0.导航
| 这个作业属于哪个课程 |
人工智能实战 |
| 这个作业的要求在哪里 |
人工智能实战第五次作业（个人） |
| 我在这个课程的目标是 |
开拓视野，积累AI实战经验 |
| 这个作业在哪个具体方面帮助我 |
了解sigmoid激活函数和交叉熵函损失数，掌握用二分类的思想实现逻辑与门和或门的方法 |
1.具体作业内容
2.过程及代码
| x1 |
0 |
0 |
1 |
1 |
| x2 |
0 |
1 |
0 |
1 |
| y |
0 |
0 |
0 |
1 |
| x1 |
0 |
0 |
1 |
1 |
| x2 |
0 |
1 |
0 |
1 |
| y |
0 |
1 |
1 |
1 |
import numpy as np
import matplotlib.pyplot as plt
# 设置逻辑与门的样本和标签数据
def Read_AND_Data():
X = np.array([0,0,1,1,0,1,0,1]).reshape(2,4)
Y = np.array([0,0,0,1]).reshape(1,4)
return X,Y
# 设置逻辑或门的样本和标签数据
def Read_OR_Data():
X = np.array([0,0,1,1,0,1,0,1]).reshape(2,4)
Y = np.array([0,1,1,1]).reshape(1,4)
return X,Y
# Sigmoid函数
def Sigmoid(x):
s=1/(1+np.exp(-x))
return s
# 前向计算
def ForwardCalculationBatch(W, B, batch_X):
Z = np.dot(W, batch_X) + B
A = Sigmoid(Z)
return A
# 反向计算
def BackPropagationBatch(batch_X, batch_Y, A):
m = batch_X.shape[1]
dZ = A - batch_Y
dB = dZ.sum(axis=1, keepdims=True)/m
dW = np.dot(dZ, batch_X.T)/m
return dW, dB
# 更新权重参数
def UpdateWeights(W, B, dW, dB, eta):
W = W - eta * dW
B = B - eta * dB
return W, B
# 计算损失函数
def CheckLoss(W, B, X, Y):
m = X.shape[1]
A = ForwardCalculationBatch(W, B, X)
# Cross Entropy
J = np.sum(-(np.multiply(Y, np.log(A)) + np.multiply(1 - Y, np.log(1 - A))))
loss = J / m
return loss
# 初始化权重值
def InitialWeights(num_input, num_output, method):
if method == "zero":
# zero
W = np.zeros((num_output, num_input))
elif method == "norm":
# normalize
W = np.random.normal(size=(num_output, num_input))
elif method == "xavier":
# xavier
W=np.random.uniform(
-np.sqrt(6/(num_input+num_output)),
np.sqrt(6/(num_input+num_output)),
size=(num_output,num_input))
B = np.zeros((num_output, 1))
return W,B
# 这里直接搬教案代码了
def train(X, Y, ForwardCalculationBatch, CheckLoss):
num_example = X.shape[1]
num_feature = X.shape[0]
num_category = Y.shape[0]
# hyper parameters
eta = 0.5
max_epoch = 10000
# W(num_category, num_feature), B(num_category, 1)
W, B = InitialWeights(num_feature, num_category, "zero")
# calculate loss to decide the stop condition
loss = 5 # initialize loss (larger than 0)
error = 2e-3 # stop condition
# if num_example=200, batch_size=10, then iteration=200/10=20
for epoch in range(max_epoch):
for i in range(num_example):
# get x and y value for one sample
x = X[:,i].reshape(num_feature,1)
y = Y[:,i].reshape(1,1)
# get z from x,y
batch_a = ForwardCalculationBatch(W, B, x)
# calculate gradient of w and b
dW, dB = BackPropagationBatch(x, y, batch_a)
# update w,b
W, B = UpdateWeights(W, B, dW, dB, eta)
# end if
# end for
# calculate loss for this batch
loss = CheckLoss(W,B,X,Y)
print(epoch,i,loss,W,B)
# end if
if loss < error:
break
# end for
return W,B, epoch, loss
# 结果可视化
def ShowResult(W,B,X,Y,title):
# 根据w, b的值画出分割线
w = -W[0,0]/W[0,1]
b = -B[0,0]/W[0,1]
x = np.array([0,1])
y = w * x + b
plt.plot(x,y)
# 画出原始样本值
for i in range(X.shape[1]):
if Y[0,i] == 0:
plt.scatter(X[0,i],X[1,i],marker="o",c='b',s=64)
else:
plt.scatter(X[0,i],X[1,i],marker="^",c='r',s=64)
plt.axis([-0.1,1.1,-0.1,1.1])
plt.title(title)
plt.show()
# 主函数
def main(logic):
if logic == "AND":
X,Y = Read_AND_Data()
elif logic == "OR":
X,Y = Read_OR_Data()
W, B, epoch, loss = train(X, Y, ForwardCalculationBatch, CheckLoss)
print("epoch=",epoch)
print("loss=",loss)
print("w=",W)
print("b=",B)
ShowResult(W,B,X,Y,logic)
if __name__ == '__main__':
main("AND")
main("OR")
3.结果展示
- 逻辑与门分割结果图
- Output
epoch= 4251
loss= 0.0019995629053717527
w= [[11.76694002 11.76546912]]
b= [[-17.81530488]]
- 逻辑或门分割结果图
- Output
epoch= 2267
loss= 0.001999175331571145
w= [[11.74573383 11.74749036]]
b= [[-5.41268583]]