IDE：PyCharm Edu 4.02
环境：Adaconda3 python3.6
关键词：sigmoid函数、批梯度上升法、随机梯度上升法
from numpy import *
import matplotlib.pyplot as plt
def loadDataSet():
dataMat = []
labelMat = []
with open('testSet.txt') as fr:
for line in fr.readlines():
lineArr = line.strip().split()
dataMat.append([1.0,float(lineArr[0]),float(lineArr[1])])
labelMat.append(int(lineArr[2]))
return dataMat,labelMat
dataMat,labelMat = loadDataSet()
def sigmoid(inX):
return 1.0/(1+exp(-inX))
# 批梯度上升算法（计算量大）
def gradAscent(dataMatIn,classLabels):
#convert to NumPy matrix
dataMatrix = mat(dataMatIn) # 100 by 3
labelMat = mat(classLabels).transpose() # 100 by 1
m,n = shape(dataMatrix)
alpha = 0.001
maxCycles = 500 #迭代次数
weights = ones((n,1)) #矩阵 3 by 1
for k in range(maxCycles):
h = sigmoid(dataMatrix*weights) # 两个矩阵类型 *表示矩阵乘法
error = labelMat-h
weights = weights + alpha * dataMatrix.transpose() * error #批梯度下降法公式
return weights
weights1 = gradAscent(dataMat,labelMat)
#print(weights1) # print(weights1.getA())
# 画出数据集和logistic回归最佳拟合直线
def plotBestFit(weights):
dataArr = array(dataMat) #二维时，array()与mat()函数效果相同
n = shape(dataArr)[0] #行数
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=30,c='red',marker='s')
ax.scatter(xcord2,ycord2,s=30,c='green')
x = arange(-3.0,3.0,0.1) # 数组（60，）
#根据sigmoid(z)函数，0是两个分类的分界处
#z=w0x0+w1x1+w2x2 令z=0，x0=1解出x1与x2的关系
y = (-weights[0]-weights[1]*x)/weights[2] # 矩阵（1,60）
# 原文 ax.plot(x,y)
ax.plot(x,y.transpose())
plt.xlabel('X1');plt.ylabel('X2')
plt.show()
#原文 plotBestFit(weights1.getA())
#print(plotBestFit(weights1))
# 随机梯度上升算法
def stocGradAscent0(dataMatrix,classLabels):
m,n = shape(dataMatrix)
alpha = 0.01
weights = ones(n) # 数组
for i in range(m):
h = sigmoid(sum(dataMatrix[i]*weights)) # 元素相乘再求和即w0x0+w1x1+w2x2
error = classLabels[i] - h
weights = weights + alpha * error * dataMatrix[i]
return weights
weights2 = stocGradAscent0(array(dataMat),labelMat)
# print(weights2)
# print(plotBestFit(weights2))
# 改进的随机梯度下降法
# alpha随着迭代次数不断减小
def stocGradAscent1(dataMatrix,classLabels,numIter=150):
m,n = shape(dataMatrix)
weights = ones(n) # 数组对象
dataMatrix = array(dataMatrix) #转换为numpy格式
for j in range(numIter):
# 原文 dataIndex = range(m)
dataIndex = list(range(m))
for i in range(m):
# 随机选择一个样本进行权重的更新
alpha = 4/(1.0+j+i)+0.001 #apha decreases with iteration, does not
randIndex = int(random.uniform(0,len(dataIndex))) #go to 0 because of the constant
h = sigmoid(sum(dataMatrix[randIndex]*weights))
error = classLabels[randIndex] - h
weights = weights + alpha * error * dataMatrix[randIndex]
del(dataIndex[randIndex])
return weights
weights3 = stocGradAscent1(dataMat,labelMat)
print(plotBestFit(weights3))
注解：
1、numpy：矩阵和数组的转换
np.mat(变量)函数 ：将对象转换为matrix
np.变量.getA()：将矩阵转换为数组
例子：批梯度下降法返回一个矩阵weight1s，而plotBestFit(weights)函数接收一个数组，
因此，调用命令为plotBestFit(weights1.getA())。
直接使用 plotBestFit(weights1)报错：x and y must have same first dimension, but have shapes (60,) and (1, 60)
解决方法：将原文的ax.plot(x,y) 改为ax.plot(x,y.transpose())
2、区分list、numpy的矩阵及数组
（1）
list对象中间有逗号[1,1,1,1,1]
print(ones(5)) #数组
print(ones((5,1))) #矩阵
[ 1. 1. 1. 1. 1.]
[[ 1.]
[ 1.]
[ 1.]
[ 1.]
[ 1.]]
（2）
矩阵对象：* 表示矩阵乘法
ndarray对象： * 表示元素乘法；dot(A,B)表示矩阵乘法。
当然，二维的ndarray与matrix相同。
python列表：print([1,2,3]*2) 结果：[1,2,3,1,2,3]
若想从列表得到数乘结果，可以使用列表生成式！
（3）记住随机梯度上升法的推导公式
weights = weights + alpha * error * dataMatrix[randIndex]