python实现简单神经网络算法

python实现二层神经网络

包括输入层和输出层

import numpy as np

#sigmoid function
def nonlin(x, deriv = False):
    if(deriv == True):
        return x*(1-x)
    return 1/(1+np.exp(-x))

#input dataset
x = np.array([[0,0,1],
             [0,1,1],
             [1,0,1],
             [1,1,1]])

#output dataset
y = np.array([[0,0,1,1]]).T

np.random.seed(1)

#init weight value
syn0 = 2*np.random.random((3,1))-1

for iter in xrange(100000):
    l0 = x                         #the first layer,and the input layer 
    l1 = nonlin(np.dot(l0,syn0))   #the second layer,and the output layer


    l1_error = y-l1

    l1_delta = l1_error*nonlin(l1,True)

    syn0 += np.dot(l0.T, l1_delta)
print "outout after Training:"
print l1

这里，

l0:输入层

l1:输出层

syn0:初始权值

l1_error:误差

l1_delta:误差校正系数

func nonlin:sigmoid函数

这里迭代次数为100时，预测结果为

迭代次数为1000时，预测结果为：

迭代次数为10000，预测结果为：

迭代次数为100000，预测结果为：

可见迭代次数越多，预测结果越接近理想值，当时耗时也越长。

python实现三层神经网络

包括输入层、隐含层和输出层

import numpy as np

def nonlin(x, deriv = False):
    if(deriv == True):
        return x*(1-x)
    else:
        return 1/(1+np.exp(-x))

#input dataset
X = np.array([[0,0,1],
             [0,1,1],
             [1,0,1],
             [1,1,1]])

#output dataset
y = np.array([[0,1,1,0]]).T

syn0 = 2*np.random.random((3,4)) - 1 #the first-hidden layer weight value
syn1 = 2*np.random.random((4,1)) - 1 #the hidden-output layer weight value

for j in range(60000):
    l0 = X                        #the first layer,and the input layer 
    l1 = nonlin(np.dot(l0,syn0))  #the second layer,and the hidden layer
    l2 = nonlin(np.dot(l1,syn1))  #the third layer,and the output layer


    l2_error = y-l2       #the hidden-output layer error

    if(j%10000) == 0:
        print "Error:"+str(np.mean(l2_error))

    l2_delta = l2_error*nonlin(l2,deriv = True)

    l1_error = l2_delta.dot(syn1.T)     #the first-hidden layer error

    l1_delta = l1_error*nonlin(l1,deriv = True)

    syn1 += l1.T.dot(l2_delta)
    syn0 += l0.T.dot(l1_delta)
print "outout after Training:"
print l2