用一條直線對數據進行擬合的過程稱為回歸。邏輯回歸分類的思想是：根據現有數據對分類邊界線建立回歸公式。
公式表示為：

一、梯度上升法

每次迭代所有的數據都參與計算。

for 循環(huán)次數:
        訓練

代碼如下：

import numpy as npimport matplotlib.pyplot as pltdef 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,labelVecdef 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 wdef 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、隨機梯度上升法

1.學習參數隨迭代次數調整，可以緩解參數的高頻波動。
2.隨機選取樣本來更新回歸參數，可以減少周期性的波動。

for 循環(huán)次數:
    for 樣本數量：
        更新學習速率
        隨機選取樣本
        訓練
        在樣本集中刪除該樣本

代碼如下：

import numpy as npimport matplotlib.pyplot as pltdef 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,labelVecdef 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 wif __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)