Artificial Neural Network by implementing the Back propagation algorithm and test the same using appropriate data sets.

Back propagation algorithm->

program->

from math import exp
from random import seed
from random import random
def initialize_network(n_inputs,n_hidden,n_outputs):
    network=list()
    hidden_layer=[{'weights':[random()for i in range(n_inputs+1)]} for i in range(n_hidden)]
    network.append(hidden_layer)
    output_layer=[{'weights':[random()for i in range(n_hidden+1)]} for i in range(n_outputs)]
    network.append(output_layer)
    return network
def activate(weights,inputs):
    activation=weights[-1]
    for i in range(len(weights)-1):
        activation+=weights[i]*inputs[i]
    return activation
def transfer(activation):
    return 1.0/(1.0+exp(-activation))
def forward_propagate(network,row):
    inputs=row
    for layer in network:
        new_inputs=[]
        for neuron in layer:
            activation=activate(neuron['weights'],inputs)
            neuron['output']=transfer(activation)
            new_inputs.append(neuron['output'])
        inputs=new_inputs
    return inputs
def transfer_derivative(output):
    return output*(1.0-output)
def backward_propagate_error(network,expected):
    for i in reversed(range(len(network))):
        layer=network[i]
        errors=list()
        if i!=len(network)-1:
            for j in range(len(layer)):
                error=0.0
                for neuron in network[i+1]:
                    error+=(neuron['weights'][j]*neuron['delta'])
                    errors.append(error)
        else:
            for j in range(len(layer)):
                neuron=layer[j]
                errors.append(expected[j]-neuron['output'])
        for j in range(len(layer)):
            neuron=layer[j]
            neuron['delta']=errors[j]*transfer_derivative(neuron['output'])    
def update_weights(network,row,l_rate):
    for i in range(len(network)):
        inputs=row[:-1]
        if i!=0:
            inputs=[neuron['output'] for neuron in network[i-1]]
            for neuron in network[i]:
                for j in range(len(inputs)):
                    neuron['weights'][j]+=l_rate*neuron['delta']*inputs[j]
                neuron['weights'][-1]+=l_rate*neuron['delta']                    
def train_network(network,train,l_rate,n_epoch,n_outputs):
    for epoch in range(n_epoch):
        sum_error=0
        for row in train:
            outputs=forward_propagate(network,row)
            expected=[0 for i in range(n_outputs)]
            expected[row[-1]]=1
            sum_error+=sum([expected[i]-outputs[i]**2 for i in range(len(expected))])
            backward_propagate_error(network,expected)
            update_weights(network,row,l_rate)
        print('>epoch=%d,lrate=%.3f,error=%.3f'%(epoch,l_rate,sum_error))
seed(1)
dataset=[[2.7810836,2.550537003,0],
         [1.465489372,2.362125076,0],
         [3.396561688,4.400293529,0],
         [1.38807019,1.850220317,0],
         [3.06407232,3.005305973,0],
         [7.627531214,2.759262235,1],
         [5.332441248,2.088626775,1],
         [6.922596716,1.77106367,1],
         [8.675418651,-0.242068655,1],
         [7.673756466,3.508563011,1]
        ]
n_inputs=len(dataset[0])-1
n_outputs=len(set([row[-1] for row in dataset]))
network=initialize_network(n_inputs,2,n_outputs)
train_network(network,dataset,0.5,20,n_outputs)
print(network)
for layer in network:

    print(layer)


Output->

>epoch=0,lrate=0.500,error=-0.857
>epoch=1,lrate=0.500,error=1.759
>epoch=2,lrate=0.500,error=3.443
>epoch=3,lrate=0.500,error=4.262
>epoch=4,lrate=0.500,error=4.624
>epoch=5,lrate=0.500,error=4.784
>epoch=6,lrate=0.500,error=4.856
>epoch=7,lrate=0.500,error=4.888
>epoch=8,lrate=0.500,error=4.902
>epoch=9,lrate=0.500,error=4.909
>epoch=10,lrate=0.500,error=4.912
>epoch=11,lrate=0.500,error=4.913
>epoch=12,lrate=0.500,error=4.914
>epoch=13,lrate=0.500,error=4.914
>epoch=14,lrate=0.500,error=4.914
>epoch=15,lrate=0.500,error=4.914
>epoch=16,lrate=0.500,error=4.914
>epoch=17,lrate=0.500,error=4.914
>epoch=18,lrate=0.500,error=4.914
>epoch=19,lrate=0.500,error=4.914
[[{'weights': [0.13436424411240122, 0.8474337369372327, 0.763774618976614], 'output': 0.99157530623528, 'delta': -0.00016301917329962238}, {'weights': [0.2550690257394217, 0.49543508709194095, 0.4494910647887381], 'output': 0.9844051047537846, 'delta': -0.0009816034444098982}], [{'weights': [0.1352957155754806, -0.06993695351348819, -0.5152093452497912], 'output': 0.42656544528564916, 'delta': -0.10434105007212165}, {'weights': [-0.38274067993191285, 0.7914341824323032, 0.07234040575369743], 'output': 0.5794832633351258, 'delta': 0.10247253219310253}]]
[{'weights': [0.13436424411240122, 0.8474337369372327, 0.763774618976614], 'output': 0.99157530623528, 'delta': -0.00016301917329962238}, {'weights': [0.2550690257394217, 0.49543508709194095, 0.4494910647887381], 'output': 0.9844051047537846, 'delta': -0.0009816034444098982}]
[{'weights': [0.1352957155754806, -0.06993695351348819, -0.5152093452497912], 'output': 0.42656544528564916, 'delta': -0.10434105007212165}, {'weights': [-0.38274067993191285, 0.7914341824323032, 0.07234040575369743], 'output': 0.5794832633351258, 'delta': 0.10247253219310253}]