CrossEntropyCost+L2 手写数字识的代码实现

本次实验我用的损失函数是CrossEntropyCost+L2

import numpy as np
import random

class Network3(object):
    def __init__(self, sizes, cost):
        self.layernumber = len(sizes)
        self.sizes = sizes
        self.default_weights()
        self.cost = cost

    def default_weights(self):
        self.biases = [np.random.rand(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 Cross_entropy(self, a, y, lamda, n):
        return (np.sum(np.nan_to_num(-y * np.log(a) - (1 - y) * np.log(1 - a)))) \
               + (lamda / (2 * n) * np.sum(w ** 2)
                  for w in self.weights)

    def evaluate(self, test_data):
        test_result = [(np.argmax(self.feedforward(x)), y)
                       for (x, y) in test_data]
        return np.sum(int(x == y) for(x, y) in test_result)

    def cost_derivate(self, out_activation, y):
        return out_activation - y

    def feedforward(self, a):
        for w, b in zip(self.weights, self.biases):
            a = sigmoid(np.dot(w, a) + b)
        return a

    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 w, b in zip(self.weights, self.biases):
            z = sigmoid(activation)
            zs.append(z)
            activation = np.dot(w, activation) + b
            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 update_mini_batch(self, mini_batch, eta, lamda, n):
        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 = [(1 - lamda / n) * 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 sgd(self, training_data, epochs, mini_batch_size, eta, lamda, 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, lamda, n)
            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))

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