http://sbp810050504.blog.51cto.com/2799422/1608064/这个网址解释了多维空间的sigmoid函数与梯度上升算法的原理,大家可以参考一下。
from numpy import *
def loadDataSet():#读数据
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(intX):#sigmoid函数
return 1.0 / (1 + exp(-intX))
def gradAscent(dataMatIn, classLabels):#Logistic回归梯度上升优化算法
dataMatrix = mat(dataMatIn)
labelMat = mat(classLabels).transpose()
m, n = shape(dataMatrix)
alpha = 0.001
maxCycles = 500
weights = ones((n, 1))
for k in range(maxCycles):
h = sigmoid(dataMatrix * weights)
error = labelMat - h
weights = weights + alpha * dataMatrix.transpose() * error
return weights
def stocGradAscent0(dataMatrix,classLabels):#随机梯度上升算法
m,n =shape(dataMatrix)
alpha = 0.01
weights =ones(n)
for i in range(m):
h = sigmoid(dataMatrix[i]*weights)
error = classLabels[i] - h
weights = weights + alpha*error*dataMatrix[i]
return weights
def stocGradAscent1(dataMatrix,classLabels,numIter=150):#改进的随机梯度上升算法
m,n =shape(dataMatrix)
weights = ones(n)
for j in range(numIter):
dataIndex = list(range(m))
for i in range(m):
alpha = 4/(1.0+j+i)+0.01
randIndex = int(random.uniform(0,len(dataIndex)))
h = sigmoid(sum(dataMatrix[randIndex]*weights))
error = classLabels[randIndex]-h
weights = weights +alpha*error*dataMatrix[randIndex]
del(dataIndex[randIndex])
return weights
def plotBestFit(weights):#数据可视化
import matplotlib.pyplot as plt
dataMat,labelMat=loadDataSet()
dataArr = array(dataMat)
n = 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='blue', marker='s')
ax.scatter(xcord2, ycord2, s=30, c='red')
x = 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()
def main():
dataArr,labelMat = loadDataSet()
weights1 = gradAscent(dataArr,labelMat)
print(weights1)
plotBestFit(weights1.getA())
dataArr, labelMat = loadDataSet()
weights2 = stocGradAscent0(array(dataArr),labelMat)
print(weights2)
plotBestFit(weights2)
dataArr, labelMat = loadDataSet()
weight3 = stocGradAscent1(array(dataArr),labelMat)
print(weight3)
plotBestFit(weight3)
if __name__ == '__main__':
main()
结果:
图片
图片一
图片二
图片三