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import numpy as np
import gzip
import pickle
class Network(object):
def __init__(self, sizes):
self.num_layers = len(sizes)#sizes 列表包含 各层神经元的数量。
self.sizes = sizes
self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
self.weights = [np.random.randn(y, x) for x,y in zip(sizes[:-1], sizes[1:])]
#例：net = Network([2,3,1]) 创建一个 第一层2个 第二层3个 第三层1个 神经元的 Network对象
def feedforward(self, a):
#当a为输入时，返回神经网络的输出
for b, w in zip(self.biases, self.weights):
a = sigmoid(np.dot(w, a) + b)
return a
def SGD(self, training_data, epochs, mini_batch_size, eta, test_data = None):
#epochs=迭代次数 eta=学习速率
if test_data: n_test = len(test_data)
n = len(training_data)
for j in range(epochs):
np.random.shuffle(training_data)
mini_batches = [training_data[k:k+mini_batch_size] for k in range(0, n, mini_batch_size)]
for mini_batch in mini_batches:
self.update_mini_batch(mini_batch, eta)
if test_data:
print("Epoch {0}: {1}/ {2}".format(j, self.evaluate(test_data), n_test))
else:
print("Epoch {0} complete".format(j))
def update_mini_batch(self, mini_batch, eta):
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:
delta_nabla_b, delta_nabla_w = self.backdrop(x, y)
nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
self.weights = [w-(eta/len(mini_batch))*nw for w, nw in zip(self.weights, nabla_w)]
self.biases = [b-(eta/len(mini_batch))*nb for b, nb in zip(self.biases, nabla_b)]
def evaluate(self, test_data): #测试当前迭代期对测试数据的效果
test_results = [(np.argmax(self.feedforward(x)), y) for (x, y) in test_data]
return sum(int(x == y) for (x, y) in test_results)
def cost_derivative(self, output_activations, y):
return output_activations - y
def backdrop(self, x, y):
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
activation = x
activations = [x]
zs = []
#z是上一层的输入
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation)+b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
delta = self.cost_derivative(activations[-1], y) * sigmoid_prime(zs[-1])
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
for l in range(2, self.num_layers):
z = zs[-l]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
return (nabla_b, nabla_w)
def sigmoid(z): #激活函数 常用于二分类 等问题 不过存在 极大值或极小值 梯度趋于0的问题
return 1.0/(1.0+np.exp(-z))
def sigmoid_prime(z): # 计算sigmoid函数的导数
return sigmoid(z)*(1-sigmoid(z))
def load_data():
with gzip.open('C:\\Users\\tt235\\Desktop\\Code\\code\\代码复现\\BP神经网络\\mnist.pkl.gz', 'rb') as f:
training_data, validation_data, test_data = pickle.load(f, encoding='latin1')
return (training_data, validation_data, test_data)
def load_data_wrapper():
tr_d, va_d, te_d = load_data()
training_inputs = [np.reshape(x, (784, 1)) for x in tr_d[0]]
training_results = [vectorized_result(y) for y in tr_d[1]]
training_data = list(zip(training_inputs, training_results))
validation_inputs = [np.reshape(x, (784, 1)) for x in va_d[0]]
validation_data = list(zip(validation_inputs, va_d[1]))
test_inputs = [np.reshape(x, (784, 1)) for x in te_d[0]]
test_data = list(zip(test_inputs, te_d[1]))
return (training_data, validation_data, test_data)
def vectorized_result(j):
e = np.zeros((10, 1))
e[j] = 1.0
return e
training_data, validation_data, test_data = load_data_wrapper()
net = Network([784, 41, 10])
net.SGD(training_data, 3, 10, 3.0, test_data = test_data) |