话说网上记录这本书内容的博客好多，而且挺多写的不错的。emmmmm，我写的这么渣我都不好意思写了。
3点半睡7点起，困困的一天，看懂了原理但愣是没看懂Logistic回归的代码，这里先贴个代码暂存一下，改天弄懂了再补。
from numpy import *
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 + exp(-inX))
def gradAscent(dataMatIn, classLabels):
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 plotBestFit(weights):
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 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 = 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 stocGradAscent0(dataMatrix, classLabels):
m, n = shape(dataMatrix)
alpha = 0.01
weights = ones(n)
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):
m, n = shape(dataMatrix)
alpha = 0.01
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 classifyVector(inX, weights):
prob = sigmoid(sum(inX * weights))
if prob > 0.5:
return 1
else:
return 0
def colicTest():
frTrain = open('horseColicTraining.txt')
frTest = open('horseColicTest.txt')
trainingSet = []
trainingLabels = []
for line in frTrain.readlines():
currLine = line.strip().split(' ')
lineArr = []
for i in range(21):
lineArr.append(float(currLine[i]))
trainingSet.append(lineArr)
trainingLabels.append(float(currLine[21]))
trainWeights = stocGradAscent1(array(trainingSet), trainingLabels, 500)
errorCount = 0
numTestVec = 0.0
for line in frTest.readlines():
numTestVec += 1.0
currLine = line.strip().split(' ')
lineArr = []
for i in range(21):
lineArr.append(float(currLine[i]))
if int(classifyVector(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)))
if __name__ == '__main__':
dataArr, labelMat = loadDataSet()
# weights = gradAscent(dataArr, labelMat)
# weights = stocGradAscent0(array(dataArr), labelMat)
weights = stocGradAscent1(array(dataArr), labelMat)
# plotBestFit(weights.getA())
plotBestFit(weights)
multiTest()
Logistic回归的目的是寻找一个非线性函数Sigmoid的最佳拟合参数，求解过程可以由最优化算法来完成。
在最优化算法中，最常用的就是梯度上升算法，而它又可以简化为随机梯度上升算法。
两者效果相当，但后者占用更少的计算资源。
此外它还是一个在线算法，可以在新数据到来时就完成参数更新，而不需要重新读取整个数据集来进行批处理运算。