BP神经网络原理及Python实现代码

本文主要讲如何不依赖TenserFlow等高级API实现一个简单的神经网络来做分类，所有的代码都在下面；在构造的数据（通过程序构造）上做了验证，经过1个小时的训练分类的准确率可以达到97%。

完整的结构化代码见于：链接地址

先来说说原理

网络构造

上面是一个简单的三层网络；输入层包含节点X1 , X2；隐层包含H1，H2；输出层包含O1。
输入节点的数量要等于输入数据的变量数目。
隐层节点的数量通过经验来确定。
如果只是做分类，输出层一般一个节点就够了。

从输入到输出的过程

1.输入节点的输出等于输入，X1节点输入x1时，输出还是x1.
2. 隐层和输出层的输入I为上层输出的加权求和再加偏置，输出为f(I) ， f为激活函数，可以取sigmoid。H1的输出为 sigmoid(w1x1 + w2x2 + b)

误差反向传播的过程

Python实现

构造测试数据

# -*- coding: utf-8 -*-
import numpy as np
from random import random as rdn

'''
说明：我们构造1000条数据，每条数据有三个属性(用a1 , a2 , a3表示)
a1 离散型 取值 1 到 10 ， 均匀分布
a2 离散型 取值 1 到 10 ， 均匀分布
a3 连续型 取值 1 到 100 ， 且符合正态分布 
各属性之间独立。

共2个分类(0 , 1)，属性值与类别之间的关系如下，
0 : a1 in [1 , 3] and a2 in [4 , 10] and a3 <= 50
1 : a1 in [1 , 3] and a2 in [4 , 10] and a3 > 50
0 : a1 in [1 , 3] and a2 in [1 , 3] and a3 > 30
1 : a1 in [1 , 3] and a2 in [1 , 3] and a3 <= 30
0 : a1 in [4 , 10] and a2 in [4 , 10] and a3 <= 50
1 : a1 in [4 , 10] and a2 in [4 , 10] and a3 > 50
0 : a1 in [4 , 10] and a2 in [1 , 3] and a3 > 30
1 : a1 in [4 , 10] and a2 in [1 , 3] and a3 <= 30
'''


def genData() :
 #为a3生成符合正态分布的数据
 a3_data = np.random.randn(1000) * 30 + 50
 data = []
 for i in range(1000) :
 #生成a1
 a1 = int(rdn()*10) + 1
 if a1 > 10 :
  a1 = 10
 #生成a2
 a2 = int(rdn()*10) + 1
 if a2 > 10 :
  a2 = 10
 #取a3
 a3 = a3_data[i] 
 #计算这条数据对应的类别
 c_id = 0
 if a1 <= 3 and a2 >= 4 and a3 <= 50 :
  c_id = 0 
 elif a1 <= 3 and a2 >= 4 and a3 > 50 :
  c_id = 1 
 elif a1 <= 3 and a2 < 4 and a3 > 30 :
  c_id = 0
 elif a1 <= 3 and a2 < 4 and a3 <= 30 :
  c_id = 1
 elif a1 > 3 and a2 >= 4 and a3 <= 50 :
  c_id = 0 
 elif a1 > 3 and a2 >= 4 and a3 > 50 :
  c_id = 1 
 elif a1 > 3 and a2 < 4 and a3 > 30 :
  c_id = 0
 elif a1 > 3 and a2 < 4 and a3 <= 30 :
  c_id = 1
 else :
  print('error')
 #拼合成字串
 str_line = str(i) + ',' + str(a1) + ',' + str(a2) + ',' + str(a3) + ',' + str(c_id)
 data.append(str_line)
 return '\n'.join(data)

激活函数

# -*- coding: utf-8 -*-
"""
Created on Sun Dec 2 14:49:31 2018

@author: congpeiqing
"""
import numpy as np

#sigmoid函数的导数为 f(x)*(1-f(x))
def sigmoid(x) :
 return 1/(1 + np.exp(-x))

网络实现

# -*- coding: utf-8 -*-
"""
Created on Sun Dec 2 14:49:31 2018

@author: congpeiqing
"""

from activation_funcs import sigmoid
from random import random

class InputNode(object) :
 def __init__(self , idx) :
 self.idx = idx
 self.output = None
  
 def setInput(self , value) :
 self.output = value
 
 def getOutput(self) :
 return self.output
 
 def refreshParas(self , p1 , p2) :
 pass
 
 
class Neurode(object) :
 def __init__(self , layer_name , idx , input_nodes , activation_func = None , powers = None , bias = None) :
 self.idx = idx 
 self.layer_name = layer_name
 self.input_nodes = input_nodes 
 if activation_func is not None :
  self.activation_func = activation_func
 else :
  #默认取 sigmoid
  self.activation_func = sigmoid
 if powers is not None :
  self.powers = powers
 else :
  self.powers = [random() for i in range(len(self.input_nodes))]
 if bias is not None :
  self.bias = bias
 else :
  self.bias = random()
 self.output = None
  
 def getOutput(self) :
 self.output = self.activation_func(sum(map(lambda x : x[0].getOutput()*x[1] , zip(self.input_nodes, self.powers))) + self.bias)
 return self.output
  
 def refreshParas(self , err , learn_rate) :
 err_add = self.output * (1 - self.output) * err 
 for i in range(len(self.input_nodes)) :
  #调用子节点
  self.input_nodes[i].refreshParas(self.powers[i] * err_add , learn_rate)
  #调节参数
  power_delta = learn_rate * err_add * self.input_nodes[i].output 
  self.powers[i] += power_delta
  bias_delta = learn_rate * err_add
  self.bias += bias_delta
 
 
class SimpleBP(object) :
 def __init__(self , input_node_num , hidden_layer_node_num , trainning_data , test_data) :
 self.input_node_num = input_node_num
 self.input_nodes = [InputNode(i) for i in range(input_node_num)]
 self.hidden_layer_nodes = [Neurode('H' , i , self.input_nodes) for i in range(hidden_layer_node_num)]
 self.output_node = Neurode('O' , 0 , self.hidden_layer_nodes)
 self.trainning_data = trainning_data
 self.test_data = test_data
 
 
 #逐条训练
 def trainByItem(self) :
 cnt = 0
 while True :
  cnt += 1
  learn_rate = 1.0/cnt
  sum_diff = 0.0
  #对于每一条训练数据进行一次训练过程
  for item in self.trainning_data :
  for i in range(self.input_node_num) :
   self.input_nodes[i].setInput(item[i])
  item_output = item[-1]
  nn_output = self.output_node.getOutput()
  #print('nn_output:' , nn_output)
  diff = (item_output-nn_output)
  sum_diff += abs(diff)
  self.output_node.refreshParas(diff , learn_rate)
  #print('refreshedParas')
  #结束条件 
  print(round(sum_diff / len(self.trainning_data) , 4))
  if sum_diff / len(self.trainning_data) < 0.1 :
  break
 
 def getAccuracy(self) :
 cnt = 0
 for item in self.test_data :
  for i in range(self.input_node_num) :
  self.input_nodes[i].setInput(item[i])
  item_output = item[-1]
  nn_output = self.output_node.getOutput()
  if (nn_output > 0.5 and item_output > 0.5) or (nn_output < 0.5 and item_output < 0.5) :
  cnt += 1
 return cnt/(len(self.test_data) + 0.0)

主调流程

# -*- coding: utf-8 -*-
"""
Created on Sun Dec 2 14:49:31 2018

@author: congpeiqing
"""
import os
from SimpleBP import SimpleBP
from GenData import genData

if not os.path.exists('data'):
 os.makedirs('data') 

#构造训练和测试数据
data_file = open('data/trainning_data.dat' , 'w')
data_file.write(genData())
data_file.close()

data_file = open('data/test_data.dat' , 'w')
data_file.write(genData())
data_file.close()


#文件格式：rec_id,attr1_value,attr2_value,attr3_value,class_id
#读取和解析训练数据
trainning_data_file = open('data/trainning_data.dat')
trainning_data = []
for line in trainning_data_file :
 line = line.strip()
 fld_list = line.split(',')
 trainning_data.append(tuple([float(field) for field in fld_list[1:]]))
trainning_data_file.close()

#读取和解析测试数据
test_data_file = open('data/test_data.dat')
test_data = []
for line in test_data_file :
 line = line.strip()
 fld_list = line.split(',')
 test_data.append(tuple([float(field) for field in fld_list[1:]]))
test_data_file.close()


#构造一个二分类网络 输入节点3个，隐层节点10个，输出节点一个
simple_bp = SimpleBP(3 , 10 , trainning_data , test_data)
#训练网络
simple_bp.trainByItem()
#测试分类准确率
print('Accuracy : ' , simple_bp.getAccuracy())
#训练时长比较长，准确率可以达到97%