成分分析
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原理
最终不断压缩团圆范围,坐落于椭圆内的点为主要影响因素,实现降维操作
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代码实现
数据:
Alcohol,Malic_Acid,Ash,Ash_Alcanity,Magnesium,Total_Phenols,Flavanoids,Nonflavanoid_Phenols,Proanthocyanins,Color_Intensity,Hue,OD280,Proline,Customer_Segment 14.23,1.71,2.43,15.6,127,2.8,3.06,0.28,2.29,5.64,1.04,3.92,1065,1 13.2,1.78,2.14,11.2,100,2.65,2.76,0.26,1.28,4.38,1.05,3.4,1050,1 13.16,2.36,2.67,18.6,101,2.8,3.24,0.3,2.81,5.68,1.03,3.17,1185,1 14.37,1.95,2.5,16.8,113,3.85,3.49,0.24,2.18,7.8,0.86,3.45,1480,1 13.24,2.59,2.87,21,118,2.8,2.69,0.39,1.82,4.32,1.04,2.93,735,1 ... 此数据为酒中不同数量成分的组合最终合成酒的种类,共分为了1,2,3三种不同种类
实现步骤:
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 PCA import matplotlib.pyplot as plt import pandas as pd import numpy as np dataset = pd.read_csv("Wine.csv") X = dataset.iloc[:, 0:-1].values y = dataset.iloc[:, -1].values # 划分数据集为训练集和测试集 X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0) # 特征缩放 sc_X = StandardScaler() X_train = sc_X.fit_transform(X_train) X_test = sc_X.transform(X_test) # 利用PCA对数据降维 pca = PCA(n_components=2) # n_components: 新的自变量的个数 X_train = pca.fit_transform(X_train) X_test = pca.transform(X_test) explained_varance = pca.explained_variance_ratio_ # 解释方差的百分比, 用来确定新自变量的个数 # 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()
输出结果:
训练结果
测试结果: