机器学习实战笔记

import numpy as np

class Network(object):

    def __init__(self, sizes):
        # 层数
        self.num_layers = len(sizes)
        # 各层神经元的数量 eg:[2,3,1]
        self.sizes = sizes
        # 偏置 eg:3x1,1
        self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
        # 权重 eg:3x2,1x3
        self.weights = [np.random.randn(y, x)
                        for x, y in zip(sizes[:-1], sizes[1:])]

    # 对应输入求输出
    # a`=σ(w·a+b)
    # σ S型激活函数
    def feedforward(self, a):
        for b, w in zip(self.biases, self.weights):
            a = sigmoid(np.dot(w, a)+b)
        return a

    # 梯度下降-小批量数据
    def SGD(self, training_data, epochs, mini_batch_size, eta,
            test_data=None):
        # training_data 是一个(x,y)元组列表，训练输入和对应的期望输出
        # epochs 迭代期数量
        # mini_batch_size 采样时的小批量数据的大小
        # eta学习速率 η 
        # test_data 如果可选参数可用则每次训练后会评估网络
        training_data = list(training_data)
        n = len(training_data)

        if test_data:
            test_data = list(test_data)
            n_test = len(test_data)

        for j in range(epochs):
            # 随机打乱数据
            random.shuffle(training_data)
            # 数据分为小块
            mini_batches = [
                training_data[k:k+mini_batch_size]
                for k in range(0, n, mini_batch_size)]
            # 训练小块数据
            for mini_batch in mini_batches:
                self.update_mini_batch(mini_batch, eta)
            # 输出验证
            if test_data:
                print("Epoch {} : {} / {}".format(j,self.evaluate(test_data),n_test));
                print(self.biases[1])
            else:
                print("Epoch {} complete".format(j))
    # 更新权值和偏置
    def update_mini_batch(self, mini_batch, eta):
        """Update the network's weights and biases by applying
        gradient descent using backpropagation to a single mini batch.
        The ``mini_batch`` is a list of tuples ``(x, y)``, and ``eta``
        is the learning rate."""
        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)]
    # 计算偏导数
    def backprop(self, x, y):
        """Return a tuple ``(nabla_b, nabla_w)`` representing the
        gradient for the cost function C_x.  ``nabla_b`` and
        ``nabla_w`` are layer-by-layer lists of numpy arrays, similar
        to ``self.biases`` and ``self.weights``."""
        nabla_b = [np.zeros(b.shape) for b in self.biases]
        nabla_w = [np.zeros(w.shape) for w in self.weights]
        # feedforward
        activation = x
        activations = [x] # list to store all the activations, layer by layer
        zs = [] # list to store all the z vectors, layer by layer
        for b, w in zip(self.biases, self.weights):
            z = np.dot(w, activation)+b
            zs.append(z)
            activation = sigmoid(z)
            activations.append(activation)
        # backward pass
        delta = self.cost_derivative(activations[-1], y) * \
            sigmoid_prime(zs[-1])
        nabla_b[-1] = delta
        nabla_w[-1] = np.dot(delta, activations[-2].transpose())
        # Note that the variable l in the loop below is used a little
        # differently to the notation in Chapter 2 of the book.  Here,
        # l = 1 means the last layer of neurons, l = 2 is the
        # second-last layer, and so on.  It's a renumbering of the
        # scheme in the book, used here to take advantage of the fact
        # that Python can use negative indices in lists.
        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 evaluate(self, test_data):
        """Return the number of test inputs for which the neural
        network outputs the correct result. Note that the neural
        network's output is assumed to be the index of whichever
        neuron in the final layer has the highest activation."""
        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 the vector of partial derivatives \partial C_x /
        \partial a for the output activations."""
        return (output_activations-y)

# S型函数 1/(1+e^-z)
def sigmoid(z):
    return 1.0/(1.0+np.exp(-z))
# S型函数导数 e^-z/(1+e^-z)^2
def sigmoid_prime(z):
    return sigmoid(z)*(1-sigmoid(z))