主成分分析PCA(降维)

import numpy as np

#初始化矩阵
data = np.array([
                 [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]
                 ])
#计算平均值

avg_x = 0.00
avg_y = 0.00
x = data[:,0]
y = data[:,1]
for i in x:
    avg_x += i
for i in y:
    avg_y += i

avg_x /= data.shape[0]
avg_y /= data.shape[0]

avg_x = round(avg_x,2)
avg_y = round(avg_y,2)

row = data.shape[0]
#计算减去平均值的矩阵
for i in range(0,row):
    data[i][0] -= avg_x
    data[i][1] -= avg_y


cov = np.cov(data[:,0],data[:,1])


eig = np.linalg.eig(cov)

#求得特征值和特征向量
evl = eig[0]
evt = eig[1]


maxx = -100
max_id = 0


#求得最大值以及最大值所对应的索引
for i in range(0,evl.shape[0]):
    if evl[i] > maxx:
        max_id = i
        maxx = evl[i]

ans_evt = evt[:,max_id]

#得到最后矩阵
final_np = data * ans_evt

#将矩阵的行元素相加得到最后结果
for i in range(0,final_np.shape[0]):
        final_np[i][0] += final_np[i][1]

final_ans = final_np[:,0]

final_ans = final_ans.reshape(final_ans.shape[0],1)

print(final_ans)