Training the neural network using matrices.

matrices-training-method.py

# We train the neural network through a process of trial and error.
# Adjusting the synaptic weights each time.
def train(self, training_set_inputs, training_set_outputs, number_of_training_iterations):
    for iteration in xrange(number_of_training_iterations):
        # Pass the training set through our neural network
        output_from_layer_1, output_from_layer_2 = self.think(training_set_inputs)

        # Calculate the error for layer 2 (The difference between the desired output
        # and the predicted output).
        layer2_error = training_set_outputs - output_from_layer_2
        layer2_delta = layer2_error * self.__sigmoid_derivative(output_from_layer_2)

        # Calculate the error for layer 1 (By looking at the weights in layer 1,
        # we can determine by how much layer 1 contributed to the error in layer 2).
        layer1_error = layer2_delta.dot(self.layer2.synaptic_weights.T)
        layer1_delta = layer1_error * self.__sigmoid_derivative(output_from_layer_1)

        # Calculate how much to adjust the weights by
        layer1_adjustment = training_set_inputs.T.dot(layer1_delta)
        layer2_adjustment = output_from_layer_1.T.dot(layer2_delta)

        # Adjust the weights.
        self.layer1.synaptic_weights += layer1_adjustment
        self.layer2.synaptic_weights += layer2_adjustment