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Logistic回归及梯度上升算法

逻辑回归

逻辑回归可以⽤来进⾏回归与分类，两者仅有略微不同，主体算法是⼀样的，本⽂以分类进⾏讲解。如下图⼆分类问题，我们希望到⼀个直线（⾼维空间为超平⾯）来将数据划分开。

梯度上升

有了以上的逻辑回归的理论基础，下⾯我们编程实现这⼀步骤。就以第⼀张图的样本为例进⾏，样本维数为2维，采⽤梯度上升算法进⾏迭代。

迭代步数⾃⼰选择

批量梯度上升

批量梯度上升每进⾏⼀次迭代更新就会计算所有样本，因此得到的模型正确率⽐较⾼，但同时计算复杂度⾼，算法耗时。计算过程如下：

代码如下

import numpy as np

import re

from pandas import DataFrame

import time as time

import matplotlib.pyplot as plt

import math

maxstep

def get_data(filename): #读取数据

f = open(filename)

data = DataFrame(columns=['x0','x1','x2','label']) #构造DataFrame存放数据，列名为x与y

line = f.readline()

line = line.strip()

p = repile(r'\s+') #由于数据由若⼲个空格分隔，构造正则表达式分隔

while line:

line = line.strip()

linedata = p.split(line)

data.set_value(len(data),['x0','x1','x2','label'],[1,float(linedata[0]),float(linedata[1]),int(linedata[2])]) #数据存⼊DataFrame

line = f.readline()

return np.array(data.loc[:,['x0','x1','x2']]),np.array(data['label'])

def sigmoid(x):

return1.0/(p(-x))

def stocGradAscent(dataMat,labelMat,alpha = 0.01): #随机梯度上升

start_time = time.time() #记录程序开始时间

m,n = dataMat.shape

weights = np.ones((n,1)) #分配权值为1

for i in range(m):

h = sigmoid(np.dot(dataMat[i],weights).astype('int64')) #注意：这⾥两个⼆维数组做内积后得到的dtype是object，需要转换成int64 error = labelMat[i]-h #误差

weights = weights + alpha*dataMat[i].reshape((3,1))*error #更新权重

duration = time.time()-start_time

print('time:',duration)

return weights

def gradAscent(dataMat,labelMat,alpha = 0.01,maxstep = 1000): #批量梯度上升

start_time = time.time()

m,n = dataMat.shape

weights = np.ones((n,1))

for i in range(maxstep):

h = sigmoid(np.dot(dataMat,weights).astype('int64')) #这⾥直接进⾏矩阵运算

labelMat = shape((100,1)) #label本为⼀维，转成2维

error = labelMat-h #批量计算误差

weights = weights + alpha*np.dot(dataMat.T,error) #更新权重

duration = time.time()-start_time

print('time:',duration)

return weights

def betterStoGradAscent(dataMat,labelMat,alpha = 0.01,maxstep = 150):

start_time = time.time()

m,n = dataMat.shape

weights = np.ones((n,1))

for j in range(maxstep):

for i in range(m):

alpha = 4/(1+i+j) + 0.01#设置更新率随迭代⽽减⼩

h = sigmoid(np.dot(dataMat[i],weights).astype('int64'))

error = labelMat[i]-h

weights = weights + alpha*dataMat[i].reshape((3,1))*error

duration = time.time()-start_time

print('time:',duration)

return weights

def show(dataMat, labelMat, weights):

#dataMat = np.mat(dataMat)

#labelMat = np.mat(labelMat)

m,n = dataMat.shape

min_x = min(dataMat[:, 1])

max_x = max(dataMat[:, 1])

xcoord1 = []; ycoord1 = []

xcoord2 = []; ycoord2 = []

for i in range(m):

if int(labelMat[i]) == 0:

xcoord1.append(dataMat[i, 1]); ycoord1.append(dataMat[i, 2])

elif int(labelMat[i]) == 1:

xcoord2.append(dataMat[i, 1]); ycoord2.append(dataMat[i, 2])

fig = plt.figure()

ax = fig.add_subplot(111)

ax.scatter(xcoord1, ycoord1, s=30, c="red", marker="s")

ax.scatter(xcoord2, ycoord2, s=30, c="green")

x = np.arange(min_x, max_x, 0.1)

效果

随机梯度：批量梯度： y = (-float(weights[0]) - float(weights[1])*x) / float(weights[2]) ax.plot(x, y)

plt.xlabel("x1"); plt.ylabel("x2")

plt.show()

if __name__=='__main__':

dataMat,labelMat = get_data('')

weights = gradAscent(dataMat,labelMat)

show(dataMat,labelMat,weights)

本文发布于:2024-09-24 13:13:31，感谢您对本站的认可！

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