Sigmoid(Logistic) Activation Function ( with python code)

by keshav

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Sigmoid Activation Function is one of the widely used activation functions in deep learning. As its name suggests the curve of the sigmoid function is S-shaped.

 

Sigmoid transforms the values between the range 0 and 1.

 

The Mathematical function of the sigmoid function is:

Derivative of the sigmoid is:

Also Read:

• Numpy Tutorials [beginners to Intermediate]
• Softmax Activation Function in Neural Network [formula included]
• Hyperbolic Tangent (tanh) Activation Function [with python code]
• ReLU Activation Function [with python code]
• Leaky ReLU Activation Function [with python code]

Python Code

 

import numpy as np
import matplotlib.pyplot as plt

# Sigmoid Activation Function
def sigmoid(x):
  return 1/(1+np.exp(-x))

# Derivative of Sigmoid
def der_sigmoid(x):
  return sigmoid(x) * (1- sigmoid(x))

# Generating data to plot
x_data = np.linspace(-10,10,100)
y_data = sigmoid(x_data)
dy_data = der_sigmoid(x_data)

# Plotting
plt.plot(x_data, y_data, x_data, dy_data)
plt.title('Sigmoid Activation Function & Derivative')
plt.legend(['sigmoid','der_sigmoid'])
plt.grid()
plt.show()

 

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