from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import axes3d
import numpy as np
from sklearn.neural_network import mlpclassifier
from sklearn.datasets import load_iris
def creat_data(n):
np.random
.seed(1)
x_11=np.random
.randint(0,100,(n,1))
x_12=np.random
.randint(0,100,(n,1))
x_13=20+np.random
.randint(0,10,(n,1))
x_21=np.random
.randint(0,100,(n,1))
x_22=np.random
.randint(0,100,(n,1))
x_23=10-np.random
.randint(0,10,(n,1))
new_x_12=x_12*np.sqrt(2)/2-x_13*np.sqrt(2)/2
new_x_13=x_12*np.sqrt(2)/2+x_13*np.sqrt(2)/2
new_x_22=x_22*np.sqrt(2)/2-x_23*np.sqrt(2)/2
new_x_23=x_22*np.sqrt(2)/2+x_23*np.sqrt(2)/2
plus_samples=np.hstack([x_11,new_x_12,new_x_13,np.ones((n,1))])
minus_samples=np.hstack([x_21,new_x_22,new_x_23,-np.ones((n,1))])
samples=np.vstack([plus_samples,minus_samples])
np.random
.shuffle(samples)
return samples
def
plot_samples
(ax,samples):
y=samples[:,-1]
y=samples[:,-1]
position_p=y==1
position_m=y==-1
ax.scatter(samples[position_p,0],samples[position_p,1],samples[position_p,2],marker='+',label='+',color='b')
ax.scatter(samples[position_m,0],samples[position_m,1],samples[position_m,2],marker='^',label='-',color='y')
fig=plt.figure()
ax=axes3d(fig)
data=creat_data(100)
plot_samples(ax,data)
ax.legend(loc='best')
plt.show()
def
perceptron
(train_data,eta,w_0,b_0):
x=train_data[:,:-1]
y=train_data[:,-1]
length=train_data.shape[0]
w=w_0
b=b_0
step_num=0
while
true:
i=0while(i1
x_i=x[i].reshape((x.shape[1],1))
y_i=y[i]
if y_i*(np.dot(np.transpose(w),x_i)+b)<=0:
w+=eta*y_i*x_i
b+=eta*y_i
break
else:
i+=1
if(i==length):
break
return(w,b,step_num)
def
creat_hyperplane
(x,y,w,b):
return (-w[0][0]*x-w[1][0]*y-b)/w[2][0]
得到w⃗ w
→，因為在計算中大量地需要w⃗ w→
def
creat_w
(train_data,alpha):
x=train_data[:,:-1]
y=train_data[:,-1]
n=train_data.shape[0]
w=np.zeros((x.shape[1],1))
for i in range(0,n):
w+=alpha[i][0]*y[i]*(x[i].reshape(x[i].size,1))
return w
def
perceptron_dual
(train_data,eta,alpha_0,b_0):
x=train_data[:,:-1]
y=train_data[:,-1]
length=train_data.shape[0]
alpha=alpha_0
b=b_0
step_num=0
while_num=0
while
true:
i=0while(i1
x_i=x[i].reshape((x.shape[1],1))
y_i=y[i]
w=creat_w(train_data,alpha)
z=y_i*(np.dot(np.transpose(w),x_i)+b)
if z<=0:
alpha[i][0]+=eta
b+=eta*y_i
break
else:
i+=1
if(i==length):
break
return (alpha,b,step_num)
data=creat_data(100)
eta,w_0,b_0=0.1,np.ones((3,1),dtype=float),1
w_1,b_1,num_1=perceptron(data,eta,w_0,b_0)
alpha,b_2,num_2=perceptron_dual(data,eta=0.1,alpha_0=np.zeros((data.shape[0]*2,1)),b_0=0)
w_2=creat_w(data,alpha)
print('w_1,b_1',w_1,b_1)
print('w_2,b_2',w_2,b_2)
fig=plt.figure()
plt.suptitle('perceptron')
ax=axes3d(fig)
#繪製樣本點
plot_samples(ax,data)
#繪製分離超平面
x=np.linspace(-30,100,100)
y=np.linspace(-30,100,100)
x,y=np.meshgrid(x,y)
z=creat_hyperplane(x,y,w_1,b_1)
z_2=creat_hyperplane(x,y,w_2,b_2)
ax.plot_su***ce(x,y,z,rstride=1,cstride=1,color='g',alpha=0.2)
ax.plot_su***ce(x,y,z,rstride=1,cstride=1,color='c',alpha=0.2)
ax.legend(loc='best'
)plt.show()
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