Logistic回归
算法优缺点：
1.计算代价不高，易于理解和实现
2.容易欠拟合，分类精度可能不高
3.适用数据类型：数值型和标称型
算法思想：
- 其实就我的理解来说，logistic回归实际上就是加了个sigmoid函数的线性回归，这个sigmoid函数的好处就在于，将结果归到了0到1这个区间里面了，并且sigmoid（0）=0.5，也就是说里面的线性部分的结果大于零小于零就可以直接计算到了。这里的求解方式是梯度上升法，具体我就不扯了，最推荐的资料还是Ng的视频，那里面的梯度下降就是啦，只不过一个是梯度上升的方向一个是下降的方向，做法什么的都一样。
- 而梯度上升（准确的说叫做“批梯度上升”）的一个缺点就是计算量太大了，每一次迭代都需要把所有的数据算一遍，这样一旦训练集大了之后，那么计算量将非常大，所以这里后面还提出了随机梯度下降，思想就是每次只是根据一个data进行修正。这样得到的最终的结果可能会有所偏差但是速度却提高了很多，而且优化之后的偏差还是很小的。随机梯度上升的另一个好处是这是一个在线算法，可以根据新数据的到来不断处理
函数：
loadDataSet()
创建数据集，这里的数据集就是在一个文件中，这里面有三行，分别是两个特征和一个标签，但是我们在读出的时候还加了X0这个属性sigmoid(inX)
sigmoid函数的计算，这个函数长这样的，基本坐标大点就和阶跃函数很像了
gradAscend(dataMatIn, classLabels)
梯度上升算法的实现，里面用到了numpy的数组，并且设定了迭代次数500次，然后为了计算速度都采取了矩阵计算，计算的过程中的公式大概是：w= w+alpha*(y-h)x[i]（一直懒得写公式，见谅。。。）gradAscendWithDraw(dataMatIn, classLabels)
上面的函数加强版，增加了一个weight跟着迭代次数的变化曲线stocGradAscent0(dataMatrix, classLabels)
这里为了加快速度用来随机梯度上升，即每次根据一组数据调整（额，好吧，这个际没有随机因为那是线面那个函数）stocGradAscentWithDraw0(dataMatrix, classLabels)
上面的函数加强版，增加了一个weight跟着迭代次数的变化曲线stocGradAscent1(dataMatrix, classLabels, numIter=150)
这就真的开始随机了，随机的主要好处是减少了周期性的波动了。另外这里还加入了alpha的值随迭代变化，这样可以让alpha的值不断的变化，但是都不会减小到0。stocGradAscentWithDraw1(dataMatrix, classLabels, numIter=150)
上面的函数加强版，增加了一个weight跟着迭代次数的变化曲线plotBestFit(wei)
根据计算的weight值画出拟合的线，直观观察效果
运行效果分析：
1、梯度上升：
2、随机梯度上升版本1
3、随机梯度上升版本2
#coding=utf-8
from numpy import * 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]))
return dataMat, labelMat def sigmoid(inX):
return 1.0/(1+exp(-inX)) def gradAscend(dataMatIn, classLabels):
dataMatrix = mat(dataMatIn)
labelMat = mat(classLabels).transpose()
m,n = shape(dataMatrix)
alpha = 0.001
maxCycle = 500
weight = ones((n,1))
for k in range(maxCycle):
h = sigmoid(dataMatrix*weight)
error = labelMat - h
weight += alpha * dataMatrix.transpose() * error
#plotBestFit(weight)
return weight def gradAscendWithDraw(dataMatIn, classLabels):
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(311,ylabel='x0')
bx = fig.add_subplot(312,ylabel='x1')
cx = fig.add_subplot(313,ylabel='x2')
dataMatrix = mat(dataMatIn)
labelMat = mat(classLabels).transpose()
m,n = shape(dataMatrix)
alpha = 0.001
maxCycle = 500
weight = ones((n,1))
wei1 = []
wei2 = []
wei3 = []
for k in range(maxCycle):
h = sigmoid(dataMatrix*weight)
error = labelMat - h
weight += alpha * dataMatrix.transpose() * error
wei1.extend(weight[0])
wei2.extend(weight[1])
wei3.extend(weight[2])
ax.plot(range(maxCycle), wei1)
bx.plot(range(maxCycle), wei2)
cx.plot(range(maxCycle), wei3)
plt.xlabel('iter_num')
plt.show()
return weight def stocGradAscent0(dataMatrix, classLabels):
m,n = shape(dataMatrix) alpha = 0.001
weight = ones(n)
for i in range(m):
h = sigmoid(sum(dataMatrix[i]*weight))
error = classLabels[i] - h
weight = weight + alpha * error * dataMatrix[i]
return weight def stocGradAscentWithDraw0(dataMatrix, classLabels):
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(311,ylabel='x0')
bx = fig.add_subplot(312,ylabel='x1')
cx = fig.add_subplot(313,ylabel='x2')
m,n = shape(dataMatrix) alpha = 0.001
weight = ones(n)
wei1 = array([])
wei2 = array([])
wei3 = array([])
numIter = 200
for j in range(numIter):
for i in range(m):
h = sigmoid(sum(dataMatrix[i]*weight))
error = classLabels[i] - h
weight = weight + alpha * error * dataMatrix[i]
wei1 =append(wei1, weight[0])
wei2 =append(wei2, weight[1])
wei3 =append(wei3, weight[2])
ax.plot(array(range(m*numIter)), wei1)
bx.plot(array(range(m*numIter)), wei2)
cx.plot(array(range(m*numIter)), wei3)
plt.xlabel('iter_num')
plt.show()
return weight def stocGradAscent1(dataMatrix, classLabels, numIter=150):
m,n = shape(dataMatrix) #alpha = 0.001
weight = ones(n)
for j in range(numIter):
dataIndex = 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]*weight))
error = classLabels[randIndex] - h
weight = weight + alpha * error * dataMatrix[randIndex]
del(dataIndex[randIndex])
return weight def stocGradAscentWithDraw1(dataMatrix, classLabels, numIter=150):
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(311,ylabel='x0')
bx = fig.add_subplot(312,ylabel='x1')
cx = fig.add_subplot(313,ylabel='x2')
m,n = shape(dataMatrix) #alpha = 0.001
weight = ones(n)
wei1 = array([])
wei2 = array([])
wei3 = array([])
for j in range(numIter):
dataIndex = 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]*weight))
error = classLabels[randIndex] - h
weight = weight + alpha * error * dataMatrix[randIndex]
del(dataIndex[randIndex])
wei1 =append(wei1, weight[0])
wei2 =append(wei2, weight[1])
wei3 =append(wei3, weight[2])
ax.plot(array(range(len(wei1))), wei1)
bx.plot(array(range(len(wei2))), wei2)
cx.plot(array(range(len(wei2))), wei3)
plt.xlabel('iter_num')
plt.show()
return weight def plotBestFit(wei):
import matplotlib.pyplot as plt
weight = wei
dataMat,labelMat = loadDataSet()
dataArr = array(dataMat)
n = shape(dataArr)[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=30, c='red', marker='s')
ax.scatter(xcord2, ycord2, s=30, c='green')
x = arange(-3.0, 3.0, 0.1)
y = (-weight[0] - weight[1]*x)/weight[2]
ax.plot(x,y)
plt.xlabel('X1')
plt.ylabel('X2')
plt.show() def main():
dataArr,labelMat = loadDataSet()
#w = gradAscendWithDraw(dataArr,labelMat)
w = stocGradAscentWithDraw0(array(dataArr),labelMat)
plotBestFit(w) if __name__ == '__main__':
main()机器学习笔记索引