我正在研究一个项目，该项目使用反向传播神经网络绘制以下函数0.6 * sin（Pi * x）+ 0.3 * cos（3 * Pi * x）。我在没有任何库帮助的情况下使用python，这是该项目的目标。我正在使用一个具有多个神经元，1个输入和1个输出的隐藏层。输入是X，输出是Y，这是每个X的方程式的结果。但是，我得到了很高的误差。我尝试添加更多隐藏层，但仍然是同样的问题。 这是我的代码。
from math import exp
from random import seed
from random import random
import random as rand
def initialize_network(n_inputs, n_hidden, n_outputs):
network = list()
hidden_layer = [{'weights':[random() for i in range(n_inputs + 1)]} for i in range(n_hidden)]
network.append(hidden_layer)
output_layer = [{'weights':[random() for i in range(n_hidden + 1)]} for i in range(n_outputs)]
network.append(output_layer)
return network
def activate(weights, inputs):
activation = weights[-1]
for i in range(len(weights)-1):
activation += weights[i] * inputs[i]
return activation
def transfer(activation):
return (1-exp(-activation))/(1+exp(-activation))
def forward_propagate(network, row):
inputs = row
for layer in network:
new_inputs = []
for neuron in layer:
activation = activate(neuron['weights'], inputs)
neuron['output'] = transfer(activation)
new_inputs.append(neuron['output'])
inputs = new_inputs
return inputs
def transfer_derivative(output):
return 0.5*(1 - output**2)
def backward_propagate_error(network, expected):
for i in reversed(range(len(network))):
layer = network[i]
errors = list()
if i != len(network)-1:
for j in range(len(layer)):
error = 0.0
for neuron in network[i + 1]:
error += (neuron['weights'][j] * neuron['delta'])
errors.append(error)
else:
for j in range(len(layer)):
neuron = layer[j]
errors.append(expected[j] - neuron['output'])
for j in range(len(layer)):
neuron = layer[j]
neuron['delta'] = errors[j] * transfer_derivative(neuron['output'])
def update_weights(network, row, l_rate,alpha):
previous = 0
for i in range(len(network)):
inputs = row[:-1]
if i != 0:
inputs = [neuron['output'] for neuron in network[i - 1]]
for neuron in network[i]:
for j in range(len(inputs)):
neuron['weights'][j] += l_rate * neuron['delta'] * inputs[j] + alpha*(previous-neuron['weights'][j])
previous = neuron['weights'][j]
# Bias weight 1
neuron['weights'][-1] += (l_rate * neuron['delta'])
def train_network(network, train, l_rate, n_outputs,alpha):
train1 = list()
output = list()
stop = False
for i in range(19):
train1.append(train[i][0])
while stop == False:
sum_error = 0
output = []
output1 = []
rand.shuffle(train)
for row in train:
outputs = forward_propagate(network, row)
expected = [row[-1] for i in range(n_outputs)]
output.append(outputs)
sum_error += 0.5*sum([(expected[i]-outputs[i])**2 for i in range(len(expected))])
backward_propagate_error(network, expected)
update_weights(network, row, l_rate,alpha)
for i in range(19):
output1.append(output[i][0])
global X
global Y
X = train1
Y = output1
print('>epoch=%d, lrate=%.3f, error=%.8f' % (n_epoch, l_rate, sum_error))
if sum_error < 0.001:
stop = True;
seed(1)
dataset = [
[0,0.3],
[5,0.366565],
[10,0.290527],
[15,0.205332],
[20,0.237094],
[25,0.418632],
[30,0.664528],
[35,0.823433],
[40,0.774376],
[45,0.505528],
[50,0.124992],
[55,-0.20353],
[60,-0.35945],
[65,-0.33565],
[70,-0.23617],
[75,-0.20304],
[80,-0.31966],
[85,-0.55282],
[90,-0.77087],
]
network = initialize_network(1, 20,1)
train_network(network, dataset, 0.3, 1,0)
x = [0,5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90]
y = [0.3,0.366565,0.290527,0.205332,0.237094,0.418632,0.664528,0.823433,0.774376,0.505525,0.12,-0.20353,-0.35945,-0.33565,-0.23167,-0.20304,-0.31966,-0.55282,-0.77087]
plt.plot(x, y)
plt.plot(X, Y)
plt.show()
Alpha用作动量因子，我认为问题可能出在这里。 我也尝试更改学习率，并向数据集中添加更多数据，但仍然存在很高的错误。
我该怎么办？
