机器学习实战Chp13： 利用PCA简化数据

• 主要参考周志华的《机器学习》，P230

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• PCA核心程序

# -*- coding: utf-8 -*-
"""
Created on Sun Jul 29 21:42:05 2018

@author: muli
"""

from numpy import *


#mean(a, axis, dtype, out，keepdims )函数
#    功能：求取均值；
#    设a为m * n矩阵举例：
#    axis 不设置值，对 m*n 个数求均值，返回一个实数
#    axis = 0：压缩行，对各列求均值，返回 1* n 矩阵
#    axis =1 ：压缩列，对各行求均值，返回 m *1 矩阵


# 数据格式处理
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 mat(datArr)


# 注意：代码中的X和W 与 周志华书上P230的X和W为转置关系
def pca(dataMat, topNfeat=9999999):
    # 求取均值
    meanVals = mean(dataMat, axis=0)
    # 归一化
    meanRemoved = dataMat - meanVals #remove mean
    # 求方差
    covMat = cov(meanRemoved, rowvar=0)
    # 特征值、特征向量
    eigVals,eigVects = linalg.eig(mat(covMat))
    # 特征值排序，从小到大排序
    eigValInd = argsort(eigVals)            #sort, sort goes smallest to largest
    # 取前topNfeat的特征值
    eigValInd = eigValInd[:-(topNfeat+1):-1]  #cut off unwanted dimensions
    # 由特征值取特征向量，构成一个特征向量的矩阵
    redEigVects = eigVects[:,eigValInd]       #reorganize eig vects largest to smallest
    # 映射到一个新的空间
    lowDDataMat = meanRemoved * redEigVects#transform data into new dimensions
    # 重构后的x值
    reconMat = (lowDDataMat * redEigVects.T) + meanVals
    # 返回 Z 和~x 
    return lowDDataMat, reconMat


# 测试模块
if __name__ == "__main__" :
    dataMat = loadDataSet('testSet.txt')
    lowDMat,reconMat = pca(dataMat,1)
    print(shape(lowDMat))

• 绘图

• PCA降维前

# -*- coding: utf-8 -*-
"""
Created on Mon Jul 30 20:03:32 2018

@author: muli
"""

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=90)
plt.xlabel('hours of direct sunlight')
plt.ylabel('liters of water')
plt.show()

• PCA降维后

# -*- coding: utf-8 -*-
"""
Created on Mon Jul 30 20:04:20 2018

@author: muli
"""

from numpy import *
import matplotlib
import matplotlib.pyplot as plt
import PCA_test


dataMat = PCA_test.loadDataSet('testSet.txt')
lowDMat, reconMat = PCA_test.pca(dataMat, 1)

#print(dataMat[:,1])
#print(dataMat[:,1].shape)
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()