PCA历程详细python代码（原创）

#PCA主成分分析，原文为文末的链接，代码为自己亲自手码

def cov_out1(dx,dy):
  #第一步：求解x，y各自的均值
  mean_x=0
  mean_y=0
  for i in range(len(dx)):
    mean_x+=dx[i]
    mean_y+=dy[i]
    # print(i)
  mean_x/=len(dx)
  mean_y/=len(dy)
  # print('mean_x:',mean_x)
  # print('mean_y:',mean_y)
  #第二步：求解xy的联合均值
  mean_xy=0
  for i in range(len(dx)):
    mean_xy+=dx[i]*dy[i]
  mean_xy/=len(dy)
  # print('mean_xy',mean_xy)
  
  return mean_xy-mean_x*mean_y
#

def cov_out2(dx,dy):
  #第一步：求解x，y各自的均值
  mean_x=0
  mean_y=0
  for i in range(len(dx)):
    mean_x+=dx[i]
    mean_y+=dy[i]
  mean_x/=len(dx)
  mean_y/=len(dy)
  # print('mean_x:',mean_x)
  # print('mean_y:',mean_y)
  #第二步：求解联合均值
  mean_x_y=0
  for i in range(len(dx)):
    mean_x_y+=(dx[i]-mean_x)*(dy[i]-mean_y)
  # print('mean_x_y',mean_x_y)
  return mean_x_y/len(dx)
#

dx=[2.5,0.5,2.2,1.9,3.1,2.3,2.0,1.0,1.5,1.1]
dy=[2.4,0.7,2.9,2.2,3.0,2.7,1.6,1.1,1.6,0.9]
# print(len(dx))
# print(len(dy))

# covx=cov_out2(dx,dx)
# covy=cov_out2(dy,dy)
# print(covx)
# print(covy)

# cov1=cov_out1(dx,dy)
# cov2=cov_out2(dx,dy)
# print(cov1)
# print(cov2)

import numpy as np


#第一步：求dx,dy的平均值
print('第一步：求dx,dy的平均值')
mean_x=np.mean(dx)
mean_y=np.mean(dy)
print(mean_x,mean_y)

#第二步：求解DataAjust
print('第二步：求解DataAjust')
dx=dx-mean_x
dy=dy-mean_y
print(dx)
print(dy)
DataAdjust=np.vstack((dx,dy))
print(DataAdjust.T)

covx=cov_out2(dx,dx)
covy=cov_out2(dy,dy)
covxy=cov_out2(dx,dy)
covyx=cov_out2(dy,dx)
print(covx)
print(covy)
print(covxy)
print(covyx)

#第三步：求解特征值和特征向量
print('第三步：求解特征值和特征向量')
cov=np.array([[covx,covxy],[covyx,covy]])
print(cov)

a,b=np.linalg.eig(cov)
print('特征值')
print(a)
print("特征矩阵")
print(b)

#第四步：将特征值由大到小排序，选取其中最大的k个（这里是1个）
print('第四步：将特征值由大到小排序，选取其中最大的k个（这里是1个）')
a_max=np.max(a)
print(a_max)
a_index=np.where(a==a_max)[0][0]
print(a_index)
b_max=b[:,a_index]
print(b_max)

#第五步：将样本点投影到选取的特征向量上
print('第五步：将样本点投影到选取的特征向量上')
finalData=np.dot(DataAdjust.T,b_max)
print(finalData)

引文：http://www.cnblogs.com/jerrylead/archive/2011/04/18/2020209.html