Python实现深度神经网络

以下是Python实现深度神经网络的基本步骤：

1.导入所需的库和模块

import numpy as np
import matplotlib.pyplot as plt

2.准备数据集

# 生成数据集
np.random.seed(0)
X, y = sklearn.datasets.make_moons(200, noise=0.20)

3.定义神经网络的结构

# 定义神经网络的结构
input_dim = 2 # 输入层维度
hidden_dim = 3 # 隐藏层维度
output_dim = 2 # 输出层维度

# 初始化权重参数
W1 = np.random.randn(input_dim, hidden_dim)
b1 = np.zeros((1, hidden_dim))
W2 = np.random.randn(hidden_dim, output_dim)
b2 = np.zeros((1, output_dim))

4.定义前向传播函数

# 定义前向传播函数
def forward(X, W1, b1, W2, b2):
    # 计算隐藏层的输入
    z1 = X.dot(W1) + b1
    # 计算隐藏层的输出
    a1 = np.tanh(z1)
    # 计算输出层的输入
    z2 = a1.dot(W2) + b2
    # 计算输出层的输出
    exp_scores = np.exp(z2)
    probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
    return z1, a1, z2, probs

5.定义损失函数

# 定义损失函数
def calculate_loss(X, y, W1, b1, W2, b2):
    num_examples = len(X)
    # 前向传播
    z1, a1, z2, probs = forward(X, W1, b1, W2, b2)
    # 计算损失
    corect_logprobs = -np.log(probs[range(num_examples), y])
    data_loss = np.sum(corect_logprobs)
    # 加上正则化项
    data_loss += reg_lambda/2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))
    return 1./num_examples * data_loss

6.定义反向传播函数

# 定义反向传播函数
def backward(X, y, z1, a1, z2, probs, W1, b1, W2, b2):
    num_examples = len(X)
    # 计算输出层的误差
    delta3 = probs
    delta3[range(num_examples), y] -= 1
    # 计算隐藏层的误差
    delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2))
    # 计算权重参数的梯度
    dW2 = (a1.T).dot(delta3)
    db2 = np.sum(delta3, axis=0, keepdims=True)
    dW1 = np.dot(X.T, delta2)
    db1 = np.sum(delta2, axis=0)
    # 加上正则化项
    dW2 += reg_lambda * W2
    dW1 += reg_lambda * W1
    return dW1, db1, dW2, db2

7.训练神经网络

# 训练神经网络
num_examples = len(X)
reg_lambda = 0.01
learning_rate = 0.01
for i in range(20000):
    # 前向传播
    z1, a1, z2, probs = forward(X, W1, b1, W2, b2)
    # 反向传播
    dW1, db1, dW2, db2 = backward(X, y, z1, a1, z2, probs, W1, b1, W2, b2)
    # 更新权重参数
    W1 -= learning_rate * dW1
    b1 -= learning_rate * db1
    W2 -= learning_rate * dW2
    b2 -= learning_rate * db2
    # 每1000次迭代输出一次损失函数的值
    if i % 1000 == 0:
        print("Loss after iteration %i: %f" % (i, calculate_loss(X, y, W1, b1, W2, b2)))