机器学习实战PCA算法
1、pca算法
def pca(dataMat, topNfeat=9999999):
meanVals = mean(dataMat, axis=0)
meanRemoved = dataMat - meanVals #remove mean
covMat = cov(meanRemoved, rowvar=0)
eigVals,eigVects = linalg.eig(mat(covMat))
eigValInd = argsort(eigVals) #sort,tsort goes smallest to largest
eigValInd = eigValInd[:-(topNfeat+1):-1] #cut off unwanted dimensions
redEigVects = eigVects[:,eigValInd] #reorganize eig vects largest to smallest
lowDDataMat = meanRemoved * redEigVect5is#transform data into new dimensions
reconMat = (lowDDataMat * redEigVects.T) + meanVals
return lowDDataMat, reconMat
in[1]：from imp import reload
in[2]：import pca
in[3]:datamat = pca.loadDataSet(r'C:\Users\16793\Desktop\machinelearninginaction\Ch05\testSet.txt')
in[4]:datamat
Out[5]:
matrix([[-1.7612000e-02, 1.4053064e+01, 0.0000000e+00],
[-1.3956340e+00, 4.6625410e+00, 1.0000000e+00],
[-7.5215700e-01, 6.5386200e+00, 0.0000000e+00],
[-1.3223710e+00, 7.1528530e+00, 0.0000000e+00],
[ 4.2336300e-01, 1.1054677e+01, 0.0000000e+00],
[ 4.0670400e-01, 7.0673350e+00, 1.0000000e+00],
[ 6.6739400e-01, 1.2741452e+01, 0.0000000e+00],
[-2.4601500e+00, 6.8668050e+00, 1.0000000e+00],
[ 5.6941100e-01, 9.5487550e+00, 0.0000000e+00],
[-2.6632000e-02, 1.0427743e+01, 0.0000000e+00],
[ 8.5043300e-01, 6.9203340e+00, 1.0000000e+00],
[ 1.3471830e+00, 1.3175500e+01, 0.0000000e+00],
[ 1.1768130e+00, 3.1670200e+00, 1.0000000e+00],
[-1.7818710e+00, 9.0979530e+00, 0.0000000e+00],
[-5.6660600e-01, 5.7490030e+00, 1.0000000e+00],
[ 9.3163500e-01, 1.5895050e+00, 1.0000000e+00],
[-2.4205000e-02, 6.1518230e+00, 1.0000000e+00],
[-3.6453000e-02, 2.6909880e+00, 1.0000000e+00],
[-1.9694900e-01, 4.4416500e-01, 1.0000000e+00],
[ 1.0144590e+00, 5.7543990e+00, 1.0000000e+00],
[ 1.9852980e+00, 3.2306190e+00, 1.0000000e+00],
[-1.6934530e+00, -5.5754000e-01, 1.0000000e+00],
[-5.7652500e-01, 1.1778922e+01, 0.0000000e+00],
[-3.4681100e-01, -1.6787300e+00, 1.0000000e+00],
[-2.1244840e+00, 2.6724710e+00, 1.0000000e+00],
[ 1.2179160e+00, 9.5970150e+00, 0.0000000e+00],
[-7.3392800e-01, 9.0986870e+00, 0.0000000e+00],
[-3.6420010e+00, -1.6180870e+00, 1.0000000e+00],
[ 3.1598500e-01, 3.5239530e+00, 1.0000000e+00],
[ 1.4166140e+00, 9.6192320e+00, 0.0000000e+00],
[-3.8632300e-01, 3.9892860e+00, 1.0000000e+00],
[ 5.5692100e-01, 8.2949840e+00, 1.0000000e+00],
[ 1.2248630e+00, 1.1587360e+01, 0.0000000e+00],
[-1.3478030e+00, -2.4060510e+00, 1.0000000e+00],
[ 1.1966040e+00, 4.9518510e+00, 1.0000000e+00],
[ 2.7522100e-01, 9.5436470e+00, 0.0000000e+00],
[ 4.7057500e-01, 9.3324880e+00, 0.0000000e+00],
[-1.8895670e+00, 9.5426620e+00, 0.0000000e+00],
[-1.5278930e+00, 1.2150579e+01, 0.0000000e+00],
[-1.1852470e+00, 1.1309318e+01, 0.0000000e+00],
[-4.4567800e-01, 3.2973030e+00, 1.0000000e+00],
[ 1.0422220e+00, 6.1051550e+00, 1.0000000e+00],
[-6.1878700e-01, 1.0320986e+01, 0.0000000e+00],
[ 1.1520830e+00, 5.4846700e-01, 1.0000000e+00],
[ 8.2853400e-01, 2.6760450e+00, 1.0000000e+00],
[-1.2377280e+00, 1.0549033e+01, 0.0000000e+00],
[-6.8356500e-01, -2.1661250e+00, 1.0000000e+00],
[ 2.2945600e-01, 5.9219380e+00, 1.0000000e+00],
[-9.5988500e-01, 1.1555336e+01, 0.0000000e+00],
[ 4.9291100e-01, 1.0993324e+01, 0.0000000e+00],
[ 1.8499200e-01, 8.7214880e+00, 0.0000000e+00],
[-3.5571500e-01, 1.0325976e+01, 0.0000000e+00],
[-3.9782200e-01, 8.0583970e+00, 0.0000000e+00],
[ 8.2483900e-01, 1.3730343e+01, 0.0000000e+00],
[ 1.5072780e+00, 5.0278660e+00, 1.0000000e+00],
[ 9.9671000e-02, 6.8358390e+00, 1.0000000e+00],
[-3.4400800e-01, 1.0717485e+01, 0.0000000e+00],
[ 1.7859280e+00, 7.7186450e+00, 1.0000000e+00],
[-9.1880100e-01, 1.1560217e+01, 0.0000000e+00],
[-3.6400900e-01, 4.7473000e+00, 1.0000000e+00],
[-8.4172200e-01, 4.1190830e+00, 1.0000000e+00],
[ 4.9042600e-01, 1.9605390e+00, 1.0000000e+00],
[-7.1940000e-03, 9.0757920e+00, 0.0000000e+00],
[ 3.5610700e-01, 1.2447863e+01, 0.0000000e+00],
[ 3.4257800e-01, 1.2281162e+01, 0.0000000e+00],
[-8.1082300e-01, -1.4660180e+00, 1.0000000e+00],
[ 2.5307770e+00, 6.4768010e+00, 1.0000000e+00],
[ 1.2966830e+00, 1.1607559e+01, 0.0000000e+00],
[ 4.7548700e-01, 1.2040035e+01, 0.0000000e+00],
[-7.8327700e-01, 1.1009725e+01, 0.0000000e+00],
[ 7.4798000e-02, 1.1023650e+01, 0.0000000e+00],
[-1.3374720e+00, 4.6833900e-01, 1.0000000e+00],
[-1.0278100e-01, 1.3763651e+01, 0.0000000e+00],
[-1.4732400e-01, 2.8748460e+00, 1.0000000e+00],
[ 5.1838900e-01, 9.8870350e+00, 0.0000000e+00],
[ 1.0153990e+00, 7.5718820e+00, 0.0000000e+00],
[-1.6580860e+00, -2.7255000e-02, 1.0000000e+00],
[ 1.3199440e+00, 2.1712280e+00, 1.0000000e+00],
[ 2.0562160e+00, 5.0199810e+00, 1.0000000e+00],
[-8.5163300e-01, 4.3756910e+00, 1.0000000e+00],
[-1.5100470e+00, 6.0619920e+00, 0.0000000e+00],
[-1.0766370e+00, -3.1818880e+00, 1.0000000e+00],
[ 1.8210960e+00, 1.0283990e+01, 0.0000000e+00],
[ 3.0101500e+00, 8.4017660e+00, 1.0000000e+00],
[-1.0994580e+00, 1.6882740e+00, 1.0000000e+00],
[-8.3487200e-01, -1.7338690e+00, 1.0000000e+00],
[-8.4663700e-01, 3.8490750e+00, 1.0000000e+00],
[ 1.4001020e+00, 1.2628781e+01, 0.0000000e+00],
[ 1.7528420e+00, 5.4681660e+00, 1.0000000e+00],
[ 7.8557000e-02, 5.9736000e-02, 1.0000000e+00],
[ 8.9392000e-02, -7.1530000e-01, 1.0000000e+00],
[ 1.8256620e+00, 1.2693808e+01, 0.0000000e+00],
[ 1.9744500e-01, 9.7446380e+00, 0.0000000e+00],
[ 1.2611700e-01, 9.2231100e-01, 1.0000000e+00],
[-6.7979700e-01, 1.2205300e+00, 1.0000000e+00],
[ 6.7798300e-01, 2.5566660e+00, 1.0000000e+00],
[ 7.6134900e-01, 1.0693862e+01, 0.0000000e+00],
[-2.1687910e+00, 1.4363200e-01, 1.0000000e+00],
[ 1.3886100e+00, 9.3419970e+00, 0.0000000e+00],
[ 3.1702900e-01, 1.4739025e+01, 0.0000000e+00]])
in[5]:datamat = pca.loadDataSet(r'C:\Users\16793\Desktop\machinelearninginaction\Ch13\testSet.txt')
in[6]:datamat
Out[7]:
matrix([[10.235186, 11.321997],
[10.122339, 11.810993],
[ 9.190236, 8.904943],
...,
[ 9.854922, 9.201393],
[ 9.11458 , 9.134215],
[10.334899, 8.543604]])
in[7]:from numpy import *
in[8]:topnfeat = 1
in[9]:meanvals = mean(datamat, axis = 0 )
in[10]:meanvals
Out[11]: matrix([[9.06393644, 9.09600218]])
in[11]:meanremoved = datamat - meanvals
in[12]:meanremoved
Out[13]:
matrix([[ 1.17124956, 2.22599482],
[ 1.05840256, 2.71499082],
[ 0.12629956, -0.19105918],
...,
[ 0.79098556, 0.10539082],
[ 0.05064356, 0.03821282],
[ 1.27096256, -0.55239818]])
in[14]:covmat = cov(meanremoved, rowvar = 0)
in[15]:covmat
Out[16]:
array([[1.05198368, 1.1246314 ],
[1.1246314 , 2.21166499]])in[16]:eigvals, eigvects = linalg.eig(mat(covmat))
in[17]:eigvals
Out[18]: array([0.36651371, 2.89713496])
in[19]:eigvects
Out[20]:
matrix([[-0.85389096, -0.52045195],
[ 0.52045195, -0.85389096]])
in[20]:eigvalind = argsort(eigvals)
in[21]:eigvalind
Out[22]: array([0, 1], dtype=int64)
in[22]:eigvalind = eigvalind[:-(topnfeat+1):-1]
in[23]:eigvalind
Out[24]: array([1], dtype=int64)
in[24]:redeigvects = eigvects[:,eigvalind]
in[25]:redeigvects
Out[26]:
matrix([[-0.52045195],
[-0.85389096]])
in[26]:rowddatamat = meanremoved * redeigvectsin[27]:rowddatamat
Out[38]:
matrix([[-2.51033597e+00],
[-2.86915379e+00],
[ 9.74108510e-02],
[-7.67782222e-01],
[ 1.02715333e+00],
[-1.44409178e+00],
[-2.17360352e+00],
[-7.73998803e-01],
[-1.09983463e+00],
[-1.70275987e+00],
[-5.39605615e-01],
[-9.15572638e-01],
[-2.42669452e+00],.......
[-5.01662249e-01],
[-5.89871235e-02],
[-1.89787138e-01]])in[27]:reconmat = (rowddatamat * redeigvects.T) + meanvals
in[28]:reconmat
Out[29]:
matrix([[10.37044569, 11.23955536],
[10.55719313, 11.54594665],
[ 9.01323877, 9.01282393],
...,
[ 9.32502753, 9.52436704],
[ 9.0946364 , 9.14637075],
[ 9.16271152, 9.2580597 ]])
in[29]:shape(reconmat)
Out[30]: (1000, 2)
因为对矩阵操作的过程中矩阵的变化不了解，所以一行一行的输出，来体现矩阵的变化。第一次写博客哈哈，写的好烂！