基于Numpy的神经网络+手写数字识别
本文代码来自Tariq Rashid所著《Python神经网络编程》
代码分为三个部分，框架如下所示：
# neural network class definition
class neuralNetwork:
# initialise the neural network
def __init__():
pass
# train the neural network
def train():
pass
# query the neural network
def query():
pass
这是一个坚实的框架，可以在这个框架之上，充实神经网络工作的详细细节。
import numpy as np
import scipy.special
import matplotlib.pyplot as plt
#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
#learning rate
self.lr = learningrate
#link weight matrices, wih and who
self.wih = np.random.normal(0.0, pow(self.hnodes, -0.5), (self.hnodes, self.inodes))
self.who = np.random.normal(0.0, pow(self.onodes, -0.5), (self.onodes, self.hnodes))
#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, targets_list to 2d array
inputs = np.array(inputs_list, ndmin=2).T
targets = np.array(targets_list, ndmin=2).T
#calculate signals into hidden layer
hidden_inputs = np.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 = np.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 = np.dot(self.who.T, output_errors)
#update the weights for the links between the hidden and output layers
self.who += self.lr * np.dot((output_errors * final_outputs * (1.0 - final_outputs)), np.transpose(hidden_outputs))
#update the weights for the links between the input and hidden layers
self.wih += self.lr * np.dot((hidden_errors * hidden_outputs * (1.0 - hidden_outputs)), np.transpose(inputs))
pass
# query the neural network
def query(self, inputs_list):
#convert inputs_list to 2d array
inputs = np.array(inputs_list, ndmin=2).T
#calculate signals into hidden layer
hidden_inputs = np.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 = np.dot(self.who, hidden_outputs)
#calculate the signals emerging from final output layer
final_outputs = self.activation_function(final_inputs)
return final_outputs
pass
使用以上定义的神经网络类：
#number of input,hidden and output nodes
input_nodes = 784
hidden_nodes = 200
output_nodes = 10
#learning rate is 0.1
learning_rate = 0.1
#create instance of neural network
n = neuralNetwork(input_nodes, hidden_nodes, output_nodes, learning_rate)
#load the minist 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()
#train the neural network
#epochs is the number of times the training data set is used for training
epochs = 5
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 = (np.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 = np.zeros(output_nodes) + 0.01
#all_values[0] is the target label for this record
targets[int(all_values[0])] = 0.99
n.train(inputs, targets)
pass
pass
#load the minist 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()
#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 the first value
correct_label = int(all_values[0])
#scale and shift the inputs
inputs = (np.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 = np.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 matche correct answer, add 0 to scorecard
scorecard.append(0)
pass
pass
#calculate the performance score, the fraction of correct answers
scorecard_array = np.asarray(scorecard)
print("performance = ", scorecard_array.sum()/scorecard_array.size)
以上训练中所用到的数据集：