python编写Logistic逻辑回归_Python

用一条直线对数据进行拟合的过程称为回归。逻辑回归分类的思想是：根据现有数据对分类边界线建立回归公式。
公式表示为：

python编写Logistic逻辑回归

一、梯度上升法

每次迭代所有的数据都参与计算。

for 循环次数:
训练

代码如下：

									import numpy as np

									import matplotlib.pyplot as plt

									def loadData():

									  labelVec = []

									  dataMat = []

									  with open('testSet.txt') as f:

									    for line in f.readlines():

									      dataMat.append([1.0,line.strip().split()[0],line.strip().split()[1]])

									      labelVec.append(line.strip().split()[2])

									  return dataMat,labelVec

									def Sigmoid(inX):

									  return 1/(1+np.exp(-inX))

									def trainLR(dataMat,labelVec):

									  dataMatrix = np.mat(dataMat).astype(np.float64)

									  lableMatrix = np.mat(labelVec).T.astype(np.float64)

									  m,n = dataMatrix.shape

									  w = np.ones((n,1))

									  alpha = 0.001

									  for i in range(500):

									    predict = Sigmoid(dataMatrix*w)

									    error = predict-lableMatrix

									    w = w - alpha*dataMatrix.T*error

									  return w

									def plotBestFit(wei,data,label):

									  if type(wei).__name__ == 'ndarray':

									    weights = wei

									  else:

									    weights = wei.getA()

									  fig = plt.figure(0)

									  ax = fig.add_subplot(111)

									  xxx = np.arange(-3,3,0.1)

									  yyy = - weights[0]/weights[2] - weights[1]/weights[2]*xxx

									  ax.plot(xxx,yyy)

									  cord1 = []

									  cord0 = []

									  for i in range(len(label)):

									    if label[i] == 1:

									      cord1.append(data[i][1:3])

									    else:

									      cord0.append(data[i][1:3])

									  cord1 = np.array(cord1)

									  cord0 = np.array(cord0)

									  ax.scatter(cord1[:,0],cord1[:,1],c='red')

									  ax.scatter(cord0[:,0],cord0[:,1],c='green')

									  plt.show()

									if __name__ == "__main__":

									  data,label = loadData()

									  data = np.array(data).astype(np.float64)

									  label = [int(item) for item in label]

									  weight = trainLR(data,label)

									  plotBestFit(weight,data,label)

二、随机梯度上升法

1.学习参数随迭代次数调整，可以缓解参数的高频波动。
2.随机选取样本来更新回归参数，可以减少周期性的波动。

python编写Logistic逻辑回归

for 循环次数:
    for 样本数量：
        更新学习速率
        随机选取样本
        训练
        在样本集中删除该样本

代码如下：

									import numpy as np

									import matplotlib.pyplot as plt

									def loadData():

									  labelVec = []

									  dataMat = []

									  with open('testSet.txt') as f:

									    for line in f.readlines():

									      dataMat.append([1.0,line.strip().split()[0],line.strip().split()[1]])

									      labelVec.append(line.strip().split()[2])

									  return dataMat,labelVec

									def Sigmoid(inX):

									  return 1/(1+np.exp(-inX))

									def plotBestFit(wei,data,label):

									  if type(wei).__name__ == 'ndarray':

									    weights = wei

									  else:

									    weights = wei.getA()

									  fig = plt.figure(0)

									  ax = fig.add_subplot(111)

									  xxx = np.arange(-3,3,0.1)

									  yyy = - weights[0]/weights[2] - weights[1]/weights[2]*xxx

									  ax.plot(xxx,yyy)

									  cord1 = []

									  cord0 = []

									  for i in range(len(label)):

									    if label[i] == 1:

									      cord1.append(data[i][1:3])

									    else:

									      cord0.append(data[i][1:3])

									  cord1 = np.array(cord1)

									  cord0 = np.array(cord0)

									  ax.scatter(cord1[:,0],cord1[:,1],c='red')

									  ax.scatter(cord0[:,0],cord0[:,1],c='green')

									  plt.show()

									def stocGradAscent(dataMat,labelVec,trainLoop):

									  m,n = np.shape(dataMat)

									  w = np.ones((n,1))

									  for j in range(trainLoop):

									    dataIndex = range(m)

									    for i in range(m):

									      alpha = 4/(i+j+1) + 0.01

									      randIndex = int(np.random.uniform(0,len(dataIndex)))

									      predict = Sigmoid(np.dot(dataMat[dataIndex[randIndex]],w))

									      error = predict - labelVec[dataIndex[randIndex]]

									      w = w - alpha*error*dataMat[dataIndex[randIndex]].reshape(n,1)

									      np.delete(dataIndex,randIndex,0)

									  return w

									if __name__ == "__main__":

									  data,label = loadData()

									  data = np.array(data).astype(np.float64)

									  label = [int(item) for item in label]

									  weight = stocGradAscent(data,label,300)  

									  plotBestFit(weight,data,label)

三、编程技巧

1.字符串提取

将字符串中的'\n', ‘\r', ‘\t', ' ‘去除，按空格符划分。

1	`string.strip().split()`

2.判断类型

1	`if` `type(secondTree[value]).__name__` `==` `'dict':`

3.乘法

numpy两个矩阵类型的向量相乘，结果还是一个矩阵

									c = a*b

									c

									Out[66]: matrix([[ 6.830482]])

两个向量类型的向量相乘，结果为一个二维数组

									b

									Out[80]: 

									array([[ 1.],

									    [ 1.],

									    [ 1.]])

									a

									Out[81]: array([1, 2, 3])

									a*b

									Out[82]: 

									array([[ 1., 2., 3.],

									    [ 1., 2., 3.],

									    [ 1., 2., 3.]])

									b*a

									Out[83]: 

									array([[ 1., 2., 3.],

									    [ 1., 2., 3.],

									    [ 1., 2., 3.]])