http://blog.csdn.net/u011239443/article/details/75008380
完整代码：https://github.com/xiaoyesoso/neural-networks-and-deep-learning/blob/master/src/network.py
初始化
# sizes 是每层节点数的数组
def __init__(self, sizes):
self.num_layers = len(sizes)
self.sizes = sizes
# randn 产生 高斯分布的随机数值矩阵
# 输入层 有没有 biases
self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
# 层与层之间 都有 weights
# y 是下一层的节点数，x 是上一层的节点数
self.weights = [np.random.randn(y, x)
for x, y in zip(sizes[:-1], sizes[1:])]
训练
# training_data 训练数据
# epochs 迭代次数
# mini_batch_size 小批数据大小
# test_data 测试数据
def SGD(self, training_data, epochs, mini_batch_size, eta,
test_data=None):
if test_data: n_test = len(test_data)
n = len(training_data)
for j in xrange(epochs):
random.shuffle(training_data)
mini_batches = [
training_data[k:k+mini_batch_size]
for k in xrange(0, n, mini_batch_size)]
for mini_batch in mini_batches:
# 这里更新模型
self.update_mini_batch(mini_batch, eta)
if test_data:
# 若 test_data ！= None，
# 预测 验证
print "Epoch {0}: {1} / {2}".format(
j, self.evaluate(test_data), n_test)
else:
print "Epoch {0} complete".format(j)
更新模型：
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:
# 得到反向传播调整
delta_nabla_b, delta_nabla_w = self.backprop(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)]
# 更新参数
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)]
反向传播
可以先回顾下方向传播的四个公式：http://blog.csdn.net/u011239443/article/details/74859614
def backprop(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 为每层的激活函数
# 输入层没有激活函数
activation = x
activations = [x]
# zs 为除了第一层外的每一层的输入
zs = []
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation)+b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# cost_derivative 就是求两者的误差
# sigmoid_prime 为 sigmoid 的导数
# 可见 公式（BP1）
delta = self.cost_derivative(activations[-1], y) * \
sigmoid_prime(zs[-1])
# 可见 公式（BP3）
nabla_b[-1] = delta
# 可见 公式（BP4）
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
for l in xrange(2, self.num_layers):
z = zs[-l]
sp = sigmoid_prime(z)
# 可见 公式（BP2）
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)
测试
回到SGD中的def evaluate：
def evaluate(self, test_data):
# np.argmax(self.feedforward(x)) 预测结果并取整
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 feedforward(self, a):
# 把测试数据代入训练好的网络
for b, w in zip(self.biases, self.weights):
a = sigmoid(np.dot(w, a)+b)
return a
这里写图片描述