损失函数为Cross entropy的手写数字识别神经网络代码与实现
损失函数为cross entropy ，
作者：mercies
weights,biases的初始化为改进的初始化
import numpy as np
import random
class Network2(object):
def _init__(self, sizes, cost):
self.layernumber = len(sizes)
self.sizes = len(sizes)
self.defualt_weights()
self.cost = cost
def defualt_weights(self):
self.biases = [np.random.randn(y, 1) for y in self.sizes[1:]]
self.weights = [np.random.randn(y, x) / np.sqrt(x)
for x, y in zip(self.sizes[:-1], self.sizes[1:])]
def cost(self, a, y):
return np.sum(np.nan_to_num(-y * np.log(a) - (1 - y) * np.log(1 - a)))
def feedforward(self, a):
for b, w in zip(self.biases, self.weights):
a = sigmoid(np.dot(w, a) + b)
return a
def evaluate(self, test_data):
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_derivate(self, out_activation, y):
return out_activation - y
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.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)]
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 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 = x
activations = [x]
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)
delta = self.cost_derivate(activations[-1], y)
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
for j in range(2, self.layernumber):
z = zs[-j]
ps = sigmoid_prime(z)
delta = np.dot(self.weights[-j+1].transpose(), delta) * ps
nabla_b[-j] = delta
nabla_w[-j] = np.dot(delta, activations[-j-1].transpose())
return nabla_b, nabla_w
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 i in range(epochs):
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(i, self.evaluate(test_data), n_test))
else:
print('Epoch{0} complete'.format(i))
def sigmoid(z):
return 1.0 / (1.0 + np.exp(-z))
def sigmoid_prime(z):
return sigmoid(z) * (1 - sigmoid(z))
作者：mercies
