请用代码实现一下BP神经网络
时间: 2023-07-17 09:57:23 浏览: 45
以下是一个简单的示例代码,用于实现一个基本的BP神经网络:
```python
import numpy as np
class NeuralNetwork:
def __init__(self, input_size, hidden_size, output_size):
self.input_size = input_size
self.hidden_size = hidden_size
self.output_size = output_size
# 初始化权重
self.weights1 = np.random.randn(self.input_size, self.hidden_size)
self.weights2 = np.random.randn(self.hidden_size, self.output_size)
# 初始化偏置
self.bias1 = np.zeros((1, self.hidden_size))
self.bias2 = np.zeros((1, self.output_size))
def forward(self, X):
# 前向传播
self.z1 = np.dot(X, self.weights1) + self.bias1
self.a1 = self.sigmoid(self.z1)
self.z2 = np.dot(self.a1, self.weights2) + self.bias2
y_pred = self.sigmoid(self.z2)
return y_pred
def backward(self, X, y, y_pred, learning_rate):
# 反向传播
delta2 = (y_pred - y) * self.sigmoid_derivative(self.z2)
dweights2 = np.dot(self.a1.T, delta2)
dbias2 = np.sum(delta2, axis=0, keepdims=True)
delta1 = np.dot(delta2, self.weights2.T) * self.sigmoid_derivative(self.z1)
dweights1 = np.dot(X.T, delta1)
dbias1 = np.sum(delta1, axis=0)
# 更新权重和偏置
self.weights2 -= learning_rate * dweights2
self.bias2 -= learning_rate * dbias2
self.weights1 -= learning_rate * dweights1
self.bias1 -= learning_rate * dbias1
def train(self, X, y, epochs, learning_rate):
for epoch in range(epochs):
# 前向传播
y_pred = self.forward(X)
# 反向传播
self.backward(X, y, y_pred, learning_rate)
# 计算损失
loss = self.mean_squared_error(y_pred, y)
# 打印损失
if epoch % 100 == 0:
print(f"Epoch {epoch+1}/{epochs} - Loss: {loss}")
def sigmoid(self, x):
return 1 / (1 + np.exp(-x))
def sigmoid_derivative(self, x):
return self.sigmoid(x) * (1 - self.sigmoid(x))
def mean_squared_error(self, y_pred, y):
return np.mean(np.square(y_pred - y))
# 示例用法
X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]]) # 输入数据
y = np.array([[0], [1], [1], [0]]) # 目标输出
# 创建一个具有2个输入节点、4个隐藏节点和1个输出节点的神经网络
nn = NeuralNetwork(2, 4, 1)
# 训练神经网络
nn.train(X, y, epochs=1000, learning_rate=0.1)
# 使用训练好的神经网络进行预测
predictions = nn.forward(X)
print("Predictions:")
print(predictions)
```
这段代码演示了一个简单的BP神经网络的实现,包括前向传播、反向传播和训练过程。通过调整参数,你可以改变神经网络的结构和训练过程,以适应不同的数据集和任务。