Backpropagation Algorithm in Python

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Python Program to Implement the Backpropagation Algorithm Artificial Neural Network

Exp. No. 4.  Build an Artificial Neural Network by implementing the Backpropagation algorithm and test the same using appropriate data sets. 

Python Program to Implement and Demonstrate Backpropagation Algorithm Machine Learning

import numpy as np

X = np.array(([2, 9], [1, 5], [3, 6]), dtype=float)
y = np.array(([92], [86], [89]), dtype=float)
X = X/np.amax(X,axis=0) #maximum of X array longitudinally
y = y/100

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

#Derivative of Sigmoid Function
def derivatives_sigmoid(x):
    return x * (1 - x)

#Variable initialization
epoch=5 #Setting training iterations
lr=0.1 #Setting learning rate

inputlayer_neurons = 2 #number of features in data set
hiddenlayer_neurons = 3 #number of hidden layers neurons
output_neurons = 1 #number of neurons at output layer
#weight and bias initialization

wh=np.random.uniform(size=(inputlayer_neurons,hiddenlayer_neurons))
bh=np.random.uniform(size=(1,hiddenlayer_neurons))
wout=np.random.uniform(size=(hiddenlayer_neurons,output_neurons))
bout=np.random.uniform(size=(1,output_neurons))

#draws a random range of numbers uniformly of dim x*y
for i in range(epoch):
    #Forward Propogation
    hinp1=np.dot(X,wh)
    hinp=hinp1 + bh
    hlayer_act = sigmoid(hinp)
    outinp1=np.dot(hlayer_act,wout)
    outinp= outinp1+bout
    output = sigmoid(outinp)
    
    #Backpropagation
    EO = y-output
    outgrad = derivatives_sigmoid(output)
    d_output = EO * outgrad
    EH = d_output.dot(wout.T)
    hiddengrad = derivatives_sigmoid(hlayer_act)#how much hidden layer wts contributed to error
    d_hiddenlayer = EH * hiddengrad
    
    wout += hlayer_act.T.dot(d_output) *lr   # dotproduct of nextlayererror and currentlayerop
    wh += X.T.dot(d_hiddenlayer) *lr
    
    print ("-----------Epoch-", i+1, "Starts----------")
    print("Input: \n" + str(X)) 
    print("Actual Output: \n" + str(y))
    print("Predicted Output: \n" ,output)
    print ("-----------Epoch-", i+1, "Ends----------\n")
        
print("Input: \n" + str(X)) 
print("Actual Output: \n" + str(y))
print("Predicted Output: \n" ,output)

Training Examples:

Normalize the input

Output

———–Epoch- 1 Starts———-
Input:
[[0.66666667 1. ]
[0.33333333 0.55555556]
[1. 0.66666667]]
Actual Output:
[[0.92]
[0.86]
[0.89]]
Predicted Output:
[[0.81951208]
[0.8007242 ]
[0.82485744]]
———–Epoch- 1 Ends———-

———–Epoch- 2 Starts———-
Input:
[[0.66666667 1. ]
[0.33333333 0.55555556]
[1. 0.66666667]]
Actual Output:
[[0.92]
[0.86]
[0.89]]
Predicted Output:
[[0.82033938]
[0.80153634]
[0.82568134]]
———–Epoch- 2 Ends———-

———–Epoch- 3 Starts———-
Input:
[[0.66666667 1. ]
[0.33333333 0.55555556]
[1. 0.66666667]]
Actual Output:
[[0.92]
[0.86]
[0.89]]
Predicted Output:
[[0.82115226]
[0.80233463]
[0.82649072]]
———–Epoch- 3 Ends———-

———–Epoch- 4 Starts———-
Input:
[[0.66666667 1. ]
[0.33333333 0.55555556]
[1. 0.66666667]]
Actual Output:
[[0.92]
[0.86]
[0.89]]
Predicted Output:
[[0.82195108]
[0.80311943]
[0.82728598]]
———–Epoch- 4 Ends———-

———–Epoch- 5 Starts———-
Input:
[[0.66666667 1. ]
[0.33333333 0.55555556]
[1. 0.66666667]]
Actual Output:
[[0.92]
[0.86]
[0.89]]
Predicted Output:
[[0.8227362 ]
[0.80389106]
[0.82806747]]
———–Epoch- 5 Ends———-

Input:
[[0.66666667 1. ]
[0.33333333 0.55555556]
[1. 0.66666667]]
Actual Output:
[[0.92]
[0.86]
[0.89]]
Predicted Output:
[[0.8227362 ]
[0.80389106]
[0.82806747]]

Summary

This tutorial discusses how to Implement and demonstrate the Backpropagation Algorithm in Python. If you like the tutorial share it with your friends. Like the Facebook page for regular updates and YouTube channel for video tutorials.