用numpy搭建三层全连接神经网络

好的,我很乐意为您介绍如何使用numpy搭建三层全连接神经网络。以下是具体步骤:

1. 导入必要的库:

import numpy as np

2. 定义激活函数及其导数:

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

def sigmoid_derivative(x):
    return sigmoid(x) * (1 - sigmoid(x))

3. 初始化网络参数:

input_layer_size = 3  # 输入层神经元数量
hidden_layer_size = 5  # 隐藏层神经元数量
output_layer_size = 1  # 输出层神经元数量

np.random.seed(42)
W1 = np.random.randn(input_layer_size, hidden_layer_size)
b1 = np.zeros((1, hidden_layer_size))
W2 = np.random.randn(hidden_layer_size, output_layer_size)
b2 = np.zeros((1, output_layer_size))

4. 定义前向传播:

def forward_propagation(X):
    Z1 = np.dot(X, W1) + b1
    A1 = sigmoid(Z1)
    Z2 = np.dot(A1, W2) + b2
    A2 = sigmoid(Z2)
    cache = (Z1, A1, Z2, A2)
    return A2, cache

5. 定义损失函数:

def compute_loss(Y_hat, Y):
    m = Y.shape[0]
    logprobs = np.multiply(np.log(Y_hat), Y) + np.multiply((1 - Y), np.log(1 - Y_hat))
    loss = -np.sum(logprobs) / m
    return loss

6. 定义反向传播:

def backward_propagation(X, Y, cache):
    m = X.shape[0]
    Z1, A1, Z2, A2 = cache
    dZ2 = A2 - Y
    dW2 = np.dot(A1.T, dZ2) / m
    db2 = np.sum(dZ2, axis=0, keepdims=True) / m
    dA1 = np.dot(dZ2, W2.T)
    dZ1 = dA1 * sigmoid_derivative(Z1)
    dW1 = np.dot(X.T, dZ1) / m
    db1 = np.sum(dZ1, axis=0, keepdims=True) / m
    grads = {"dW1": dW1, "db1": db1, "dW2": dW2, "db2": db2}
    return grads

7. 定义更新参数函数:

def update_parameters(grads, learning_rate):
    W1 -= learning_rate * grads["dW1"]
    b1 -= learning_rate * grads["db1"]
    W2 -= learning_rate * grads["dW2"]
    b2 -= learning_rate * grads["db2"]

8. 训练模型:

def train(X, Y, iterations=10000, learning_rate=0.01):
    for i in range(iterations):
        Y_hat, cache = forward_propagation(X)
        loss = compute_loss(Y_hat, Y)
        grads = backward_propagation(X, Y, cache)
        update_parameters(grads, learning_rate)
        
        if i % 1000 == 0:
            print(f"Iteration {i}, Loss: {loss:.4f}")

9. 使用模型进行预测:

def predict(X):
    Y_hat, _ = forward_propagation(X)
    return Y_hat > 0.5

通过以上步骤,我们就使用numpy搭建了一个简单的三层全连接神经网络。这个网络包含一个输入层,一个隐藏层和一个输出层。