主成分分析法 python实现（转）加注释

'''

@author: Garvin

'''

from numpy import *

import matplotlib.pyplot as plt

def loadDataSet(fileName, delim='\t'):

  fr = open(fileName)

  #一次性把所有的数据全部读入计算机，然后按照delim分隔符进行分割

  stringArr = [line.strip().split(delim) for line in fr.readlines()]

  #通过map函数，把读到的数据全部转换成float类型的值

  datArr = [map(float,line) for line in stringArr]

  return mat(datArr)

def pca(dataMat, topNfeat=9999999):

  #求矩阵中每一列的均值

  meanVals = mean(dataMat, axis=0)

  #去除均值

  meanRemoved = dataMat - meanVals #remove mean

  #求协方差

  covMat = cov(meanRemoved, rowvar=0)

  #求特征值和特征向量

  eigVals,eigVects = linalg.eig(mat(covMat))

  #求出特征值从小到大元素对应的坐标，坐标计算从0开始

  eigValInd = argsort(eigVals) #sort, sort goes smallest to largest

  #切片处理，找到最大的前topNfeat特征值

  eigValInd = eigValInd[:-(topNfeat+1):-1]  #cut off unwanted dimensions

  #找到最大特征值对应的特征向量

  redEigVects = eigVects[:,eigValInd]   #reorganize eig vects largest to smallest

  #得到低维度的矩阵

  lowDDataMat = meanRemoved * redEigVects#transform data into new dimensions

  #低维度的矩阵乘以原矩阵的转置加上均值，得到降维之后的矩阵

  reconMat = (lowDDataMat * redEigVects.T) + meanVals

  return lowDDataMat, reconMat

def plotBestFit(dataSet1,dataSet2):  

  dataArr1 = array(dataSet1)

  dataArr2 = array(dataSet2)

  n = shape(dataArr1)[0] 

  n1=shape(dataArr2)[0]

  xcord1 = []; ycord1 = []

  xcord2 = []; ycord2 = []

  xcord3=[];ycord3=[]

  j=0

  for i in range(n):

    

      xcord1.append(dataArr1[i,0]); ycord1.append(dataArr1[i,1])

      xcord2.append(dataArr2[i,0]); ycord2.append(dataArr2[i,1])  

  fig = plt.figure()

  ax = fig.add_subplot(111)

  ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')

  ax.scatter(xcord2, ycord2, s=30, c='green')

  

  plt.xlabel('X1'); plt.ylabel('X2');

  plt.show()

if __name__=='__main__':

   mata=loadDataSet('/Users/hakuri/Desktop/testSet.txt')  

   a,b= pca(mata, 2)