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
105.0,2,0.89,510.0138.0,3,0.27,595.0135.0,3,0.27,596.0106.0,2,0.83,486.0105.0,2,0.89,510.0105.0,2,0.89,510.0143.0,3,0.83,560.0108.0,2,0.91,450.0
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):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 randomrandom.seed(0)
def rand(a, b): return (b - a) * random.random() + adef make_matrix(m, n, fill=0.0):
mat = [] for i in range(m): mat.append([fill] * n) return matdef 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 errordef 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]