5、python程式碼（PCA案例）

#-*- coding:utf-8-*-
from numpy import *
import numpy as np
import cv2
import matplotlib.pyplot as plt

def zeroMean(dataMat):
    meanVal=np.mean(dataMat,axis=0)    #axis=0表示按照列求均值
    newData=dataMat-meanVal            #減均值
    return newData,meanVal             #返回結果
#機器學習實戰
def loadDataSet(filename,delim = "\t"):
    fr = open(filename)
    stringArr = [line.strip().split(delim) for line in fr.readlines()]
    datArr = [map(float, line) for line in stringArr]
    return np.mat(datArr)
def PCA_SVD(dataMat,k=2):
    newData,meanVals=zeroMean(dataMat)
    covMat=np.cov(newData,rowvar=0)                   
    U, S, V = np.linalg.svd(covMat)

    n_eigVect=U[:,:k]                            #最大的k個特徵值對應的特徵向量
    lowDataMat=newData*n_eigVect                 #低維特徵空間的資料
    reconMat=(lowDataMat*n_eigVect.T)+meanVals   #重構資料
    return lowDataMat,reconMat

data=loadDataSet("F:/DEEP LEARNING PAPERS/machinelearninginaction/Ch13/testSet.txt")
lowdataMat,reconMat=PCA_SVD(data,2)
fig1 = plt.figure()
fig2=plt.figure()
ax = fig1.add_subplot(111)
ay=fig2.add_subplot(111)
ax.scatter(data[:,0].flatten().A[0], data[:,1].flatten().A[0], marker='^',  s = 10 )
ay.scatter(lowdataMat[:,0].flatten().A[0], lowdataMat[:,1].flatten().A[0],marker='o', s = 20 , c ='red' )
plt.show()
 

參考資料：

[1]  https://en.wikipedia.org/wiki/Singular_value_decomposition

[2] https://www.cnblogs.com/pinard/p/6251584.html   (這個博主良心)