BP神经网络原理及Python实现代码

Python  /  管理员 发布于 7年前   534

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 npfrom 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 <= 501 : a1 in [1 , 3] and a2 in [4 , 10] and a3 > 500 : a1 in [1 , 3] and a2 in [1 , 3] and a3 > 301 : a1 in [1 , 3] and a2 in [1 , 3] and a3 <= 300 : a1 in [4 , 10] and a2 in [4 , 10] and a3 <= 501 : a1 in [4 , 10] and a2 in [4 , 10] and a3 > 500 : a1 in [4 , 10] and a2 in [1 , 3] and a3 > 301 : 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 sigmoidfrom random import randomclass 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 osfrom SimpleBP import SimpleBPfrom GenData import genDataif 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%

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