implement of deep neural network --- python

import numpy as np
import random

def sigmoid(z):
return 1.0/(1.0 + np.exp(-z))
def sigmoid_prime(z):
return sigmoid(z)*(1.0-sigmoid(z))

class Net(object):
def __init__(self,sizes):
self.layer_num = len(sizes)
self.sizes = sizes
self.bias = [ 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:]) ]

def feedward(self,a):
a = np.array([a]).transpose()
print a
for b,w in zip(self.bias, self.weights):
a = sigmoid( np.dot(w,a) + b )
print w.shape, a.shape
return a

def SDG(self, training_data, epochs, mini_batch_size, eta):
n = len(training_data)
for j in xrange(epochs):
random.shuffle(training_data)
mini_batchs = [ training_data[k:k+mini_batch_size]
for k in xrange(0,n,mini_batch_size) ]
for mini_batch in mini_batchs:
self.update_mini_batch(mini_batch, eta)
if j%100 ==0:
print 'epoch{0} complete..'.format(j)

def update_mini_batch(self, mini_batch, eta):

nabla_b = [ np.zeros(b.shape) for b in self.bias ]
nabla_w = [ np.zeros(w.shape) for w in self.weights ]

for x,y in mini_batch:
delta_b, delta_w = self.backprop(x,y)
nabla_b = [ nb+dnb for nb, dnb in zip(nabla_b, delta_b) ]
nabla_w = [ nw+bnw for nw, bnw in zip(nabla_w, delta_w) ]

self.weights = [ w-(eta/len(mini_batch))*nw for w,nw in zip(self.weights, nabla_w) ]
self.bias = [ b-(eta/len(mini_batch))*nb for b,nb in zip(self.bias, nabla_b) ]

def backprop(self,x,y):
nabla_b = [ np.zeros(b.shape) for b in self.bias ]
nabla_w = [ np.zeros(w.shape) for w in self.weights ]

# feedward
activation = np.array([x]).transpose()

#print activation
activations = [activation]
zs = []
for b,w in zip(self.bias, self.weights):
z = np.dot(w, activation)+b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)

# backward
delta = self.cost_derivate(activations[-1],y) * sigmoid_prime(zs[-1])
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
for l in xrange(2, self.layer_num):
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 cost_derivate(self, output_activations, y):
return (output_activations-y)

xx = Net([2,3,3,1])
traindata = [([1,1],3),([1,0],2),([0,0],0), ([0,1],1),([1,1],3),([1,0],2),([0,0],0), ([0,1],1)]
xx.SDG(traindata, 100, 4, 0.5)

--------------------analysis----------------------

--------------------reference------------------------
http://neuralnetworksanddeeplearning.com/