转至：https://blog.csdn.net/langb2014/article/details/50488727
输入数据变为房价预测：
105.0,2,0.89,510.0
105.0,2,0.89,510.0
138.0,3,0.27,595.0
135.0,3,0.27,596.0
106.0,2,0.83,486.0
105.0,2,0.89,510.0
105.0,2,0.89,510.0
143.0,3,0.83,560.0
108.0,2,0.91,450.0
最近写论文时用到一个方法，是基于神经网络的最优组合预测，主要思想如下：在建立由回归模型、灰色预测模型、BP神经网络预测模型组成的组合预测模型库的基础上,利用以上三种单一预测模型的组合构成BP神经网络组合预测模型。（我是参考的参考这篇文章：路玉龙,韩靖,余思婧,张鸿雁.BP神经网络组合预测在城市生活垃圾产量预测中应用）
我的目的
我需要用BP神经网络来做连续预测。关于BP神经网络的python实现网上有很多，但大多是用于分类决策，于是不得不搞清楚原理改代码。
以下是我参考的一篇BP神经网络的分类决策的实现（我的连续预测的代码是基于下面这个链接改的，在此致谢一下）：
https://www.cnblogs.com/Finley/p/5946000.html
修改思路：
（1）最后一层不激活，直接输出。或者说把激活函数看作f(x)=x
（2）损失函数函数改为MSE
代码
代码中用两个#——-围起来的就是我更正的部分。
import math
import random
random.seed(0)
def rand(a, b):
return (b - a) * random.random() + a
def make_matrix(m, n, fill=0.0):
mat = []
for i in range(m):
mat.append([fill] * n)
return mat
def sigmoid(x):
return 1.0 / (1.0 + math.exp(-x))
def sigmoid_derivative(x):
return x * (1 - x)
class BPNeuralNetwork:
def __init__(self):
self.input_n = 0
self.hidden_n = 0
self.output_n = 0
self.input_cells = []
self.hidden_cells = []
self.output_cells = []
self.input_weights = []
self.output_weights = []
self.input_correction = []
self.output_correction = []
def setup(self, ni, nh, no):
self.input_n = ni + 1
self.hidden_n = nh
self.output_n = no
# init cells
self.input_cells = [1.0] * self.input_n
self.hidden_cells = [1.0] * self.hidden_n
self.output_cells = [1.0] * self.output_n
# init weights
self.input_weights = make_matrix(self.input_n, self.hidden_n)
self.output_weights = make_matrix(self.hidden_n, self.output_n)
# random activate
for i in range(self.input_n):
for h in range(self.hidden_n):
self.input_weights[i][h] = rand(-0.2, 0.2)
for h in range(self.hidden_n):
for o in range(self.output_n):
self.output_weights[h][o] = rand(-2.0, 2.0)
# init correction matrix
self.input_correction = make_matrix(self.input_n, self.hidden_n)
self.output_correction = make_matrix(self.hidden_n, self.output_n)
def predict(self, inputs):
# activate input layer
for i in range(self.input_n - 1):
self.input_cells[i] = inputs[i]#输入层输出值
# activate hidden layer
for j in range(self.hidden_n):
total = 0.0
for i in range(self.input_n):
total += self.input_cells[i] * self.input_weights[i][j]#隐藏层输入值
self.hidden_cells[j] = sigmoid(total)#隐藏层的输出值
# activate output layer
for k in range(self.output_n):
total = 0.0
for j in range(self.hidden_n):
total += self.hidden_cells[j] * self.output_weights[j][k]
#-----------------------------------------------
# self.output_cells[k] = sigmoid(total)
self.output_cells[k] =total#输出层的激励函数是f(x)=x
#-----------------------------------------------
return self.output_cells[:]
def back_propagate(self, case, label, learn, correct):#x,y,修改最大迭代次数， 学习率λ， 矫正率μ三个参数.
# feed forward
self.predict(case)
# get output layer error
output_deltas = [0.0] * self.output_n
for o in range(self.output_n):
error = label[o] - self.output_cells[o]
#-----------------------------------------------
# output_deltas[o] = sigmoid_derivative(self.output_cells[o]) * error
output_deltas[o] = error
#-----------------------------------------------
# get hidden layer error
hidden_deltas = [0.0] * self.hidden_n
for h in range(self.hidden_n):
error = 0.0
for o in range(self.output_n):
error += output_deltas[o] * self.output_weights[h][o]
hidden_deltas[h] = sigmoid_derivative(self.hidden_cells[h]) * error
# update output weights
for h in range(self.hidden_n):
for o in range(self.output_n):
change = output_deltas[o] * self.hidden_cells[h]
self.output_weights[h][o] += learn * change + correct * self.output_correction[h][o]#？？？？？？？？？？
self.output_correction[h][o] = change
# update input weights
for i in range(self.input_n):
for h in range(self.hidden_n):
change = hidden_deltas[h] * self.input_cells[i]
self.input_weights[i][h] += learn * change + correct * self.input_correction[i][h]
self.input_correction[i][h] = change
# get global error
error = 0.0
for o in range(len(label)):
error += 0.5 * (label[o] - self.output_cells[o]) ** 2
return error
def train(self, cases, labels, limit=10000, learn=0.05, correct=0.1):
for j in range(limit):
error = 0.0
for i in range(len(cases)):
label = labels[i]
case = cases[i]
error += self.back_propagate(case, label, learn, correct)
def test(self):
cases = [
[10.5,2,0.89],
[10.5,2,0.89],
[13.8,3,0.27],
[13.5,3,0.27],
]
labels = [[0.51], [0.51], [0.595], [0.596]]
self.setup(3, 5, 1)
self.train(cases, labels, 10000, 0.05, 0.1)
for case in cases:
print(self.predict(case))
if __name__ == '__main__':
nn = BPNeuralNetwork()
nn.test()
实验结果：
[0.5095123779256603]
[0.5095123779256603]
[0.5952606219141522]
[0.5939697670509705]