机器学习实战(Machine Learning in Action)学习笔记————09.利用PCA简化数据
关键字:PCA、主成分分析、降维
作者:米仓山下
时间:2018-11-15
机器学习实战(Machine Learning in Action,@author: Peter Harrington)
源码下载地址:https://www.manning.com/books/machine-learning-in-action
git@github.com:pbharrin/machinelearninginaction.git
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关于PCA的理解,要理解方差、协方差、协方差矩阵、特征值、特征向量等概念。主成分分析,研究变量间的关系,就是要寻找协方差矩阵的特征向量和特征值就等价于拟合一条能保留最大方差的直线或主成分。
特征向量描绘了方阵(协方差矩阵)的固有属性,即在方阵作用(变换)下,不会发生方向变化的向量。特征向量是线性变换的不变轴。看到对微信公总号【机器之心】上把PAC原理解释非常好的文章
【教程 | 从特征分解到协方差矩阵:详细剖析和实现PCA算法】地址https://mp.weixin.qq.com/s/tJ_FbL2nFQfkvKqpQJ8kmg
#输入数据:
import numpy as np
x=np.array([2.5,0.5,2.2,1.9,3.1,2.3,2,1,1.5,1.1])
y=np.array([2.4,0.7,2.9,2.2,3,2.7,1.6,1.1,1.6,0.9])
#归一化数据:
mean_x=np.mean(x)
mean_y=np.mean(y)
scaled_x=x-mean_x
scaled_y=y-mean_y
data=np.matrix([[scaled_x[i],scaled_y[i]] for i in range(len(scaled_x))])
#绘制散点图查看数据分布:
import matplotlib.pyplot as plt
plt.plot(scaled_x,scaled_y,'o')
plt.show()
#求协方差矩阵:
cov=np.cov(scaled_x,scaled_y)
#求协方差矩阵的特征值和特征向量:
eig_val, eig_vec = np.linalg.eig(cov)
#求出特征向量后,我们需要选择降维后的数据维度 k(n 维数据降为 k 维数据),但我们的数据只有两维,所以只能降一维:
eig_pairs = [(np.abs(eig_val[i]), eig_vec[:,i]) for i in range(len(eig_val))]
eig_pairs.sort(reverse=True)
feature=eig_pairs[0][1]
#转化得到降维后的数据:
new_data_reduced=np.transpose(np.dot(feature,np.transpose(data))
>>> eig_val
array([0.0490834 , 1.28402771])
>>> eig_vec
array([[-0.73517866, -0.6778734 ],
[ 0.6778734 , -0.73517866]])
>>>
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机器学习实战中PAC函数如下:
from numpy import *
def pca(dataMat, topNfeat=9999999):
meanVals = mean(dataMat, axis=0) #计算平均值
meanRemoved = dataMat - meanVals #去中心化
covMat = cov(meanRemoved, rowvar=0) #协方差矩阵
eigVals,eigVects = linalg.eig(mat(covMat)) #特征值、特征向量
eigValInd = argsort(eigVals) #排序
eigValInd = eigValInd[:-(topNfeat+1):-1] #截取topNfeat特征值、特征向量
redEigVects = eigVects[:,eigValInd] #reorganize eig vects largest to smallest
lowDDataMat = meanRemoved * redEigVects #对去中心化数据进行变换
reconMat = (lowDDataMat * redEigVects.T) + meanVals #变换后的矩阵乘以特征向量构成的矩阵的转置(等于它的逆),又变换回去了,如果是只选取前k个特征向量,则转换回去后其他维度信息损失
return lowDDataMat, reconMat
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测试:
1. python createFig1.py #将测试数据'testSet.txt'绘制成散点图
'''
Created on Jun 1, 2011 @author: Peter
'''
from numpy import *
import matplotlib
import matplotlib.pyplot as plt n = 1000 #number of points to create
xcord0 = []
ycord0 = []
xcord1 = []
ycord1 = []
markers =[]
colors =[]
fw = open('testSet.txt','w')
for i in range(n):
[r0,r1] = random.standard_normal(2)
fFlyer = r0 + 9.0
tats = 1.0*r1 + fFlyer + 0
xcord0.append(fFlyer)
ycord0.append(tats)
fw.write("%f\t%f\n" % (fFlyer, tats)) fw.close()
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(xcord0,ycord0, marker='^', s=30)
plt.xlabel('hours of direct sunlight')
plt.ylabel('liters of water')
plt.show()
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" alt="" width="436" height="327" />
2. python createFig2.py #将测试数据'testSet.txt'绘制成散点图(蓝色);将原始数据经过主成分分析之后,只保留一个主成分,然后逆变换回去(只有一个主成分信息)的散点图(红色)
'''
Created on Jun 1, 2011 @author: Peter
'''
from numpy import *
import matplotlib
import matplotlib.pyplot as plt
import pca dataMat = pca.loadDataSet('testSet.txt')
lowDMat, reconMat = pca.pca(dataMat, 1) fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(dataMat[:,0].tolist(), dataMat[:,1].tolist(), marker='^', s=30)
ax.scatter(reconMat[:,0].tolist(), reconMat[:,1].tolist(), marker='o', s=30, c='red')
plt.show()
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" alt="" width="446" height="334" />
3. python createFig3.py #对比主成分分析前后散点图。上图为原始数据散点图,下图为主成分变换之后,将第一成分和零构成的散点图。
'''
Created on Jun 1, 2011 @author: Peter
'''
from numpy import *
import matplotlib
import matplotlib.pyplot as plt
import pca n = 1000 #number of points to create
xcord0 = []; ycord0 = []
xcord1 = []; ycord1 = []
xcord2 = []; ycord2 = []
markers =[]
colors =[]
fw = open('testSet3.txt','w')
for i in range(n):
groupNum = int(3*random.uniform())
[r0,r1] = random.standard_normal(2)
if groupNum == 0:
x = r0 + 16.0
y = 1.0*r1 + x
xcord0.append(x)
ycord0.append(y)
elif groupNum == 1:
x = r0 + 8.0
y = 1.0*r1 + x
xcord1.append(x)
ycord1.append(y)
elif groupNum == 2:
x = r0 + 0.0
y = 1.0*r1 + x
xcord2.append(x)
ycord2.append(y)
fw.write("%f\t%f\t%d\n" % (x, y, groupNum)) fw.close()
fig = plt.figure()
ax = fig.add_subplot(211)
ax.scatter(xcord0,ycord0, marker='^', s=90)
ax.scatter(xcord1,ycord1, marker='o', s=50, c='red')
ax.scatter(xcord2,ycord2, marker='v', s=50, c='yellow')
ax = fig.add_subplot(212)
myDat = pca.loadDataSet('testSet3.txt')
lowDDat,reconDat = pca.pca(myDat[:,0:2],1)
label0Mat = lowDDat[nonzero(myDat[:,2]==0)[0],:2][0] #get the items with label 0
label1Mat = lowDDat[nonzero(myDat[:,2]==1)[0],:2][0] #get the items with label 1
label2Mat = lowDDat[nonzero(myDat[:,2]==2)[0],:2][0] #get the items with label 2
#ax.scatter(label0Mat[:,0],label0Mat[:,1], marker='^', s=90)
#ax.scatter(label1Mat[:,0],label1Mat[:,1], marker='o', s=50, c='red')
#ax.scatter(label2Mat[:,0],label2Mat[:,1], marker='v', s=50, c='yellow')
ax.scatter(label0Mat[:,0].tolist(),zeros(shape(label0Mat)[0]), marker='^', s=90)
ax.scatter(label1Mat[:,0].tolist(),zeros(shape(label1Mat)[0]), marker='o', s=50, c='red')
ax.scatter(label2Mat[:,0].tolist(),zeros(shape(label2Mat)[0]), marker='v', s=50, c='yellow')
plt.show()
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" alt="" width="462" height="346" />
4. python createFig4.py #前20个主成分对应的方差百分比。大部分方差包含在前几个方差中。数据变换后对应的方差即为特征值【主成份分析最大方差等于特征值的证明问题】
'''
Created on Jun 14, 2011 @author: Peter
'''
from numpy import *
import matplotlib
import matplotlib.pyplot as plt
import pca dataMat = pca.replaceNanWithMean() #below is a quick hack copied from pca.pca()
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, sort goes smallest to largest
eigValInd = eigValInd[::-1]#reverse
sortedEigVals = eigVals[eigValInd]
total = sum(sortedEigVals)
varPercentage = sortedEigVals/total*100 fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(range(1, 21), varPercentage[:20], marker='^')
plt.xlabel('Principal Component Number')
plt.ylabel('Percentage of Variance')
plt.show()
aaarticlea/png;base64,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" 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