logisic回歸梯度更新公式.png
數(shù)據(jù)分布.png
#!/usr/bin/python3
import numpy as np
from math import *
import matplotlib.pyplot as plt
def Simulation():
X=np.random.rand(100,2)
X=np.mat(X)
X1=X[:,0]
X2=X[:,1]
Noise=np.random.normal(0,0.09,[100,1])
y=X1+X2+Noise
#y=X1+X2+Noise
y=np.where(y> 1, 1, 0)
#return y,X1,X2,Y
d=np.hstack([y,X1,X2])
return d
def visualize(d):
#The Label 0 and 1 data
k=np.where(d[:,0]==1)[0]
Label_T=d[k]
k=np.where(d[:,0]==0)[0]
Label_F=d[k]
plt.figure()
plt.scatter(Label_T[:,1].tolist(),Label_T[:,2].tolist(),c='r',marker="^",label="T")
plt.scatter(Label_F[:,1].tolist(),Label_F[:,2].tolist(),c='b',marker="s",label="F")
plt.title('Scatter Plot Of Simulation Data ')
plt.xlabel('X1')
plt.ylabel('X2')
plt.legend(loc='upper right')
#plt.show()
return plt
def draw_boundary(w,d):
plt=visualize(d)
x1=np.linspace(0,1,20)
x2=-( w[0,0]+w[0,1]*x1)/w[0,2]
plt.plot(x1,x2)
plt.show()
def Sigmoid(X,W):
Y=1/(1+np.exp(-X*(W.T)))
return Y
def GD(iteratons,X,Y,alpha=0.01):
N=X.shape[1]+1
M=X.shape[0]
W=np.random.rand(1,N)
X0=np.ones((M,1))
X=np.hstack([X0,X])
for i in range(iteratons):
H=Sigmoid(X,W)
delta_W=(H-Y).T*X
W+=-alpha*delta_W/M
return W
def SGD(threshold,X,Y,alpha=0.01):
N=X.shape[1]+1
M=X.shape[0]
W=np.random.rand(1,N)
X0=np.ones((M,1))
X=np.hstack([X0,X])
while 1:
i=np.random.randint(0,M,[1,1]) #randomly select 10 samples
i=i.tolist()[0]
SX=X[i,:];SY=Y[i,]
H=Sigmoid(SX,W)
delta_W=(H-SY).T*SX
delta_w=np.sum(delta_W)
if abs(delta_w)<threshold: break
W+=-alpha*delta_W/M
return W
if __name__ == '__main__':
#Generating Simulation data
d=Simulation()
Y=d[:,0]
X=d[:,1:3]
#visualize
plt=visualize(d)
plt.show()
#GD
w=GD(10000,X,Y)
draw_boundary(w,d)
#SGD
w=SGD(0.2,X,Y)
draw_boundary(w,d)
設(shè)置學(xué)習(xí)率alpha很重要疑苔，感覺隨機(jī)梯度下降不容易收斂副瀑。
logistic回歸決策邊界.png
