Logistic迴歸

Logistic函式

繪圖方法

>>> 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()
 

其在近0點陡峭的上升特點決定了它可以將一個迴歸問題轉換為一個分類問題。

在ml/dt.py中的資料生成

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中的繪圖

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

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


#繪圖
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])

分類器程式碼

# -*- coding: UTF-8 -*-
'''
Logistic 迴歸
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

#生成該矩陣的增廣矩陣，新增最後一列（全部為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

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


#梯度下降法學習
#alpha 學習因子
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

    #生成增廣矩陣
    X = augment(X)
    ndim += 1


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

    while cha > ep:
        #計算y = wx + b 
        ypred =X*w
        #計算 logistic
        ypred = sigmoid(ypred)
        #計算誤差
        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

測試

'''
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)