Make a neural network with Python
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MNIST in CSV

• Import Libraries
import numpy
# scipy.special for the sigmoid function expit()
import scipy.special
# library for plotting arrays
import matplotlib.pyplot
# ensure the plots are inside this notebook, not an external window
%matplotlib inline
• Class of neural network
# neural network class definition
class neuralNetwork:

# initialise the neural network
def __init__(self, inputnodes, hiddennodes, outputnodes, learningrate):
# set number of nodes in each input, hidden, output layer
self.inodes = inputnodes
self.hnodes = hiddennodes
self.onodes = outputnodes

# link weight matrices, wih and who
# weights inside the arrays are w_i_j, where link is from node i to node j in the next layer
# w11 w21
# w12 w22 etc
self.wih = numpy.random.normal(0.0, pow(self.inodes, -0.5), (self.hnodes, self.inodes))
self.who = numpy.random.normal(0.0, pow(self.hnodes, -0.5), (self.onodes, self.hnodes))

# learning rate
self.lr = learningrate

# activation function is the sigmoid function
self.activation_function = lambda x: scipy.special.expit(x)

pass

# train the neural network
def train(self, inputs_list, targets_list):
# convert inputs list to 2d array
inputs = numpy.array(inputs_list, ndmin=2).T
targets = numpy.array(targets_list, ndmin=2).T

# calculate signals into hidden layer
hidden_inputs = numpy.dot(self.wih, inputs)
# calculate the signals emerging from hidden layer
hidden_outputs = self.activation_function(hidden_inputs)

# calculate signals into final output layer
final_inputs = numpy.dot(self.who, hidden_outputs)
# calculate the signals emerging from final output layer
final_outputs = self.activation_function(final_inputs)

# output layer error is the (target - actual)
output_errors = targets - final_outputs
# hidden layer error is the output_errors, split by weights, recombined at hidden nodes
hidden_errors = numpy.dot(self.who.T, output_errors)

# update the weights for the links between the hidden and output layers
self.who += self.lr * numpy.dot((output_errors * final_outputs * (1.0 - final_outputs)), numpy.transpose(hidden_outputs))

# update the weights for the links between the input and hidden layers
self.wih += self.lr * numpy.dot((hidden_errors * hidden_outputs * (1.0 - hidden_outputs)), numpy.transpose(inputs))

pass
# query the neural network
def query(self, inputs_list):
# convert inputs list to 2d array
inputs = numpy.array(inputs_list, ndmin=2).T

# calculate signals into hidden layer
hidden_inputs = numpy.dot(self.wih, inputs)
# calculate the signals emerging from hidden layer
hidden_outputs = self.activation_function(hidden_inputs)

# calculate signals into final output layer
final_inputs = numpy.dot(self.who, hidden_outputs)
# calculate the signals emerging from final output layer
final_outputs = self.activation_function(final_inputs)

return final_outputs
• Create an instance
# number of input, hidden and output nodes
input_nodes = 784
hidden_nodes = 200
output_nodes = 10

# learning rate
learning_rate = 0.2

# create instance of neural network
n = neuralNetwork(input_nodes,hidden_nodes,output_nodes, learning_rate)
• Import training set
# load the mnist training data CSV file into a list
training_data_file = open("mnist_dataset/mnist_train.csv", 'r')
training_data_list = training_data_file.readlines()
training_data_file.close()
• Training
#epochs is the number of times the training data set is used for training
epochs = 2
for e in range(epochs):
# go through all records in the training data set
for record in training_data_list:
# split the record by the ',' commas
all_values = record.split(',')
# scale and shift the inputs
inputs = (numpy.asfarray(all_values[1:]) / 255.0 * 0.99) + 0.01
# create the target output values (all 0.01, except the desired label which is 0.99)
targets = numpy.zeros(output_nodes) + 0.01
# all_values is the target label for this record
targets[int(all_values)] = 0.99
n.train(inputs, targets)
pass
pass
• Import test set
# load the mnist test data CSV file into a list
test_data_file = open("mnist_dataset/mnist_test.csv", 'r')
test_data_list = test_data_file.readlines()
test_data_file.close()
• Testing
#test the neural network
#scorecard for how well the network performs, initially empty
scorecard = []
# go through all the records in the test data set
for record in test_data_list:
# split the record by the ',' commas
all_values = record.split(',')
# correct answer is first value
correct_label = int(all_values)
# scale and shift the inputs
inputs = (numpy.asfarray(all_values[1:]) / 255.0 * 0.99) + 0.01
# query the network
outputs = n.query(inputs)
# the index of the highest value corresponds to the label
label = numpy.argmax(outputs)
# append correct or incorrect to list
if (label == correct_label):
# network's answer matches correct answer, add 1 to scorecard
scorecard.append(1)
else:
# network's answer doesn't match correct answer, add 0 to scorecard
scorecard.append(0)
pass

pass
print(scorecard)
• Performance Score
# calculate the performance score, the fraction of correct answers
scorecard_array = numpy.asarray(scorecard)
print ("performance = ", scorecard_array.sum() / scorecard_array.size)
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