PCA降维技术代码实现

Author: =

PCA/PCA.py

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+#-*-coding:utf8-*-
+'''
+Created on 2016-5-15
+
+@author: thinkgamer
+'''
+from numpy import *
+
+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)
+
+#dataMat对应数据集，N个特征
+def pca(dataMat, topNfeat=9999999):
+    meanVals = mean(dataMat, axis = 0)   #求平均值
+    meanRemoved = dataMat - meanVals #去平均值
+    covMat = cov(meanRemoved,rowvar=0) #计算协防差矩阵
+    eigVals, eigVects = linalg.eig(mat(covMat))
+    eigValInd = argsort(eigVals)
+    #从小到大对N个值排序
+    eigValInd = eigValInd[: -(topNfeat + 1) : -1]
+    redEigVects = eigVects[:, eigValInd]
+    #将数据转换到新空间
+    lowDDataMat = meanRemoved * redEigVects
+    reconMat = (lowDDataMat * redEigVects.T) + meanVals
+    return lowDDataMat, reconMat
+
+#测试
+dataMat = loadDataSet("testSet.txt")
+lowDMat, reconMat = pca(dataMat,1)
+print shape(lowDMat)
+
+'''
+#show
+import matplotlib
+import matplotlib.pyplot as plt
+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() 
+'''
+
+#将NaN替换成平均值函数
+def replaceNanWithMean(): 
+    datMat = loadDataSet('secom.data', ' ')
+    numFeat = shape(datMat)[1]
+    for i in range(numFeat):
+        meanVal = mean(datMat[nonzero(~isnan(datMat[:,i].A))[0],i]) #values that are not NaN (a number)
+        datMat[nonzero(isnan(datMat[:,i].A))[0],i] = meanVal  #set NaN values to mean
+    return datMat
+
+#加载数据               
+dataMat = replaceNanWithMean()
+#去除均值
+meanVals = mean(dataMat, axis=0)
+meanRemoved = dataMat - meanVals        
+#计算协方差               
+covMat = cov(meanRemoved, rowvar=0)
+
+#特征值分析
+eigVals,   eigVects = linalg.eig(mat(covMat))               
+print eigVals