主成分分析（PCA）

主成分分析（PCA）

import numpy as np
import matplotlib.pyplot as plt

data = np.matrix([[2.5,2.4],[0.5,0.7],[2.2,2.9],[1.9,2.2],[3.1,3.0],
                  [2.3,2.7],[2,1.6],[1,1.1],[1.5,1.6],[1.1,0.9]])
average = np.mean(data,axis=0)
data_adjust = np.zeros((10,2))

#生成新的data_adjust
for i in range(10):
    for k in range(2):
        if k == 0:
            data_adjust[i, k] = data[i, k] - average.item(0)
        else:
            data_adjust[i, k] = data[i, k] - average.item(1)

#协方差
cov = np.cov(data_adjust,rowvar=False)

#特征值和特征向量
eigenvalues, eigenvectors = np.linalg.eig(cov)

#选特征值和特征向量
eigenvalues_max = eigenvalues.item(0)
i = 0;max = 0
for eigenvalue in eigenvalues:
    if eigenvalues_max < eigenvalue:
        eigenvalues_max = eigenvalue
        max = i
    i += 1
eigenvalues_max = eigenvectors[:,max]
eigenvalues_max = eigenvalues_max.reshape(-1,1)

#投影
final_data = np.dot(data_adjust,eigenvalues_max)
print(final_data)

实验结果：

[[-0.82797019]
 [ 1.77758033]
 [-0.99219749]
 [-0.27421042]
 [-1.67580142]
 [-0.9129491 ]
 [ 0.09910944]
 [ 1.14457216]
 [ 0.43804614]
 [ 1.22382056]]