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 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、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 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)

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*bcOut[66]: matrix([[ 6.830482]])

两个向量类型的向量相乘，结果为一个二维数组

bOut[80]: array([[ 1.], [ 1.], [ 1.]])aOut[81]: array([1, 2, 3])a*bOut[82]: array([[ 1., 2., 3.], [ 1., 2., 3.], [ 1., 2., 3.]])b*aOut[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。