BP神经网络2个权重如何用衰减来正则化网络,matlab代码
时间: 2023-03-08 17:46:00 浏览: 94
可以使用L2正则化,即在损失函数中添加一个惩罚项,类似于:loss = loss + λ * (w1^2 + w2^2),其中λ为正则化系数,w1和w2分别为两个权重值。Matlab代码可以参考如下:net.performParam.regularization = 0.01;
net.performParam.normalization = 'none';
net = train(net, x, t);
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bp神经网络预测模型l2正则化代码
下面是一个使用L2正则化的BP神经网络预测模型的代码示例(使用Python语言和PyTorch框架):
```python
import torch
import torch.nn as nn
import torch.optim as optim
class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.fc1 = nn.Linear(10, 5)
self.fc2 = nn.Linear(5, 1)
def forward(self, x):
x = torch.relu(self.fc1(x))
x = self.fc2(x)
return x
net = Net()
criterion = nn.MSELoss()
optimizer = optim.SGD(net.parameters(), lr=0.01, momentum=0.9, weight_decay=0.01)
for epoch in range(100):
running_loss = 0.0
for i, data in enumerate(trainloader, 0):
inputs, labels = data
optimizer.zero_grad()
outputs = net(inputs)
loss = criterion(outputs, labels)
l2_regularization = 0.0
for param in net.parameters():
l2_regularization += torch.norm(param, 2)
loss += 0.01 * l2_regularization
loss.backward()
optimizer.step()
running_loss += loss.item()
print('Epoch %d loss: %.3f' % (epoch + 1, running_loss / len(trainloader)))
```
这个代码示例中,我们定义了一个包含两个全连接层的神经网络模型,采用MSE损失函数和SGD优化器。在每次迭代中,我们对网络参数进行L2正则化,将L2范数乘以0.01加入到损失函数中,从而对网络参数进行约束。在训练过程中,我们通过计算L2范数来计算正则化项的值。
BP神经网络正则化代码
BP神经网络正则化是为了避免过拟合现象而进行的一种处理方法,主要有L1正则化和L2正则化两种方式。其中L1正则化的处理方法是将权重矩阵中的每个元素都乘以一个小于1的缩小因子,而L2正则化的处理方法是将权重矩阵中的每个元素都乘以一个小于1的缩小因子的平方。
以下是一个使用L2正则化的BP神经网络代码示例:
```
import numpy as np
class NeuralNetwork:
def __init__(self, input_dim, hidden_dim, output_dim, lambda_val):
self.input_dim = input_dim
self.hidden_dim = hidden_dim
self.output_dim = output_dim
self.lambda_val = lambda_val
self.W1 = np.random.randn(self.input_dim, self.hidden_dim) / np.sqrt(self.input_dim)
self.b1 = np.zeros((1, self.hidden_dim))
self.W2 = np.random.randn(self.hidden_dim, self.output_dim) / np.sqrt(self.hidden_dim)
self.b2 = np.zeros((1, self.output_dim))
def sigmoid(self, x):
return 1.0 / (1.0 + np.exp(-x))
def sigmoid_prime(self, x):
return self.sigmoid(x) * (1 - self.sigmoid(x))
def feedforward(self, X):
self.z1 = np.dot(X, self.W1) + self.b1
self.a1 = self.sigmoid(self.z1)
self.z2 = np.dot(self.a1, self.W2) + self.b2
exp_scores = np.exp(self.z2)
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
return probs
def calculate_loss(self, X, y):
num_examples = len(X)
probs = self.feedforward(X)
logprobs = -np.log(probs[range(num_examples), y])
data_loss = np.sum(logprobs)
data_loss += self.lambda_val/2 * (np.sum(np.square(self.W1)) + np.sum(np.square(self.W2)))
return 1./num_examples * data_loss
def predict(self, X):
probs = self.feedforward(X)
return np.argmax(probs, axis=1)
def backpropagation(self, X, y):
num_examples = len(X)
delta3 = self.feedforward(X)
delta3[range(num_examples), y] -= 1
dW2 = (self.a1.T).dot(delta3)
db2 = np.sum(delta3, axis=0, keepdims=True)
delta2 = delta3.dot(self.W2.T) * self.sigmoid_prime(self.z1)
dW1 = np.dot(X.T, delta2)
db1 = np.sum(delta2, axis=0)
dW2 += self.lambda_val * self.W2
dW1 += self.lambda_val * self.W1
return dW1, db1, dW2, db2
def train(self, X, y, num_passes=20000, learning_rate=0.01):
for i in range(num_passes):
dW1, db1, dW2, db2 = self.backpropagation(X,y)
self.W1 -= learning_rate * dW1
self.b1 -= learning_rate * db1
self.W2 -= learning_rate * dW2
self.b2 -= learning_rate * db2
if i % 1000 == 0:
print("Loss after iteration %i: %f" %(i, self.calculate_loss(X,y)))
```
以上代码中,NeuralNetwork类的构造函数中输入参数依次为输入层维度、隐藏层维度、输出层维度和正则化因子。其中,初始化权重矩阵时使用的是随机高斯分布,并且通过除以根号下输入层或隐藏层维度来缩放权重矩阵。在feedforward方法中,首先计算z值和激活函数值,然后通过softmax函数计算输出概率。在calculate_loss方法中,计算交叉熵损失和L2正则化损失之和。在backpropagation方法中,首先计算输出层误差,然后反向传播计算隐藏层误差,最后计算梯度并添加L2正则化项。在train方法中,迭代训练神经网络并打印出每一次迭代后的损失值。