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