《机器学习实战》PCA降维

---

 

注释：由于各方面原因，理论部分不做介绍，网上很多自行百度吧！

---

 pca.py

import numpy as np
import matplotlib.pyplot as plt
import math

def  loadDataSet(filename, delin = '\t'):
    fr = open(filename)
    #读取分割存入数组
    stringArr = [line.strip().split(delin) for line in fr.readlines()]
    dataArr   = [list(map(float,line)) for line in stringArr]
    return np.mat(dataArr)
def pca(dataMat, topNfeet = 9999999):
    meanVals = np.mean(dataMat,axis=0)#求取平均值
    meanRemoved = dataMat - meanVals
    covMat = np.cov(meanRemoved,rowvar=0)#方差
    eigVals, eigVects= np.linalg.eig(np.mat(covMat))#求解特征向量和特征值
    eigValInd = np.argsort(eigVals)#对特征值进行排序
    eigValInd = eigValInd[:-(topNfeet+1):-1]#最后的-1是防止越界的，当然你可以在前面加一个判断
    redEigVects = eigVects[:,eigValInd]
    lowDDataMat = meanRemoved*redEigVects #
    reconMat = (lowDDataMat * redEigVects.T) + meanVals
    return lowDDataMat, reconMat

main.py

import PCA
import matplotlib.pyplot as plt

if __name__ == "__main__":

    dataMat = PCA.loadDataSet('testSet.txt')
    lowDMat, reconMat = PCA.pca(dataMat,1)
    fig = plt.figure()
    ax  = fig.add_subplot(111)
    ax.scatter(dataMat[:,0].flatten().A[0],dataMat[:,1].flatten().A[0],marker = '^',s=90)
    ax.scatter(reconMat[:,0].flatten().A[0],reconMat[:,1].flatten().A[0],marker = "o",s=50,c='red')
    plt.show()

对丢失的值进行替代：

#零的数据都转化为平均值
def replaceNanWithMean():
    dataMat = loadDataSet('secom.data',' ')
    numFeat = dataMat.shape[1]
    for i in range(numFeat):
        meanVal = np.mean(dataMat[np.nonzero(~np.isnan(dataMat[:,i].A))[0],i])
        dataMat[np.nonzero(np.isnan(dataMat[:,i].A))[0],i] = meanVal
    return dataMat