| 项目 | 内容 |
|---|---|
| 这个作业属于哪个课程 | 人工智能实战2019 |
| 这个作业的要求在哪里 | 作业要求 |
| 我在这个课程的目标是 | 将机器学习理论与实践相结合，获得一定的项目经验，提高编程能力 |
| 这个作业在哪个具体方面帮助我实现目标 | 使用sigmoid激活函数和二分类交叉熵函损失数 |
| 我的GitHub链接 | https://github.com/QiangLiu404 |
正文
一、样本与特征：
- 逻辑与门的样本和特征
| Example | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| x1 | 0 | 0 | 1 | 1 |
| x2 | 0 | 1 | 0 | 1 |
| y | 0 | 0 | 0 | 1 |
- 逻辑或门的样本和特征
| Example | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| x1 | 0 | 0 | 1 | 1 |
| x2 | 0 | 1 | 0 | 1 |
| y | 0 | 1 | 1 | 1 |
二、代码实现：
1.逻辑或门 OR
import numpy as np
from matplotlib import pyplot as plt
def sigmod(x):
S=1/(1+np.exp(-x))
return S
def Forward(w,b,x):
z = np.dot(w, x) + b
N=sigmod(z)
return N
def Back(x,y,N,Data_size):
dz=N-y
db=dz.sum(axis=1,keepdims=True)/Data_size
dw=np.dot(dz,x.T)/Data_size
return dw,db
def UpWeight(w,b,dw,db,eta):
w=w-eta*dw
b=b-eta*db
return w,b
def Loss(w,b,X,Y,Data_size):
size=Data_size
A=Forward(w,b,X)
n1 = 1 - Y
n2 = np.log(1-A)
n3 = np.log(A)
n4 = np.multiply(n1,n2)
n5 = np.multiply(Y,n3)
LOSS = np.sum(-(n4 + n5))
loss = LOSS/size
return loss
def Show(w,b,X,Y,Data_size):
w1 = w[0,0]
w2 = w[0,1]
w = -w1/w2
b = -b[0,0]/w1
x = np.array([0,1])
y = w * x + b
plt.plot(x,y,color='r',label='y='+str(round(w,3))+'x+'+str(round(b,3)))
# plot data
for i in range (Data_size):
if Y[0,i] == 0:
plt.scatter(X[0,i],X[1,i],marker='o',c='r',s=40)
else:
plt.scatter(X[0,i],X[1,i],marker='*',c='b',s=40)
plt.axis([-0.2,1.3,-0.2,1.3])
plt.title('OR')
plt.xlabel("X1")
plt.ylabel("X2")
plt.show()
eta = 0.6
w = np.array([0,0]).reshape(1,2)
b = np.array([0]).reshape(1,1)
eps = 1e-2
max_epoch = 10000
loss = 1
X = np.array([0,0,1,1,0,1,0,1]).reshape(2,4)
Y = np.array([0,1,1,1]).reshape(1,4)
Data_features = X.shape[0]
Data_size = X.shape[1]
for epoch in range(max_epoch):
for i in range(Data_size):
x = X[:,i].reshape(2,1)
y = Y[:,i].reshape(1,1)
z = Forward(w,b,x)
dW, dB = Back(x,y,z,Data_size)
w, b = UpWeight(w,b,dW,dB,eta)
loss = Loss(w,b,X,Y,Data_size)
print(epoch,i,loss,w,b)
if loss < eps:
break
print("epoch=%d,loss=%f,w1=%f,w2=%f,b=%f" %(epoch,loss,w[0,0],w[0,1],b))
Show(w,b,X,Y,Data_size)
结果：
epoch=1546,loss=0.009995,w1=8.515211,w2=8.517734,b=-3.791060图片：
2.逻辑与门 AND
import numpy as np
from matplotlib import pyplot as plt
def sigmod(x):
S=1/(1+np.exp(-x))
return S
def Forward(w,b,x):
z = np.dot(w, x) + b
N=sigmod(z)
return N
def Back(x,y,N,Data_size):
dz=N-y
db=dz.sum(axis=1,keepdims=True)/Data_size
dw=np.dot(dz,x.T)/Data_size
return dw,db
def UpWeight(w,b,dw,db,eta):
w=w-eta*dw
b=b-eta*db
return w,b
def Loss(w,b,X,Y,Data_size):
size=Data_size
A=Forward(w,b,X)
n1 = 1 - Y
n2 = np.log(1-A)
n3 = np.log(A)
n4 = np.multiply(n1,n2)
n5 = np.multiply(Y,n3)
LOSS = np.sum(-(n4 + n5))
loss = LOSS/size
return loss
def Show(w,b,X,Y,Data_size):
w1 = w[0,0]
w2 = w[0,1]
w = -w1/w2
b = -b[0,0]/w1
x = np.array([0,1])
y = w * x + b
plt.plot(x,y,color='r',label='y='+str(round(w,3))+'x+'+str(round(b,3)))
# plot data
for i in range (Data_size):
if Y[0,i] == 0:
plt.scatter(X[0,i],X[1,i],marker='o',c='r',s=40)
else:
plt.scatter(X[0,i],X[1,i],marker='*',c='b',s=40)
plt.axis([-0.2,1.3,-0.2,1.3])
plt.title('AND')
plt.xlabel("X1")
plt.ylabel("X2")
plt.show()
eta = 0.6
w = np.array([0,0]).reshape(1,2)
b = np.array([0]).reshape(1,1)
eps = 1e-2
max_epoch = 10000
loss = 1
X = np.array([0,0,1,1,0,1,0,1]).reshape(2,4)
Y = np.array([0,0,0,1]).reshape(1,4)
Data_features = X.shape[0]
Data_size = X.shape[1]
for epoch in range(max_epoch):
for i in range(Data_size):
x = X[:,i].reshape(2,1)
y = Y[:,i].reshape(1,1)
z = Forward(w,b,x)
dW, dB = Back(x,y,z,Data_size)
w, b = UpWeight(w,b,dW,dB,eta)
loss = Loss(w,b,X,Y,Data_size)
print(epoch,i,loss,w,b)
if loss < eps:
break
print("epoch=%d,loss=%f,w1=%f,w2=%f,b=%f" %(epoch,loss,w[0,0],w[0,1],b))
Show(w,b,X,Y,Data_size)
结果：
epoch=2872,loss=0.009998,w1=8.537218,w2=8.535023,b=-12.970825图片：
