目录
1、算法介绍
logistic回归是统计学习中的经典分类方法，因为实现代价不高和不错的分类效率被广为推崇。logistic回归是建立在线性回归（详见之前发的博文）基础上，通过Sigmoid函数将目标回归值转化为二分类模型（可变形为多分类）。
2、logistic函数（Sigmoid曲线）
其中z = w*x + b(就是划分数据集的超平面（w，b），将数据的正例划分在超平面的一侧，负例在超平面的另一侧。w是超平面的回归系数）
因为在负例中，z = w*x + b < 0，所以通过logistic函数计算后值小于0.5，而正例中则大于0.5。在训练出模型后（求出回归系数和偏移量），就可以通过对测试数据进行测试，如果值大于阈值（0.5）就会被划分在正例中。
3、训练模型
梯度上升法
4、代码实现
import numpy as np
import matplotlib.pyplot as plt
def loadDataSet():
#加载数据集
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):
#Sigmoid曲线函数
return 1.0 / (1 + np.exp(-inX))
def gradAscent(dataMatIn, classLabels):
#梯度上升优化算法
dataMatrix = np.mat(dataMatIn)
labelMat = np.mat(classLabels).transpose()
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
return weights
def stocGradAscent0(dataMatrix, classLabels):
#随机梯度上升算法
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
def stocGradAscent1(dataMatrix, classLabels, numIter=150):
#改进的随机梯度上升算法
m, n = np.shape(dataMatrix)
weights = np.ones(n) # initialize to all ones
for j in range(numIter):
dataIndex = range(m)
for i in range(m):
alpha = 4 / (1.0 + j + i) + 0.0001
randIndex = int(np.random.uniform(0, len(dataIndex)))
h = sigmoid(sum(dataMatrix[randIndex] * weights))
error = classLabels[randIndex] - h
weights = weights + alpha * error * dataMatrix[randIndex]
del (list(dataIndex)[randIndex])
return weights
def classifyVector(inX, weights):
#测试数据
prob = sigmoid(sum(inX * weights))
if prob > 0.5:
return 1.0
else:
return 0.0
def plotBestFit(weights):
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()
if __name__ == '__main__':
x,y = loadDataSet()
ws = stocGradAscent1(np.array(x),y)
plotBestFit(ws)数据集补充：
-0.017612 14.053064 0
-1.395634 4.662541 1
-0.752157 6.538620 0
-1.322371 7.152853 0
0.423363 11.054677 0
0.406704 7.067335 1
0.667394 12.741452 0
-2.460150 6.866805 1
0.569411 9.548755 0
-0.026632 10.427743 0
0.850433 6.920334 1
1.347183 13.175500 0
1.176813 3.167020 1
-1.781871 9.097953 0
-0.566606 5.749003 1
0.931635 1.589505 1
-0.024205 6.151823 1
-0.036453 2.690988 1
-0.196949 0.444165 1
1.014459 5.754399 1
1.985298 3.230619 1
-1.693453 -0.557540 1
-0.576525 11.778922 0
-0.346811 -1.678730 1
-2.124484 2.672471 1
1.217916 9.597015 0
-0.733928 9.098687 0
-3.642001 -1.618087 1
0.315985 3.523953 1
1.416614 9.619232 0
-0.386323 3.989286 1
0.556921 8.294984 1
1.224863 11.587360 0
-1.347803 -2.406051 1
1.196604 4.951851 1
0.275221 9.543647 0
0.470575 9.332488 0
-1.889567 9.542662 0
-1.527893 12.150579 0
-1.185247 11.309318 0
-0.445678 3.297303 1
1.042222 6.105155 1
-0.618787 10.320986 0
1.152083 0.548467 1
0.828534 2.676045 1
-1.237728 10.549033 0
-0.683565 -2.166125 1
0.229456 5.921938 1
-0.959885 11.555336 0
0.492911 10.993324 0
0.184992 8.721488 0
-0.355715 10.325976 0
-0.397822 8.058397 0
0.824839 13.730343 0
1.507278 5.027866 1
0.099671 6.835839 1
-0.344008 10.717485 0
1.785928 7.718645 1
-0.918801 11.560217 0
-0.364009 4.747300 1
-0.841722 4.119083 1
0.490426 1.960539 1
-0.007194 9.075792 0
0.356107 12.447863 0
0.342578 12.281162 0
-0.810823 -1.466018 1
2.530777 6.476801 1
1.296683 11.607559 0
0.475487 12.040035 0
-0.783277 11.009725 0
0.074798 11.023650 0
-1.337472 0.468339 1
-0.102781 13.763651 0
-0.147324 2.874846 1
0.518389 9.887035 0
1.015399 7.571882 0
-1.658086 -0.027255 1
1.319944 2.171228 1
2.056216 5.019981 1
-0.851633 4.375691 1
-1.510047 6.061992 0
-1.076637 -3.181888 1
1.821096 10.283990 0
3.010150 8.401766 1
-1.099458 1.688274 1
-0.834872 -1.733869 1
-0.846637 3.849075 1
1.400102 12.628781 0
1.752842 5.468166 1
0.078557 0.059736 1
0.089392 -0.715300 1
1.825662 12.693808 0
0.197445 9.744638 0
0.126117 0.922311 1
-0.679797 1.220530 1
0.677983 2.556666 1
0.761349 10.693862 0
-2.168791 0.143632 1
1.388610 9.341997 0
0.317029 14.739025 0
参考书籍：
《统计学习方法》--李航
《机器学习实战》--Peter