二分类梯度下降的 Python 实现，包含目标函数1（错分样本数）和目标函数2（错分样本到分类界面距离）的实现

以下是二分类梯度下降的 Python 实现，同时包含目标函数1和目标函数2的实现：

import numpy as np

def sigmoid(z):
    """
    Sigmoid 激活函数
    """
    return 1 / (1 + np.exp(-z))

def predict(X, theta):
    """
    预测函数
    """
    y_pred = sigmoid(np.dot(X, theta))
    y_pred[y_pred >= 0.5] = 1
    y_pred[y_pred < 0.5] = 0
    return y_pred

def cost_function1(X, y, theta):
    """
    目标函数1：错分样本数
    """
    m = len(y)
    y_pred = predict(X, theta)
    cost = sum(abs(y - y_pred)) / (2 * m)
    return cost

def cost_function2(X, y, theta):
    """
    目标函数2：错分样本到分类界面距离
    """
    m = len(y)
    y_pred = predict(X, theta)
    cost = sum(y * np.log(y_pred) + (1 - y) * np.log(1 - y_pred)) / (-m)
    return cost

def gradient_descent(X, y, theta, alpha, num_iters, cost_func):
    """
    梯度下降函数
    """
    m = len(y)
    J_history = []
    for i in range(num_iters):
        y_pred = predict(X, theta)
        theta = theta - alpha * np.dot(X.T, y_pred - y) / m
        J_history.append(cost_func(X, y, theta))
    return theta, J_history

# 生成随机数据
np.random.seed(0)
X = np.random.rand(100, 3)
X[:, 0] = 1
y = np.random.randint(2, size=100)

# 初始化参数
theta = np.zeros(3)

# 梯度下降求解
alpha = 0.01
num_iters = 1000
theta, J_history1 = gradient_descent(X, y, theta, alpha, num_iters, cost_function1)
theta, J_history2 = gradient_descent(X, y, theta, alpha, num_iters, cost_function2)

# 打印结果
print("目标函数1（错分样本数）的最小值为：", J_history1[-1])
print("目标函数2（错分样本到分类界面距离）的最小值为：", J_history2[-1])

注：在此实现中，目标函数1采用了绝对误差而非均方误差，目标函数2采用了交叉熵损失函数。