BP神经网络代码实现

1.用sigmoid(x)函数激活：

其导数f'(x)=f(x)(1-f(x))

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
 
def sigmoid(x):
    return 1/(1+np.exp(-x))
 
def BP(data_tr, data_te, maxiter=1000):
    data_tr, data_te = np.array(data_tr), np.array(data_te)
    
    net_in = np.array([0.0, 0, -1])
    out_in = np.array([0.0, 0, 0, 0, -1])   # 输出层的输入，即隐层的输出
    
    w_mid = np.random.rand(3, 4) # 隐层神经元的权值&阈值
    w_out = np.random.rand(5)    # 输出层神经元的权值&阈值
 
    delta_w_out = np.zeros([5])      # 输出层权值&阈值的修正量
    delta_w_mid = np.zeros([3,4])   # 中间层权值&阈值的修正量
    
    yita = 1.75                           # η： 学习速率
    Err = np.zeros([maxiter])             # 记录总体样本每迭代一次的错误率
 
    # 1.样本总体训练的次数
    for it in range(maxiter):
 
        # 衡量每一个样本的误差
        err = np.zeros([len(data_tr)])
 
        # 2.训练集训练一遍
        for j in range(len(data_tr)):
            net_in[:2] = data_tr[j, :2]                       # 存储当前对象前两个属性值
            real = data_tr[j, 2]
 
            # 3.当前对象进行训练
            for i in range(4):
                out_in[i] = sigmoid(sum(net_in*w_mid[:, i]))  # 计算输出层输入
            res = sigmoid(sum(out_in * w_out))                # 获得训练结果
 
            err[j] = abs(real - res)
 
            # --先调节输出层的权值与阈值
            delta_w_out = yita*res*(1-res)*(real-res)*out_in  # 权值调整
            delta_w_out[4] = -yita*res*(1-res)*(real-res)     # 阈值调整
            w_out = w_out + delta_w_out
 
            # --隐层权值和阈值的调节
            for i in range(4):
                # 权值调整
                delta_w_mid[:, i] = yita * out_in[i] * (1 - out_in[i]) * w_out[i] * res * (1 - res) * (real - res) * net_in
                # 阈值调整
                delta_w_mid[2, i] = -yita * out_in[i] * (1 - out_in[i]) * w_out[i] * res * (1 - res) * (real - res)
            w_mid = w_mid + delta_w_mid
        Err[it] = err.mean()
    plt.plot(Err)
    plt.show()
 
    # 存储预测误差
    err_te = np.zeros([ len(data_te)  ])
 
    # 预测样本len(data_te)个
    for j in range( len(data_te)  ):
        net_in[:2] = data_te[j, :2]                         # 存储数据
        real = data_te[j, 2]                                # 真实结果
 
        # net_in和w_mid的相