def loadDataSet():
dataMat = []; labelMat = []
fr = open('testSet.txt')
for line in fr.readlines():
lineArr = line.strip().split()
dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])
labelMat.append(int(lineArr[2]))
return dataMat, labelMat
def sigmoid(inX):
return 1.0 / (1 + np.exp(-inX))
def gradAscent(dataMatIn, classLabels):
dataMatrix = np.mat(dataMatIn) #convert to NumPy matrix
labelMat = np.mat(classLabels).transpose() #convert to NumPy matrix
m, n = np.shape(dataMatrix)
alpha = 0.001
maxCycles = 500
weights = np.ones((n, 1))
for k in range(maxCycles): #heavy on matrix operations
h = sigmoid(dataMatrix*weights) #matrix mult
error = (labelMat - h) #vector subtraction
weights = weights + alpha * dataMatrix.transpose()* error #matrix mult
return weights
(获得梯度上升的参数weight,回归系数)
def plotBestFit(weights):
import matplotlib.pyplot as plt
dataMat, labelMat = loadDataSet()
dataArr = np.array(dataMat)
n = np.shape(dataArr)[0]
xcord1 = []; ycord1 = []
xcord2 = []; ycord2 = []
for i in range(n):
if int(labelMat[i]) == 1:
xcord1.append(dataArr[i, 1]); ycord1.append(dataArr[i, 2])
else:
xcord2.append(dataArr[i, 1]); ycord2.append(dataArr[i, 2])
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')
ax.scatter(xcord2, ycord2, s=30, c='green')
x = np.arange(-3.0, 3.0, 0.1)
y = (-weights[0]-weights[1]*x)/weights[2]
ax.plot(x, y)
plt.xlabel('X1'); plt.ylabel('X2')
plt.show()
随机梯度上升算法:通过每次用一个样本点来更新回归系数,减少算法复杂度
def stocGradAscent0(dataMatrix, classLabels):
m, n = np.shape(dataMatrix)
alpha = 0.01
weights = np.ones(n) #initialize to all ones
for i in range(m):
h = sigmoid(sum(dataMatrix[i]*weights))
error = classLabels[i] - h
weights = weights + alpha * error * dataMatrix[i]
return weights
改进随机梯度上升算法:
def stocGradAscent1(dataMatrix, classLabels, numIter=150):
m, n = np.shape(dataMatrix)
weights = np.ones(n) #initialize to all ones
for j in range(numIter):
dataIndex = list(range(m))
for i in range(m):
alpha = 4/(1.0+j+i)+0.0001 #apha decreases with iteration, does not
randIndex = int(np.random.uniform(0, len(dataIndex)))#go to 0 because of the constant
h = sigmoid(sum(dataMatrix[randIndex]*weights))
error = classLabels[randIndex] - h
weights = weights + alpha * error * dataMatrix[randIndex]
del(dataIndex[randIndex])
return weights
示例:从疝气病预测病马死亡率
def classifyVector(inX, weights):
prob = sigmoid(sum(inX*weights))
if prob > 0.5: return 1.0
else: return 0.0
def colicTest():
frTrain = open('horseColicTraining.txt'); frTest = open('horseColicTest.txt')
trainingSet = []; trainingLabels = []
for line in frTrain.readlines():
currLine = line.strip().split('\t')
lineArr = []
for i in range(21):
lineArr.append(float(currLine[i]))
trainingSet.append(lineArr)
trainingLabels.append(float(currLine[21]))
trainWeights = stocGradAscent1(np.array(trainingSet), trainingLabels, 1000)
errorCount = 0; numTestVec = 0.0
for line in frTest.readlines():
numTestVec += 1.0
currLine = line.strip().split('\t')
lineArr = []
for i in range(21):
lineArr.append(float(currLine[i]))
if int(classifyVector(np.array(lineArr), trainWeights)) != int(currLine[21]):
errorCount += 1
errorRate = (float(errorCount)/numTestVec)
print("the error rate of this test is: %f" % errorRate)
return errorRate
def multiTest():
numTests = 10; errorSum = 0.0
for k in range(numTests):
errorSum += colicTest()
print("after %d iterations the average error rate is: %f" % (numTests, errorSum/float(numTests)))