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.]])

以上就是本文的全部内容，希望对大家的学习有所帮助，也希望大家多多支持三水点靠木。