Neural Network

 

Simple Neural Network in Python

Step 01:

import numpy as np

import matplotlib.pyplot as plt # to plot error during training

Step 02: input

inputs=np.array([[0,1,0],

[0,1,1], [1,1,0],[1,0,1]])

Step 03: output

outputs=np.array([[0],[0],[1],[1]])

Step 04: create NeuralNetwork class

class NeuralNetwork:

Step 05: intialize variables in class

def __init__(self, inputs, outputs):

self.inputs = inputs

self.outputs = outputs

Step 06: initialize weights as .50 for simplicity

self.weights = np.array([[.50], [.50], [.50]])

self.error_history = []

self.epoch_list = []

Step 07: activation function ==> S(x) = 1/1+e^(-x)

def sigmoid(self, x, deriv=False):

if deriv == True:

return x * (1 — x)

return 1 / (1 + np.exp(-x))

Step 08: data will flow through the neural network.

def feed_forward(self):

self.hidden = self.sigmoid(np.dot(self.inputs, self.weights))

Step 09: going backwards through the network to update weights

def backpropagation(self):

self.error = self.outputs — self.hidden

delta = self.error * self.sigmoid(self.hidden, deriv=True)

self.weights += np.dot(self.inputs.T, delta)

Step 10: train the neural net for 25,000 iterations

def train(self, epochs=25000):

for epoch in range(epochs):

Step 11: flow forward and produce an output

self.feed_forward()

Step 12: go back though the network to make corrections based on the output

self.backpropagation()

Step 13: keep track of the error history over each epoch

self.error_history.append(np.average(np.abs(self.error)))

self.epoch_list.append(epoch)

Step 14: function to predict output on new and unseen input data

def predict(self, new_input):

prediction = self.sigmoid(np.dot(new_input, self.weights))

return prediction

Step 15: create neural network

NN = NeuralNetwork(inputs, outputs)

Step 16: train neural network

NN.train()

Step 17: create two new examples to predict

example = np.array([[1, 1, 0]])

example_2 = np.array([[0, 1, 1]])

Step 18: print the predictions for both examples

print(NN.predict(example), ‘ — Correct: ‘, example[0][0])

print(NN.predict(example_2), ‘ — Correct: ‘, example_2[0][0])

Step 19: plot the error over the entire training duration

plt.figure(figsize=(15,5))

plt.plot(NN.epoch_list, NN.error_history)

plt.xlabel(‘Epoch’)

plt.ylabel(‘Error’)

plt.show()