![深度学习---手写字体识别程序分析(python) 深度学习---手写字体识别程序分析(python)](https://image.shishitao.com:8440/aHR0cHM6Ly9ia3FzaW1nLmlrYWZhbi5jb20vdXBsb2FkL2NoYXRncHQtcy5wbmc%2FIQ%3D%3D.png?!?w=700&webp=1)
我想大部分程序员的第一个程序应该都是“hello world”,在深度学习领域,这个“hello world”程序就是手写字体识别程序。
这次我们详细的分析下手写字体识别程序,从而可以对深度学习建立一个基本的概念。
1.初始化权重和偏置矩阵,构建神经网络的架构
import numpy as np
class network():
def __init__(self, sizes):
self.num_layers = len(sizes)
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:)) ]
在实例化一个神经网络时,去初始化权重和偏置的矩阵,例如
network0 = network([784, 30, 10])
可以初始化一个3层的神经网络, 各层神经元的个数分别为 784, 30 , 10
2. 如何去反向传播计算代价函数的梯度?
这个过程可以大概概括如下:
(1)正向传播,获得每个神经元的带权输出和激活因子(a)
(2)计算输出层的误差
(3)反向传播计算每一层的误差和梯度
用python实现的代码如下:
def backprop(self, x, y):
delta_w = [ np.zeros(w.shape) for w in self.weights]
delta_b = [ np.zeros(b.shape) for b in self.biases ]
#计算每个神经元的带权输入z及激活值
zs = []
activation = x
activations = [x]
for b,w in zip(self.biases, self.weights):
z = np.dot(w, activation) + b
zs.append(z)
activation = sigmod(z)
activations.append(activation)
#计算输出层误差(这里采用的是二次代价函数)
delta = (activations[-1] - y) * sigmod_prime(zs[-1])
delta_w[-1] = np.dot(delta, activations[-2].transpose())
delta_b[-1] = delta
#反向传播
for l in xrange(2, self.num_layers):
delta = np.dot(delta_w[-l+1].transpose(),delta)*sigmod_prime(zs[-l])
delta_w[-l] = np.dot(delta, activations[-l-1].transpose())
delta_b[-l] = delta
return delta_w, delta_b
3.如何梯度下降,更新权重和偏置?
通过反向传播获得了更新权重和偏置的增量,进一步进行更新,梯度下降。
def update_mini_batch(self, mini_batch, eta):
delta_w = [ np.zeros(w.shape) for w in self.weights ]
delta_b = [ np.zeros(b.shape) for b in self.biases ]
for x,y in mini_batch:
(这里针对一个小批量内所有样本,应用反向传播,积累权重和偏置的变化)
delta_w_p, delta_b_p = self.backprop(x,y)
delta_w = [ dt_w + dt_w_p for dt_w,dt_w_p in zip(delta_w, delta_w_p)]
delta_b = [ dt_b + dt_b_p for dt_b,dt_b_p in zip(delta_b, delta_b_p)]
self.weights = [ w-(eta/len(mini_batch)*nw) for w,nw in zip(self.weights, delta_w)]
self.biases = [ b-(eta/len(mini_batch)*nb) for b,nb in zip(self.biases, delta_b)]
def SGD(self, epochs, training_data, mini_batch_size,eta, test_data=None):
if test_data:
n_tests = len(tast_data)
n_training_data = len(training_data)
for i in xrange(0, epochs):
random.shuffle(training_data)
mini_batches = [ training_data[k:k+mini_batch_size]
for k in xrange(0, n_training_data, mini_batch_size)
]
for mini_batch in mini_batches:
self.update_mini_batch(mini_batch, eta)