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的相乘过程
for i in range(4):
# 输入层到隐层的传输过程
out_in[i] = sigmoid(sum(net_in*w_mid[:, i]))
res = sigmoid(sum(out_in*w_out)) # 网络预测结果输出
err_te[j] = abs(real-res) # 预测误差
print('res:', res, ' real:', real)
plt.plot(err_te)
plt.show()
if "__main__" == __name__:
# 1.读取样本
data_tr = pd.read_csv("D:\\人工智能\\3.3 data_tr.txt")
data_te = pd.read_csv("D:\\人工智能\\3.3 data_te.txt")
BP(data_tr, data_te, maxiter=1000)
仿造sigmoid(x)函数实现tanh函数和ReLU函数的激活
！！！注意：
以下两个代码实现中的学习速率不能太大，否者就会出现以下这种情况：
res值一样，明显出错。
于是我在代码中增加了print(sum(net_in*w_mid[:, i]))
运行中出现了：
原因：
学习速率太大，会出现震荡，出现震荡，会导致你的梯度值特别大，很可能出现溢出这种情况。这个梯度值可能是inf,-inf。
而以下这些操作都会导致nan的产生,这些都是不确定的操作
np.inf/np.inf
0*np.inf
具体可以看(40条消息) nan值的出现_run_session的博客-CSDN博客_nan值
2.用tanh函数激活：
其导数为f'(x)=1-f(x)*f(x)
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
def tanh(x):
return (np.exp(x) - np.exp(-x)) / (np.exp(x) + np.exp(-x))
def BP(data_tr, data_te, maxiter=500):
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 = 0.20 # 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] = tanh (sum(net_in*w_mid[:, i])) # 计算输出层输入
res = tanh (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*(1-res*res)*(real-res)*out_in # 权值调整 f'(x)=1-f(x)*f(x)
delta_w_out[4] = -yita*(1-res*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 * (1 - out_in[i] * out_in[i]) * w_out[i] * (1 - res * res) * (real - res) * net_in
# 阈值调整
delta_w_mid[2, i] = -yita * (1 - out_in[i] * out_in[i]) * w_out[i] * (1 - res * 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([ 100 ])
# 预测样本len(data_te)个
for j in range( 100 ):
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的相乘过程
for i in range(4):
# 输入层到隐层的传输过程
out_in[i] = tanh(sum(net_in*w_mid[:, i]))
res = tanh(sum(out_in*w_out)) # 网络预测结果输出
err_te[j] = abs(real-res) # 预测误差
print('res:', res, ' real:', real)
plt.plot(err_te)
plt.show()
if "__main__" == __name__:
# 1.读取样本
data_tr = pd.read_csv("D:\\人工智能\\3.3 data_tr.txt")
data_te = pd.read_csv("D:\\人工智能\\3.3 data_te.txt")
BP(data_tr, data_te, maxiter=500)3.用ReLU函数激活：
其导数f'(x)=1,x>0;f'(x)=0,x<=0
这里要求学习速率要特别低，我设了0.01
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
def ReLU(x):
return np.where(x > 0, x, 0)
def ReLUd(x):
return np.where(x > 0, 1, 0)
def BP(data_tr, data_te, maxiter=2000):
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
Err = []
yita = 0.01 # 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] = ReLU(sum(net_in*w_mid[:, i])) # 计算输出层输入
res = ReLU(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
delta_w_out = yita*(real-res)*out_in*ReLUd(res) # 权值调整
delta_w_out[4] = -yita*(real-res)*ReLUd(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 * w_out[i]* (real - res) * net_in*ReLUd(res)
# 阈值调整
delta_w_mid[2, i] = -yita * w_out[i] * (real - res)*ReLUd(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的相乘过程
for i in range(4):
# 输入层到隐层的传输过程
out_in[i] = ReLU(sum(net_in*w_mid[:, i]))
res = ReLU(sum(out_in*w_out)) # 网络预测结果输出
err_te[j] = abs(real-res) # 预测误差
print('res:', res, ' real:', real)
plt.plot(err_te)
plt.show()
if "__main__" == __name__:
# 1.读取样本
data_tr = pd.read_csv("D:\\人工智能\\3.3 data_tr.txt")
data_te = pd.read_csv("D:\\人工智能\\3.3 data_te.txt")
BP(data_tr, data_te, maxiter=2000)若要解决出现nan的问题，可以看(40条消息) 解决输出为nan的问题_Tchunren的博客-CSDN博客_网络输出为nan