1 sigmoid
1.1 sigmoid函数的公式
\[f(x)= \frac{1}{1+e^{-x}}
\]
1.2 sigmoid函数的导数公式
\[f\'(x)= f(x)\cdot [1-f(x)]
\]
1.3 sigmoid函数代码实现
class SigmoidActivator(object):
def sigmoid(self,x):
return 1.0/(1.0+np.exp(-x))
def sigmoid_derivative(self,x):
return self.sigmoid(x)*(1-self.sigmoid(x))
def sigmoid_graph(self):
x = np.arange(-8,8,1)
y = self.sigmoid(x)
y_derivative = self.sigmoid_derivative(x)
plt.plot(x,y,\'g:\')
plt.plot(x,y_derivative,\'r-\')
plt.legend([\'sigmoid\', \'sigmoid_derivative\'])
plt.show()
效果图：
if __name__ == \'__main__\':
x = 3
# Sigmoid
sig = SigmoidActivator()
sig.sigmoid(x)
sig.sigmoid_derivative(x)
sig.sigmoid_graph()
2 tanh
2.1 tanh函数的公式
\[f(x)=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}
\]
2.2 tanh函数的导数公式
\[f(x)=1-[f(x)]^{2}
\]
2.3 tanh函数代码实现
class TanhActivator(object):
def tanh(self,x):
return 2.0/(1+np.exp(-2*x))-1.0
def tanh_derivative(self,x):
return 1-self.tanh(x)*self.tanh(x)
def tanh_graph(self):
x = np.arange(-8,8,1)
y = self.tanh(x)
y_derivative = self.tanh_derivative(x)
plt.plot(x,y,\'g:\')
plt.plot(x,y_derivative,\'r-\')
plt.title("tanh函数及其导数（正反向）")
plt.legend([\'tanh\',\'tanh_dervative\'])
plt.show()
效果图：
if __name__ == \'__main__\':
x = 3
#tanh
tanh = TanhActivator()
tanh.tanh(x)
tanh.tanh_derivative(x)
tanh.tanh_graph()
3 Relu
3.1 Relu函数的公式
\[f(x)=\left\{\begin{matrix}
x, & x\geq 0\\
0,& x< 0
\end{matrix}\right. \]
3.2 Relu函数的导数公式
\[f^{\'}(x)=\left\{\begin{matrix}
1, & x\geq 0\\
0, & x< 0
\end{matrix}\right. \]
3.3 Relu函数代码实现
class ReluActivator(object):
def Relu(self,x):
return np.maximum(x,0.0)
def Relu_derivative(self,x):
return np.where(x>0,1,0)
def Relu_gragh(self):
x = np.arange(-8,8,0.1)
y = self.Relu(x)
y_derivative = self.Relu_derivative(x)
plt.plot(x,y,\'g:\')
plt.plot(x,y_derivative,\'r-\')
plt.title("Relu函数及其导数（正反向）")
plt.legend([\'Relu\',\'Relu_derivative\'])
plt.show()
效果图：
if __name__ == \'__main__\':
x = 3
#ReLU
relu = ReluActivator()
relu.Relu(x)
relu.Relu_derivative(x)
relu.Relu_gragh()