降维

主成分分析：

因子载荷矩阵和特殊方差矩阵的估计：

主成分法，主因子法，极大似然法

 1 #协方差矩阵
 2 import numpy as np
 3 X = [[2, 0, -1.4],
 4 [2.2, 0.2, -1.5],
 5 [2.4, 0.1, -1],
 6 [1.9, 0, -1.2]]
 7 print(np.cov(np.array(X).T))
 8 
 9 #特征值与特征向量
10 w, v = np.linalg.eig(np.array([[1, -2], [2, -3]]))
11 print('特征值：{}
特征向量：{}'.format(w,v))
12 
13 
14 #鸢尾花数据集的降维
15 import matplotlib.pyplot as plt
16 from sklearn.decomposition import PCA
17 from sklearn.datasets import load_iris
18 
19 data = load_iris()
20 y = data.target
21 X = data.data
22 pca = PCA(n_components=2)
23 reduced_X = pca.fit_transform(X)
24 
25 red_x, red_y = [], []
26 blue_x, blue_y = [], []
27 green_x, green_y = [], []
28 for i in range(len(reduced_X)):
29     if y[i] == 0:
30         red_x.append(reduced_X[i][0])
31         red_y.append(reduced_X[i][1])
32     elif y[i] == 1:
33         blue_x.append(reduced_X[i][0])
34         blue_y.append(reduced_X[i][1])
35     else:
36         green_x.append(reduced_X[i][0])
37         green_y.append(reduced_X[i][1])
38 plt.scatter(red_x, red_y, c='r', marker='x')
39 plt.scatter(blue_x, blue_y, c='b', marker='D')
40 plt.scatter(green_x, green_y, c='g', marker='.')
41 plt.show()

参考：炼数成金