深度学习
Environment Setup
!pip install numpy scipy matplotlib ipython scikit-learn pandas pillow
Introduction to Artificial Neural Network
Activation Function
Step function
import numpy as np
import matplotlib.pylab as plt
def step_function(x):
return np.array(x>0, dtype=np.int)
x = np.arange(-5.0, 5.0, 0.1)
y = step_function(x)
plt.plot(x, y)
plt.ylim(-0.1, 1.1)
plt.show()
Sigmoid Function
import numpy as np
import matplotlib.pylab as plt
def sigmoid(x):
return 1 / (1 + np.exp(-x))
# x = np.array([-1.0, 1.0, 2.0])
# print(y)
x = np.arange(-5.0, 5.0, 0.1)
y = sigmoid(x)
plt.plot(x, y)
plt.ylim(-0.1, 1.1)
plt.show()
Relu Function
$$ f(x)=max(0,x) $$
import numpy as np
import matplotlib.pylab as plt
def relu(x):
return np.maximum(0, x)
# x = np.array([-5.0, 5.0, 0.1])
# print(y)
x = np.arange(-6.0, 6.0, 0.1)
y = relu(x)
plt.plot(x, y)
plt.ylim(-1, 6)
plt.show()
损失函数
平方和误差
Sum of squared error $$ E = \frac{1}{2} \sum_{k} (y_k -t_k)^2 $$
Cross Entropy error
$$ E = - \sum_k t_k log\ y_k $$