{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 导入必要的库\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.datasets import make_classification\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import accuracy_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_and_plot_dataset():\n",
    "    # 生成一个逻辑回归的数据集\n",
    "    x, y = make_classification(n_samples=100, n_features=2, \n",
    "                               n_informative=2, n_redundant=0, \n",
    "                               n_clusters_per_class=1, random_state=42)\n",
    "    # 可视化数据集\n",
    "    plt.scatter(x[:, 0], x[:, 1], c=y, cmap='viridis')\n",
    "    plt.xlabel('Feature 1')\n",
    "    plt.ylabel('Feature 2')\n",
    "    plt.title('Logistic Regression Dataset')\n",
    "    plt.show()\n",
    "    return x,y\n",
    "x,y = generate_and_plot_dataset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def logistic_regression_analysis(x, y):\n",
    "    # 创建逻辑回归模型\n",
    "    model = LogisticRegression()\n",
    "\n",
    "    # 拟合模型\n",
    "    model.fit(x, y)\n",
    "\n",
    "    # 预测\n",
    "    y_pred = model.predict(x)\n",
    "\n",
    "    # 计算准确率\n",
    "    accuracy = accuracy_score(y, y_pred)\n",
    "    print(f'模型准确率: {accuracy:.2f}')\n",
    "\n",
    "    # 绘制决策边界\n",
    "    # 创建网格以绘制决策边界\n",
    "    xx, yy = np.meshgrid(np.arange(x[:, 0].min() - 1, x[:, 0].max() + 1, 0.01),\n",
    "                         np.arange(x[:, 1].min() - 1, x[:, 1].max() + 1, 0.01))\n",
    "\n",
    "    # 预测网格点的类别\n",
    "    Z = model.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "    Z = Z.reshape(xx.shape)\n",
    "\n",
    "    # 绘制决策边界\n",
    "    plt.contourf(xx, yy, Z, alpha=0.8, cmap='viridis')\n",
    "    plt.scatter(x[:, 0], x[:, 1], c=y, edgecolors='k', marker='o', cmap='viridis')\n",
    "    plt.xlabel('Feature 1')\n",
    "    plt.ylabel('Feature 2')\n",
    "    plt.title('Logistic Regression Decision Boundary')\n",
    "    plt.show()\n",
    "\n",
    "# 调用函数\n",
    "logistic_regression_analysis(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 手动实现\n",
    "$$\n",
    "f_{\\vec{w},b}(x) = g(z) = \\frac{1}{1 + e^{-(\\vec{w} \\cdot \\vec{x} + b)}}\n",
    "$$\n",
    "\n",
    "$$\n",
    "J(\\vec{w},b) = -\\frac{1}{m} \\sum_{i=1}^{m} \\left( y^{(i)}\\ln(f_{\\vec{w},b}(x^{(i)})) + (1-y^{(i)})\\ln(1-f_{\\vec{w},b}(x^{(i)})) \\right)\n",
    "$$\n",
    "\n",
    "$$\n",
    "w_j = w_j - \\alpha \\frac{\\partial J(\\vec{w},b)}{\\partial w_j}\n",
    "$$\n",
    "\n",
    "$$\n",
    "b = b - \\alpha \\frac{\\partial J(\\vec{w},b)}{\\partial b}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial J(\\vec{w},b)}{\\partial w_j} = \\frac{1}{m} \\sum_{i=1}^{m} (f_{\\vec{w},b}(x^{(i)}) - y^{(i)})x_j^{(i)}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial J(\\vec{w},b)}{\\partial b} = \\frac{1}{m} \\sum_{i=1}^{m} (f_{\\vec{w},b}(x^{(i)}) - y^{(i)})\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cost_vectorized(w, b):\n",
    "    m = x.shape[0]\n",
    "    z = np.dot(x, w) + b\n",
    "    f_wb = sigmoid(z)\n",
    "    cost = (-1/m) * np.sum(y * np.log(f_wb) + (1 - y) * np.log(1 - f_wb))\n",
    "    return cost\n",
    "    \n",
    "def sigmoid(z):\n",
    "    return 1/(1+np.exp(-z))\n",
    "    \n",
    "def gradient_descent(w, b, alpha, num_iterations):\n",
    "    m = len(x)\n",
    "    for i in range(num_iterations):\n",
    "        z = np.dot(w, x.T) + b\n",
    "        f_wb = sigmoid(z)\n",
    "        w -= alpha * 1/m * np.dot(x.T, (f_wb-y))\n",
    "        b -= alpha * 1/m * np.sum(f_wb-y)\n",
    "    return w, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if __name__ == \"__main__\":\n",
    "    w = np.zeros(x.shape[1])\n",
    "    b = 0\n",
    "    alpha = 0.04\n",
    "    num_iterations = 50000\n",
    "    w, b = gradient_descent(w, b, alpha, num_iterations)\n",
    "    print(w, b)\n",
    "    loss = compute_cost_vectorized(w, b)\n",
    "    print(loss)\n",
    "    \n",
    "    plt.figure(dpi=600)\n",
    "    # 绘制数据点\n",
    "    plt.scatter(x[:, 0], x[:, 1], c=y, cmap='viridis', edgecolors='k')\n",
    "\n",
    "    # 计算决策边界\n",
    "    x_min, x_max = x[:, 0].min() - 1, x[:, 0].max() + 1\n",
    "    y_min, y_max = x[:, 1].min() - 1, x[:, 1].max() + 1\n",
    "    xx = np.linspace(x_min, x_max, 100)\n",
    "    # 计算对应的y值: w1*x + w2*y + b = 0 => y = -(w1*x + b)/w2\n",
    "    if w[1] != 0:\n",
    "        yy = -(w[0] * xx + b) / w[1]\n",
    "        plt.plot(xx, yy, color='red', label='Decision Boundary')\n",
    "    else:\n",
    "        # 当w2=0时，决策边界为垂直线x = -b/w1\n",
    "        x_boundary = -b / w[0]\n",
    "        plt.axvline(x=x_boundary, color='red', label='Decision Boundary')\n",
    "\n",
    "    plt.xlabel('Feature 1')\n",
    "    plt.ylabel('Feature 2')\n",
    "    plt.title('Logistic Regression Decision Boundary')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  }
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