python编写Logistic逻辑回归

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：

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。

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。

string.strip().split()

2.判断类型

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.]])

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