第五章 Logistic回归
PS：个人笔记 根据《机器学习实战》这本书，Jack-Cui的博客，以及深度眸的视频进行学习
1 改进的随机梯度上升算法
from matplotlib.font_manager import FontProperties
import matplotlib.pyplot as plt
import numpy as np
import random
def loadDataSet():
dataMat = []
labelMat = []
fr = open('testSet.txt')
for line in fr.readlines():
lineArr = line.strip().split()
dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])
labelMat.append(int(lineArr[2]))
fr.close()
return dataMat, labelMat
def sigmoid(inX):
return 1.0 / (1 + np.exp(-inX))
def plotBestFit(weights):
dataMat, labelMat = loadDataSet()
dataArr = np.array(dataMat)
n = np.shape(dataMat)[0]
xcord1 = []; ycord1 = []
xcord2 = []; ycord2 = []
for i in range(n):
if int(labelMat[i]) == 1:
xcord1.append(dataArr[i,1]); ycord1.append(dataArr[i,2])
else:
xcord2.append(dataArr[i,1]); ycord2.append(dataArr[i,2])
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(xcord1, ycord1, s = 20, c = 'red', marker = 's',alpha=.5)
ax.scatter(xcord2, ycord2, s = 20, c = 'green',alpha=.5)
x = np.arange(-3.0, 3.0, 0.1)
y = (-weights[0] - weights[1] * x) / weights[2]
ax.plot(x, y)
plt.title('BestFit')
plt.xlabel('X1'); plt.ylabel('X2')
plt.show()
"""
函数说明:改进的随机梯度上升算法
Parameters:
dataMatrix - 数据数组
classLabels - 数据标签
numIter - 迭代次数
Returns:
weights - 求得的回归系数数组(最优参数)
"""
def stocGradAscent1(dataMatrix, classLabels, numIter=150):
m,n = np.shape(dataMatrix) # m=100,n=3
weights = np.ones(n) #参数初始化,weights:[1,1,1]
for j in range(numIter): #j = 0
dataIndex = list(range(m)) #dataIndex:[0,...,99]
for i in range(m): #i = 0 ,循环起到加总的作用
alpha = 4/(1.0+j+i)+0.01 #⭐降低alpha的大小，每次减小1/(j+i)。改进之处，迭代的速度会更快，4.01
randIndex = int(random.uniform(0,len(dataIndex))) #随机选取样本，0-99随机选一个数
h = sigmoid(sum(dataMatrix[randIndex]*weights)) #选择随机选取的一个样本，计算h=hθ(Xi)
error = classLabels[randIndex] - h #计算误差 这里就是Y-hθ(Xi)
weights = weights + alpha * error * dataMatrix[randIndex] #更新回归系数，这里就是θ+α[Y-hθ(Xi)]*Xi，上面循环起到加总的作用
del(dataIndex[randIndex]) #删除已经使用的样本，这里就不会重复抽取了
return weights #weights其实就是更新了150*100次。
if __name__ == '__main__':
dataMat, labelMat = loadDataSet()
weights = stocGradAscent1(np.array(dataMat), labelMat)
plotBestFit(weights)
二个改进之处：
①alpha在每次迭代的时候都会调整，越来越小，不会变成0，因为有一个常数项（先开始大后来小，符合梯度变化。）注意J是迭代次数。
②更新回归系数时，只是用一个样本点，并且选择的样本点是随机的，每次迭代不使用已经用过的样本点（减少计算量）
2 回归系数与迭代次数的关系
from matplotlib.font_manager import FontProperties
import matplotlib.pyplot as plt
import numpy as np
import random
def loadDataSet():
dataMat = []
labelMat = []
fr = open('testSet.txt')
for line in fr.readlines():
lineArr = line.strip().split()
dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])
labelMat.append(int(lineArr[2]))
fr.close()
return dataMat, labelMat
def sigmoid(inX):
return 1.0 / (1 + np.exp(-inX))
def gradAscent(dataMatIn, classLabels):
dataMatrix = np.mat(dataMatIn)
labelMat = np.mat(classLabels).transpose()
m, n = np.shape(dataMatrix)
alpha = 0.01
maxCycles = 500
weights = np.ones((n,1))
weights_array = np.array([])
for k in range(maxCycles):
h = sigmoid(dataMatrix * weights)
error = labelMat - h
weights = weights + alpha * dataMatrix.transpose() * error
weights_array = np.append(weights_array,weights)
weights_array = weights_array.reshape(maxCycles,n)
return weights.getA(),weights_array
def stocGradAscent1(dataMatrix, classLabels, numIter=150):
m,n = np.shape(dataMatrix)
weights = np.ones(n)
weights_array = np.array([])
for j in range(numIter):
dataIndex = list(range(m))
for i in range(m):
alpha = 4/(1.0+j+i)+0.01
randIndex = int(random.uniform(0,len(dataIndex)))
h = sigmoid(sum(dataMatrix[randIndex]*weights))
error = classLabels[randIndex] - h
weights = weights + alpha * error * dataMatrix[randIndex]
weights_array = np.append(weights_array,weights,axis=0)
del(dataIndex[randIndex])
weights_array = weights_array.reshape(numIter*m,n)
return weights,weights_array
"""
函数说明:绘制回归系数与迭代次数的关系
Parameters:
weights_array1 - 回归系数数组1
weights_array2 - 回归系数数组2
Returns:
无
"""
def plotWeights(weights_array1,weights_array2):
font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14) #设置汉字格式
fig, axs = plt.subplots(nrows=3, ncols=2,sharex=False, sharey=False, figsize=(20,10))
x1 = np.arange(0, len(weights_array1), 1)
axs[0][0].plot(x1,weights_array1[:,0]) #weights_array1[:,0]代表W0
axs0_title_text = axs[0][0].set_title(u'梯度上升算法：回归系数与迭代次数关系',FontProperties=font)
axs0_ylabel_text = axs[0][0].set_ylabel(u'W0',FontProperties=font)
plt.setp(axs0_title_text, size=20, weight='bold', color='black')
plt.setp(axs0_ylabel_text, size=20, weight='bold', color='black')
axs[1][0].plot(x1,weights_array1[:,1]) #weights_array1[:,1]代表W1
axs1_ylabel_text = axs[1][0].set_ylabel(u'W1',FontProperties=font)
plt.setp(axs1_ylabel_text, size=20, weight='bold', color='black')
axs[2][0].plot(x1,weights_array1[:,2]) #weights_array1[:,2]代表W2
axs2_xlabel_text = axs[2][0].set_xlabel(u'迭代次数',FontProperties=font)
axs2_ylabel_text = axs[2][0].set_ylabel(u'W1',FontProperties=font)
plt.setp(axs2_xlabel_text, size=20, weight='bold', color='black')
plt.setp(axs2_ylabel_text, size=20, weight='bold', color='black')
x2 = np.arange(0, len(weights_array2), 1)
axs[0][1].plot(x2,weights_array2[:,0])
axs0_title_text = axs[0][1].set_title(u'改进的随机梯度上升算法：回归系数与迭代次数关系',FontProperties=font)
axs0_ylabel_text = axs[0][1].set_ylabel(u'W0',FontProperties=font)
plt.setp(axs0_title_text, size=20, weight='bold', color='black')
plt.setp(axs0_ylabel_text, size=20, weight='bold', color='black')
axs[1][1].plot(x2,weights_array2[:,1])
axs1_ylabel_text = axs[1][1].set_ylabel(u'W1',FontProperties=font)
plt.setp(axs1_ylabel_text, size=20, weight='bold', color='black')
axs[2][1].plot(x2,weights_array2[:,2])
axs2_xlabel_text = axs[2][1].set_xlabel(u'迭代次数',FontProperties=font)
axs2_ylabel_text = axs[2][1].set_ylabel(u'W2',FontProperties=font)
plt.setp(axs2_xlabel_text, size=20, weight='bold', color='black')
plt.setp(axs2_ylabel_text, size=20, weight='bold', color='black')
plt.show()
if __name__ == '__main__':
dataMat, labelMat = loadDataSet()
weights1,weights_array1 = stocGradAscent1(np.array(dataMat), labelMat)
weights2,weights_array2 = gradAscent(dataMat, labelMat)
plotWeights(weights_array1, weights_array2)
上图左侧相当于遍历整个数据集20次的时候，回归系数已收敛。训练已完成。
上图右侧当迭代次数为300多次的时候，回归系数才收敛。