Logistic回归 Python实现

Logistic回归

>>> import numpy as np
>>> x = np.arange(-10,10,0.1)
>>> y = 1/(1+np.exp(-x))
>>> import matplotlib.pyplot as plt
>>> plt.plot(x,y)
[<matplotlib.lines.Line2D object at 0x00000000054FFE10>]
>>> plt.show()

在ml/dt.py中的数据生成

def createD3():
np.random.seed(101)
ndim = 2
n2  =10
a = 3+5*np.random.randn(n2,ndim)
b = 18+4*np.random.randn(n2,ndim)
X = np.concatenate((a,b))
ay = np.zeros(n2)
by = np.ones(n2)
ylabel = np.concatenate((ay,by))
return {'X':X,'ylabel':ylabel}

ml/fig.py中的绘图

# -*- coding: UTF-8 -*-
'''
Created on 2016-4-24

@author: Administrator
'''
import numpy as np
import operator
import matplotlib.pyplot as plt

#绘图
def plotData(ds,type='o'):
X= ds['X']
y=ds['ylabel']
n = X.shape[0]
cn = len(np.unique(y))
cs = ['r','g']
dd  = np.arange(n)
for i in range(2):
index= y == i
xx=X[dd[index]]
plt.plot(xx[:,0],xx[:,1],type,markerfacecolor=cs[i],markersize=14)

xmax = np.max(X[:,0])
xmin = np.min(X[:,0])
ymax = np.max(X[:,1])
ymin = np.min(X[:,1])
print xmin,xmax,ymin,ymax
dx = xmax - xmin
dy = ymax - ymin
plt.axis([xmin-dx*0.1, xmax + dx*0.1, ymin-dy*0.1, ymax +dy*0.1])

分类器代码

# -*- coding: UTF-8 -*-
'''
Logistic 回归
Created on 2016-4-26

@author: taiji1985
'''
import numpy as np
import operator
import matplotlib.pyplot as plt
def sigmoid(X):
return 1.0/(1+np.exp(-X))
pass

#生成该矩阵的增广矩阵，添加最后一列（全部为1）
def augment(X):
n,ndim = X.shape
a = np.mat(np.ones((n,1)))
return np.concatenate((X,a),axis=1)

def classify(X,w):
X = np.mat(X)
w = np.mat(w)
if w.shape[0] < w.shape[1]:
w = w.T

#增广
X= augment(X)
d = X*w
r = np.zeros((X.shape[0],1))
r[d>0] = 1
return r
pass

#梯度下降法学习
#alpha 学习因子
def learn(dataset,alpha=0.001):
X= dataset['X']
ylabel = dataset['ylabel']
n,ndim = X.shape
cls_label = np.unique(ylabel)
cn=len(cls_label)

X = np.mat(X)
ylabel = np.mat(ylabel).T

#生成增广矩阵
X = augment(X)
ndim += 1

max_c = 500
w = np.ones((ndim,1))
i = 0
ep= 0.0001
cha = 1

while cha > ep:
#计算y = wx + b
ypred =X*w
#计算 logistic
ypred = sigmoid(ypred)
#计算误差
error = ylabel - ypred
cha = alpha*X.T*error
w = w + cha
cha = np.abs( np.sum(cha))
print i,w.T
i=i+1

return w

测试

'''
Created on 2016-4-26

@author: Administrator
'''
from ml import lsd
from ml import dt
from ml import fig
import numpy as np

import matplotlib.pyplot as plt

ds = dt.createD3()
w = lsd.learn(ds,0.01)

#draw line
lx = [0, -w[2]/w[0]]
ly = [-w[2]/w[1],0]

plt.figure()

fig.plotData(ds, 'o')

plt.plot(lx,ly)

plt.show()

ypred = lsd.classify(ds['X'],w)
ylabel = np.mat(ds['ylabel']).T

print ypred
print ylabel

dist = np.sum(ypred != ylabel)
print dist,len(ylabel), 1.0*dist/len(ylabel)