pip install numpy matplotlib

import numpy as np
import matplotlib.pyplot as plt

# 1. 加載數(shù)據(jù)集（構(gòu)造二維特征的二分類數(shù)據(jù)，添加偏置項(xiàng)）
def load_dataset():
    """
    加載數(shù)據(jù)集，返回特征矩陣、標(biāo)簽矩陣、測試集
    """
    data_mat = []  # 特征矩陣（含偏置項(xiàng)）
    label_mat = []  # 標(biāo)簽矩陣
    # 構(gòu)造訓(xùn)練數(shù)據(jù)（模擬文章中的數(shù)據(jù)集分布）
    fr = [
        "3.542485\t1.977398\t0",
        "3.018896\t2.556416\t0",
        "7.551510\t-1.580030\t1",
        "2.114999\t-0.004466\t0",
        "8.127113\t1.274372\t1",
        "7.108772\t-0.986906\t1",
        "2.326297\t0.265213\t0",
        "0.207971\t-0.438046\t0",
        "6.332009\t0.469543\t1",
        "6.172788\t-2.044329\t1",
        "3.645780\t3.410627\t0",
        "3.125951\t-0.160513\t0",
        "2.912122\t-0.206010\t0",
        "8.307974\t-0.422311\t1",
        "5.286862\t0.660109\t1"
    ]
    for line in fr:
        line_arr = line.strip().split('\t')
        # 特征：[偏置項(xiàng)1, 特征1, 特征2]
        data_mat.append([1.0, float(line_arr[0]), float(line_arr[1])])
        label_mat.append(int(line_arr[2]))
    # 構(gòu)造測試集（4個(gè)樣本，模擬文章中的測試數(shù)據(jù)）
    test_set = [
        [1.0, 7.635630, 0.215151],
        [1.0, 6.383078, -1.012999],
        [1.0, 7.192221, -0.130088],
        [1.0, 8.348103, 1.071160]
    ]
    return np.asmatrix(data_mat), np.asmatrix(label_mat).transpose(), np.asmatrix(test_set)

# 2. Sigmoid函數(shù)（將線性輸出映射到0-1區(qū)間）
def sigmoid(in_x):
    """
    Sigmoid激活函數(shù)
    :param in_x: 輸入（線性回歸輸出）
    :return: 0-1之間的概率值
    """
    return 1.0 / (1 + np.exp(-in_x))

# 3. 批量梯度上升訓(xùn)練邏輯回歸模型
def grad_ascent(data_mat_in, class_labels):
    """
    批量梯度上升法求解最優(yōu)權(quán)重
    :param data_mat_in: 特征矩陣（m×n）
    :param class_labels: 標(biāo)簽矩陣（m×1）
    :return: 最優(yōu)權(quán)重矩陣（n×1）
    """
    data_matrix = np.asmatrix(data_mat_in)
    label_mat = np.asmatrix(class_labels)
    m, n = np.shape(data_matrix)       # m：樣本數(shù)，n：特征數(shù)（含偏置）
    alpha = 0.001  # 學(xué)習(xí)率（與文章一致）
    max_cycles = 500  # 迭代次數(shù)（與文章一致）
    weights = np.ones((n, 1))  # 初始化權(quán)重為1

    for k in range(max_cycles):
        h = sigmoid(data_matrix * weights)  # 預(yù)測概率（m×1）
        error = (label_mat - h)  # 誤差（m×1）
        # 梯度上升更新權(quán)重：weights = weights + alpha * X.T * (y - h)
        weights = weights + alpha * data_matrix.transpose() * error
    return weights

# 4. 隨機(jī)梯度上升（可選，用于對(duì)比）
def stoc_grad_ascent0(data_mat_in, class_labels):
    """
    隨機(jī)梯度上升法（單樣本更新）
    """
    m, n = np.shape(data_mat_in)
    alpha = 0.01
    weights = np.ones(n)  # 一維數(shù)組
    for i in range(m):
        h = sigmoid(sum(data_mat_in[i] * weights))
        error = class_labels[i] - h
        weights = weights + alpha * error * data_mat_in[i]
    return np.mat(weights).transpose()

# 5. 預(yù)測函數(shù)
def classify_vector(in_x, weights):
    """
    根據(jù)權(quán)重預(yù)測類別，并輸出概率
    :param in_x: 單個(gè)樣本特征（1×n）
    :param weights: 最優(yōu)權(quán)重（n×1）
    :return: 預(yù)測概率、預(yù)測類別（0/1）
    """
    prob = sigmoid(in_x * weights)
    label = 1.0 if prob > 0.5 else 0.0
    return prob[0, 0], label

# 6. 繪制決策邊界
def plot_best_fit(weights, data_mat, label_mat):
    """
    繪制樣本點(diǎn)和邏輯回歸的決策邊界
    """
    data_arr = np.array(data_mat)
    n = np.shape(data_arr)[0]
    xcord1 = []; ycord1 = []  # 類別1的樣本
    xcord2 = []; ycord2 = []  # 類別0的樣本

    # 區(qū)分兩類樣本
    for i in range(n):
        if int(label_mat[i]) == 1:
            xcord1.append(data_arr[i, 1])
            ycord1.append(data_arr[i, 2])
        else:
            xcord2.append(data_arr[i, 1])
            ycord2.append(data_arr[i, 2])

    # 繪制散點(diǎn)圖
    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.scatter(xcord1, ycord1, s=30, c='blue', marker='o', label='Class 1')
    ax.scatter(xcord2, ycord2, s=30, c='red', marker='x', label='Class 0')

    # 計(jì)算決策邊界（sigmoid(z)=0.5 → z=0 → w0 + w1x1 + w2x2 = 0 → x2 = (-w0 -w1x1)/w2）
    x = np.arange(-1.0, 10.0, 0.1)
    y = (-weights[0, 0] - weights[1, 0] * x) / weights[2, 0]
    ax.plot(x, y, c='green', label='Decision Boundary')

    # 設(shè)置坐標(biāo)軸和圖例
    plt.xlabel('Feature 1')
    plt.ylabel('Feature 2')
    plt.legend(loc='upper left')
    plt.title('Logistic Regression Decision Boundary')
    plt.show()

# 主函數(shù)：執(zhí)行邏輯回歸完整流程
if __name__ == "__main__":
    # 1. 加載數(shù)據(jù)
    data_mat, label_mat, test_set = load_dataset()
    print("數(shù)據(jù)集加載完成，訓(xùn)練樣本數(shù)：", np.shape(data_mat)[0])
    print("測試樣本數(shù)：", np.shape(test_set)[0])

    # 2. 測試Sigmoid函數(shù)
    print("\nSigmoid函數(shù)測試：sigmoid(0) =", sigmoid(0))
    print("sigmoid(2) =", sigmoid(2))
    print("sigmoid(-2) =", sigmoid(-2))

    # 3. 訓(xùn)練模型（批量梯度上升）
    weights = grad_ascent(data_mat, label_mat)
    print("\n批量梯度上升得到的最優(yōu)權(quán)重：")
    print(weights)

    # 可選：隨機(jī)梯度上升訓(xùn)練
    # weights_stoc = stoc_grad_ascent0(np.array(data_mat), np.array(label_mat).flatten())
    # print("\n隨機(jī)梯度上升得到的最優(yōu)權(quán)重：")
    # print(weights_stoc)

    # 4. 測試集預(yù)測
    print("\n測試集預(yù)測結(jié)果：")
    for i in range(np.shape(test_set)[0]):
        prob, label = classify_vector(test_set[i], weights)
        print(f"測試樣本{i+1}：預(yù)測概率={prob:.4f}，預(yù)測類別={int(label)}")

    # 5. 繪制決策邊界
    plot_best_fit(weights, data_mat, label_mat)