python实现神经网络模型算法
今天，厾罗和大家分享用Python实现神经网络模型算法，仅用于技术学习交流。
实现技巧
1.导入依赖库
主要是安装相关的依赖库。本文实现的环境为：python 3.7。
from __future__ import division import math import random import pandas as pd
2.构建BP神经网络类
主要是构建三层反向传播神经网络类。
""" 三层反向传播神经网络 """ class NN: def __init__(self, ni, nh, no): self.ni = ni + 1 # 输入层节点 self.nh = nh + 1 # 隐藏层节点 self.no = no # 输出层种类 self.ai = [1.0] * self.ni self.ah = [1.0] * self.nh self.ao = [1.0] * self.no self.wi = self.makeMatrix(self.ni, self.nh) # 输出层到隐藏层的映射矩阵 self.wo = self.makeMatrix(self.nh, self.no) # 隐藏层到输出层的映射矩阵 for i in range(self.ni): for j in range(self.nh): self.wi[i][j] = self.rand(-0.2, 0.2) for j in range(self.nh): for k in range(self.no): self.wo[j][k] = self.rand(-2, 2) #前向传播，激活神经网络的所有节点 def update(self, inputs): if len(inputs) != self.ni - 1: print(len(inputs),self.ni - 1) raise ValueError('与输入层节点数不符！') for i in range(self.ni - 1): self.ai[i] = inputs[i] for j in range(self.nh): # self.nh表示隐藏层的节点数 sum = 0.0 # 激活项a = g(z) z = Θ^T x ;sum相当于z，每次循环归零 for i in range(self.ni): #通过循环z = Θ^T x ，因为Θ、x均为向量 sum = sum + self.ai[i] * self.wi[i][j] #〖 Z〗^((2))=Θ^((1)) a^((1)) self.ah[j] = self.sigmoid(sum) # a^((2))=g(z^((2)))，这里使用sigmoid()函数作为激活函数 for k in range(self.no): sum = 0.0 for j in range(self.nh): sum = sum + self.ah[j] * self.wo[j][k] #〖 Z〗^((3))=Θ^((2)) a^((2)) self.ao[k] = self.sigmoid(sum) # a^((3))=g(z^((3))) return self.ao[:] #反向传播,计算节点激活项的误差 def backPropagate(self, targets, lr): # targets为某样本实际种类分类，lr为梯度下降算法的学习率 output_deltas = [0.0] * self.no for k in range(self.no): error = targets[k] - np.round_(self.ao[k]) output_deltas[k] = self.dsigmoid(self.ao[k]) * error # 计算隐藏层的误差 hidden_deltas = [0.0] * self.nh for j in range(self.nh): error = 0.0 for k in range(self.no): error = error + output_deltas[k] * self.wo[j][k] hidden_deltas[j] = self.dsigmoid(self.ah[j]) * error # 更新输出层权重 for j in range(self.nh): # 反向传播算法，求出每个节点的误差后，反向更新权重 for k in range(self.no): change = output_deltas[k] * self.ah[j] self.wo[j][k] = self.wo[j][k] + lr * change # 更新输入层权重 for i in range(self.ni): for j in range(self.nh): change = hidden_deltas[j] * self.ai[i] self.wi[i][j] = self.wi[i][j] + lr * change # 计算误差 error = 0.0 for k in range(self.no): error += 0.5 * (targets[k] - np.round_(self.ao[k])) ** 2 return error #用测试集输出准确率 def test(self, patterns): count = 0 num=0 for p in patterns: target = p[1] result = self.update(p[0]) print(p[0], ':', target, '->', np.round_(result)) num=0 for k in range(self.no): if (target[k] == np.round_(result[k])): num +=1 print(num) if num==3: count +=1 print("******************",(target) == (np.round_(result)),"******************") accuracy = int(float(count / len(patterns))*100) print('accuracy: %-.9f' % accuracy,"%") #输出训练过后神经网络的权重矩阵 def weights(self): print('输入层权重:') for i in range(self.ni): print(self.wi[i]) print() print('输出层权重:') for j in range(self.nh): print(self.wo[j]) #用训练集训练神经网络 def train(self, patterns, iterations=1000, lr=0.1): for i in range(iterations): error = 0.0 for p in patterns: inputs = p[0] targets = p[1] self.update(inputs) error = error + self.backPropagate(targets, lr) if i % 100 == 0: print("percent：",int(i/iterations*100),"%",' error: %-.9f' % error) #生成区间[a, b)内的随机数 def rand(self, a, b): return (b - a) * random.random() + a # 生成大小 I*J 的矩阵，默认零矩阵 def makeMatrix(self, I, J, fill=0.0): m = [] for i in range(I): m.append([fill] * J) return m # 函数 sigmoid，bp神经网络前向传播的激活函数 def sigmoid(self, x): return 1.0 / (1.0 + math.exp(-x)) # 函数 sigmoid 的导数，反向传播时使用 def dsigmoid(self, x): return x * (1 - x)
3.读取数据并进行预处理
主要是读取构建分类模型的数据，并进行预处理。
data = [] raw = pd.read_csv('iris.csv') raw_data = raw.values raw_feature = raw_data[1:, 1:5] for i in range(len(raw_feature)): ele = [] ele.append(list(raw_feature[i])) if raw_data[i][5] == 0: ele.append([0, 0,1]) elif raw_data[i][5] == 1: ele.append([0,1, 0]) elif raw_data[i][5] == 2: ele.append([1, 1,1]) else: ele.append([0, 0,0]) data.append(ele)
4.利用构建的BP神经网络预测类，创建神经网络模型
主要是用BP神经网络预测类创建神经网络类模型。
nn = NN(4, 10, 3)
5.BP分类模型训练及预测
主要是划分训练集和测试集，并进行BP分类模型训练和预测。
training = data[1:100] test = data[101:] nn.train(training, iterations=1000) nn.test(test)
完整源代码
from __future__ import division import math import random import pandas as pd import numpy as np """ 三层反向传播神经网络 """ class NN: def __init__(self, ni, nh, no): self.ni = ni + 1 # 输入层节点 self.nh = nh + 1 # 隐藏层节点 self.no = no # 输出层种类 self.ai = [1.0] * self.ni self.ah = [1.0] * self.nh self.ao = [1.0] * self.no self.wi = self.makeMatrix(self.ni, self.nh) # 输出层到隐藏层的映射矩阵 self.wo = self.makeMatrix(self.nh, self.no) # 隐藏层到输出层的映射矩阵 for i in range(self.ni): for j in range(self.nh): self.wi[i][j] = self.rand(-0.2, 0.2) for j in range(self.nh): for k in range(self.no): self.wo[j][k] = self.rand(-2, 2) #前向传播，激活神经网络的所有节点 def update(self, inputs): if len(inputs) != self.ni - 1: print(len(inputs),self.ni - 1) raise ValueError('与输入层节点数不符！') for i in range(self.ni - 1): self.ai[i] = inputs[i] for j in range(self.nh): # self.nh表示隐藏层的节点数 sum = 0.0 # 激活项a = g(z) z = Θ^T x ;sum相当于z，每次循环归零 for i in range(self.ni): #通过循环z = Θ^T x ，因为Θ、x均为向量 sum = sum + self.ai[i] * self.wi[i][j] #〖 Z〗^((2))=Θ^((1)) a^((1)) self.ah[j] = self.sigmoid(sum) # a^((2))=g(z^((2)))，这里使用sigmoid()函数作为激活函数 for k in range(self.no): sum = 0.0 for j in range(self.nh): sum = sum + self.ah[j] * self.wo[j][k] #〖 Z〗^((3))=Θ^((2)) a^((2)) self.ao[k] = self.sigmoid(sum) # a^((3))=g(z^((3))) return self.ao[:] #反向传播,计算节点激活项的误差 def backPropagate(self, targets, lr): # targets为某样本实际种类分类，lr为梯度下降算法的学习率 output_deltas = [0.0] * self.no for k in range(self.no): error = targets[k] - np.round_(self.ao[k]) output_deltas[k] = self.dsigmoid(self.ao[k]) * error # 计算隐藏层的误差 hidden_deltas = [0.0] * self.nh for j in range(self.nh): error = 0.0 for k in range(self.no): error = error + output_deltas[k] * self.wo[j][k] hidden_deltas[j] = self.dsigmoid(self.ah[j]) * error # 更新输出层权重 for j in range(self.nh): # 反向传播算法，求出每个节点的误差后，反向更新权重 for k in range(self.no): change = output_deltas[k] * self.ah[j] self.wo[j][k] = self.wo[j][k] + lr * change # 更新输入层权重 for i in range(self.ni): for j in range(self.nh): change = hidden_deltas[j] * self.ai[i] self.wi[i][j] = self.wi[i][j] + lr * change # 计算误差 error = 0.0 for k in range(self.no): error += 0.5 * (targets[k] - np.round_(self.ao[k])) ** 2 return error #用测试集输出准确率 def test(self, patterns): count = 0 num=0 for p in patterns: target = p[1] result = self.update(p[0]) print(p[0], ':', target, '->', np.round_(result)) num=0 for k in range(self.no): if (target[k] == np.round_(result[k])): num +=1 print(num) if num==3: count +=1 print("******************",(target) == (np.round_(result)),"******************") accuracy = int(float(count / len(patterns))*100) print('accuracy: %-.9f' % accuracy,"%") #输出训练过后神经网络的权重矩阵 def weights(self): print('输入层权重:') for i in range(self.ni): print(self.wi[i]) print() print('输出层权重:') for j in range(self.nh): print(self.wo[j]) #用训练集训练神经网络 def train(self, patterns, iterations=1000, lr=0.1): for i in range(iterations): error = 0.0 for p in patterns: inputs = p[0] targets = p[1] self.update(inputs) error = error + self.backPropagate(targets, lr) if i % 100 == 0: print("percent：",int(i/iterations*100),"%",' error: %-.9f' % error) #生成区间[a, b)内的随机数 def rand(self, a, b): return (b - a) * random.random() + a # 生成大小 I*J 的矩阵，默认零矩阵 def makeMatrix(self, I, J, fill=0.0): m = [] for i in range(I): m.append([fill] * J) return m # 函数 sigmoid，bp神经网络前向传播的激活函数 def sigmoid(self, x): return 1.0 / (1.0 + math.exp(-x)) # 函数 sigmoid 的导数，反向传播时使用 def dsigmoid(self, x): return x * (1 - x) if __name__ == '__main__': data = [] raw = pd.read_csv('iris.csv') raw_data = raw.values raw_feature = raw_data[1:, 1:5] for i in range(len(raw_feature)): ele = [] ele.append(list(raw_feature[i])) if raw_data[i][5] == 0: ele.append([0, 0,1]) elif raw_data[i][5] == 1: ele.append([0,1, 0]) elif raw_data[i][5] == 2: ele.append([1, 1,1]) else: ele.append([0, 0,0]) data.append(ele) nn = NN(4, 10, 3) training = data[1:100] test = data[101:] nn.train(training, iterations=1000) nn.test(test)
