PCA成分分析算法（降维）

import numpy as np
import math
import operator
x=np.array([2.5,0.5,2.2,1.9,3.1,2.3,2,1,1.5,1.1])
y=np.array([2.4,0.7,2.9,2.2,3.0,2.7,1.6,1.1,1.6,0.9])
X=np.sum(x)/10
Y=np.sum(y)/10
print (X,Y)#求解平均值

1.81 1.9100000000000001

x1=np.array(x-X)
x1

array([ 0.69, -1.31,  0.39,  0.09,  1.29,  0.49,  0.19, -0.81, -0.31,
       -0.71])

y1=np.array(y-Y)
y1

array([ 0.49, -1.21,  0.99,  0.29,  1.09,  0.79, -0.31, -0.81, -0.31,
       -1.01])

data = np.c_[x1,y1]
print (data)

[[ 0.69  0.49]
 [-1.31 -1.21]
 [ 0.39  0.99]
 [ 0.09  0.29]
 [ 1.29  1.09]
 [ 0.49  0.79]
 [ 0.19 -0.31]
 [-0.81 -0.81]
 [-0.31 -0.31]
 [-0.71 -1.01]]

cov_=np.cov(data)
print (cov_)#求解协方差

[[0.61655556 0.61544444]
 [0.61544444 0.71655556]]

eigen = np.linalg.eig(cov_)
print (eigen)#第一个特征值，后面是特征向量

(array([0.0490834 , 1.28402771]), array([[-0.73517866, -0.6778734 ],
       [ 0.6778734 , -0.73517866]]))

data_max=np.max([0.490834,1.28402771])
print (data_max)#求出特征值里面比较大的那个，对应的特征向量是[ -0.6778734 , -0.73517866]

1.28402771

t=np.array([[-0.6778734],
          [-0.73517866]])
print(t)

[[-0.6778734 ]
 [-0.73517866]]

data_finally=np.dot(data,t)#注意顺序，特征向量在后面
print (data_finally)

[[-0.82797019]
 [ 1.77758033]
 [-0.9921975 ]
 [-0.27421042]
 [-1.67580143]
 [-0.91294911]
 [ 0.09910944]
 [ 1.14457217]
 [ 0.43804614]
 [ 1.22382056]]