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from numpy import *
import matplotlib.pyplot as plt
def loadSimpData():
datMat = matrix([
[1., 2.1],
[2., 1.1],
[1.3, 1.],
[1., 1.],
[2., 1.]
])
classLabels = [1.0, 1.0, -1.0, -1.0, 1.0]
return datMat, classLabels
#弱分类器分类，返回致函1/-1的numpy数组
def stumpClassify(dataMatrix, dimen, threshVal, threshIneq):
retArray = ones((shape(dataMatrix)[0], 1))
if threshIneq == 'lt':
retArray[dataMatrix[:, dimen] <= threshVal] = -1.0
else:
retArray[dataMatrix[:, dimen] > threshVal] = -1.0
return retArray
#构造弱分类器单层决策树
def buildStupm(dataArr, classLabels, D):
dataMatrix = mat(dataArr); labelMat = mat(classLabels).T
m, n = shape(dataMatrix)
numSteps = 10.0; bestStump = {}; bestClasEst = mat(zeros((m,1)))
minError = inf
for i in range(n):
rangeMin = dataMatrix[:, i].min()
rangeMax = dataMatrix[:, i].max()
stepSize = (rangeMax - rangeMin)/numSteps
for j in range(-1, int(numSteps) + 1):
for inequal in ['lt', 'gt']:
threshVal = (rangeMin + float(j) * stepSize)
predictedVals = \
stumpClassify(dataMatrix, i, threshVal, inequal)
errArr = mat(ones((m,1)))
errArr[predictedVals == labelMat] = 0
weightedError = D.T * errArr
print 'split: dim %d, thresh %.2f, thresh ineqal:' \
'%s, the weighted error is %.3f' % (i, threshVal, inequal, weightedError)
if weightedError < minError:
minError = weightedError
bestClasEst = predictedVals.copy()
bestStump['dim'] = i
bestStump['thresh'] = threshVal
bestStump['ineq'] = inequal
return bestStump, minError, bestClasEst
#结合弱分类器构造更强的分类器
def adaBoostTrainDS(dataArr, classLabels, numIt = 40):
weakClassArr = []
m = shape(dataArr)[0]
D = mat(ones((m,1)) / m)
aggClassEst = mat(zeros((m,1)))
for i in range(numIt):
bestStump, error, classEst = buildStupm(dataArr, classLabels, D)
print 'D:', D.T
alpha = float(0.5 * log((1.0 - error)/ max(error, 1e-16)))
bestStump['alpha'] = alpha
weakClassArr.append(bestStump)
print 'classEst: ', classEst.T
expon = multiply(-1 * alpha * mat(classLabels).T, classEst)
D = multiply(D, exp(expon))
D = D/D.sum()
aggClassEst += alpha * classEst
print 'aggClassEst: ', aggClassEst.T
aggErrors = multiply(sign(aggClassEst) != mat(classLabels).T, ones((m,1)))
errorRate = aggErrors.sum()/m
print 'total error: ', errorRate, '\n'
if errorRate == 0.0: break
return weakClassArr, aggClassEst
#预测分类函数
def adaClassify(datToClass, classifierArr):
dataMatrix = mat(datToClass)
m = shape(dataMatrix)[0]
aggClassEst = mat(zeros((m,1)))
for i in range(len(classifierArr)):
classEst = stumpClassify(dataMatrix, classifierArr[i]['dim'],\
classifierArr[i]['thresh'],\
classifierArr[i]['ineq'])
aggClassEst += classifierArr[i]['alpha']*classEst
print aggClassEst
return sign(aggClassEst)
#读数据（病马分析）
def loadDataSet(filename):
numFeat = len(open(filename).readline().split('\t'))
dataMat = []; labelMat = []
fr = open(filename)
for line in fr.readlines():
lineArr = []
curLine = line.strip().split('\t')
for i in range(numFeat - 1):
lineArr.append(float(curLine[i]))
dataMat.append(lineArr)
labelMat.append(float(curLine[-1]))
return dataMat, labelMat
#ROC作图分析
def plotROC(predStrengths, classLabels):
import matplotlib.pyplot as plt
cur = (1.0,1.0) #cursor
ySum = 0.0 #variable to calculate AUC
numPosClas = sum(array(classLabels)==1.0)
yStep = 1/float(numPosClas); xStep = 1/float(len(classLabels)-numPosClas)
sortedIndicies = predStrengths.argsort()#get sorted index, it's reverse
fig = plt.figure()
fig.clf()
ax = plt.subplot(111)
#loop through all the values, drawing a line segment at each point
for index in sortedIndicies.tolist()[0]:
if classLabels[index] == 1.0:
delX = 0; delY = yStep;
else:
delX = xStep; delY = 0;
ySum += cur[1]
#draw line from cur to (cur[0]-delX,cur[1]-delY)
ax.plot([cur[0],cur[0]-delX],[cur[1],cur[1]-delY], c='b')
cur = (cur[0]-delX,cur[1]-delY)
ax.plot([0,1],[0,1],'b--')
plt.xlabel('False positive rate'); plt.ylabel('True positive rate')
plt.title('ROC curve for AdaBoost horse colic detection system')
ax.axis([0,1,0,1])
plt.show()
print "the Area Under the Curve is: ",ySum*xStep
datArr, labelArr = loadDataSet('d:/horseColicTraining2.txt')
classifierArray, aggClassEst = adaBoostTrainDS(datArr, labelArr, 10)
plotROC(aggClassEst.T, labelArr)
# print classifierArray
#
# datMat, classLabels = loadSimpData()
# D = mat(ones((5,1))/5)
# #print buildStupm(datMat, classLabels, D)
# fig = plt.figure()
# ax = fig.add_subplot(111)
# for i in range(len(classLabels)):
# if classLabels[i] == 1.0:
# print datMat[i,0]
# ax.scatter(datMat[i,0], datMat[i,1], marker='o')
# else:
# ax.scatter(datMat[i,0], datMat[i,1], marker='^')
# plt.show()
# classifierArray = adaBoostTrainDS(datMat, classLabels, 9)
# print classifierArray