3_逻辑回归.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f62b57e3",
   "metadata": {},
   "source": [
    "# 逻辑回归"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0584555",
   "metadata": {},
   "source": [
    "## (1)梯度下降实现逻辑回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 386,
   "id": "89b1ae22",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 387,
   "id": "199bbe8d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# def sigmoid(z):\n",
    "#     return 1/(1+np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "id": "117637fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# def gradient_descent(X, y, rate, iterations=10000):\n",
    "#     m = len(y) \n",
    "#     X = np.c_[np.ones(m), X]  # 添加常数项\n",
    "#     theta = np.zeros(X.shape[1])  # 初始化参数，包括截距\n",
    "#     cost_record = np.zeros(iterations)  # 用来记录cost function的变化\n",
    "    \n",
    "#     for i in range(iterations):\n",
    "#         h = sigmoid(np.dot(X, theta))\n",
    "        \n",
    "#         # 计算梯度\n",
    "#         gradient = np.dot(X.T, (h-y))\n",
    "        \n",
    "#         # 更新参数\n",
    "#         theta = theta - rate * gradient\n",
    "        \n",
    "#         # 记录cost function\n",
    "#         cost = -np.dot(y.T, np.log(sigmoid(np.dot(X, theta)))) - np.dot((1-y).T, np.log(1-sigmoid(np.dot(X, theta))))\n",
    "#         cost_record[i] = cost\n",
    "        \n",
    "#     return theta, cost_record"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 462,
   "id": "67d2a9f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "class LogisticRegression:\n",
    "    def __init__(self, learning_rate=0.01, num_iterations=10000):\n",
    "        self.learning_rate = learning_rate\n",
    "        self.num_iterations = num_iterations\n",
    "        self.weights = None\n",
    "        self.bias = None\n",
    "        self.loss_record = []\n",
    "        self.gradient_record = []\n",
    "        self.accuracy_record = []\n",
    "\n",
    "    def sigmoid(self, z):\n",
    "        return 1 / (1 + np.exp(-z))\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        m, n = X.shape\n",
    "        self.weights = np.zeros(n)\n",
    "        self.bias = 0\n",
    "\n",
    "        for iteration in range(self.num_iterations):\n",
    "            # 计算预测值\n",
    "            z = np.dot(X, self.weights) + self.bias\n",
    "            predictions = self.sigmoid(z)\n",
    "\n",
    "            # 计算损失函数\n",
    "            cost = -1/m * np.sum(y * np.log(predictions) + (1 - y) * np.log(1 - predictions))\n",
    "            self.loss_record.append(cost)\n",
    "\n",
    "            # 计算梯度\n",
    "            dw = 1/m * np.dot(X.T, (predictions - y))\n",
    "\n",
    "            db = 1/m * np.sum((predictions - y))\n",
    "            self.gradient_record.append(np.linalg.norm(dw))\n",
    "            \n",
    "            # 计算准确率\n",
    "            accuracy = self.compute_accuracy(predictions.round(), y)\n",
    "            self.accuracy_record.append(accuracy)\n",
    "\n",
    "            # 更新参数\n",
    "            self.weights -= (self.learning_rate * dw)\n",
    "            self.bias -= self.learning_rate * db\n",
    "            \n",
    "        return self.loss_record, self.gradient_record\n",
    "    \n",
    "    def compute_accuracy(self, predictions, y):\n",
    "        accuracy = np.mean(predictions == y)\n",
    "        return accuracy\n",
    "\n",
    "    def predict(self, X):\n",
    "        z = np.dot(X, self.weights) + self.bias\n",
    "        predictions = self.sigmoid(z)\n",
    "        return (predictions > 0.5).astype(int)\n",
    "    \n",
    "    def plot_accuracy(self):\n",
    "        plt.plot(range(1, self.num_iterations + 1), self.accuracy_record, marker='o', color='green')\n",
    "        plt.title('Accuracy over iterations')\n",
    "        plt.xlabel('Iterations')\n",
    "        plt.ylabel('Accuracy')\n",
    "        plt.show()\n",
    "    \n",
    "    def get_theta(self):\n",
    "        return self.weights, self.bias\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "id": "5217314d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw(num_iterations, loss_record, gradient_norm_record):\n",
    "    plt.figure(figsize=(10, 4))\n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.plot(range(num_iterations), loss_record)\n",
    "    plt.xlabel('迭代次数')\n",
    "    plt.ylabel('损失函数值')\n",
    "    plt.title('损失函数变化')\n",
    "    \n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.plot(range(num_iterations), gradient_norm_record)\n",
    "    plt.xlabel('迭代次数')\n",
    "    plt.ylabel('梯度模')\n",
    "    plt.title('梯度模变化')\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cbc80d1",
   "metadata": {},
   "source": [
    "## (2)鸢尾花数据集"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9163bc8a",
   "metadata": {},
   "source": [
    "iris 数据中有三个标签，需要考虑如何使用二分类算法解决多分类问题"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 391,
   "id": "2aa898ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import accuracy_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "id": "601a126f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 4)\n",
      "['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n",
      "['setosa' 'versicolor' 'virginica']\n"
     ]
    }
   ],
   "source": [
    "# 加载iris数据集\n",
    "iris = load_iris()\n",
    "X = iris.data\n",
    "y = iris.target\n",
    "print(X.shape)\n",
    "\n",
    "feature_names = iris.feature_names\n",
    "print(feature_names)\n",
    "\n",
    "target_names = iris.target_names\n",
    "print(target_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 393,
   "id": "8e773e11",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "# 标准化\n",
    "scaler = StandardScaler()\n",
    "X_scaled = scaler.fit_transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35f21907",
   "metadata": {},
   "source": [
    "### OvO"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a48a69d",
   "metadata": {},
   "source": [
    "思路：训练三个分类器，每个分类器对两个类别进行分类，最后通过三个分类器的结果“投票”决定划分的类别"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32339e21",
   "metadata": {},
   "source": [
    "#### 分类器1（setosa vs. versicolor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 394,
   "id": "b60d3837",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X_scaled, y, test_size=0.2, random_state=66)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 395,
   "id": "ef080a5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "indices_01 = (y_train == 0) | (y_train == 1)  # 找出类别为0和1的索引\n",
    "indices_01_t = (y_test == 0) | (y_test == 1)\n",
    "\n",
    "X_train_1 = X_train[indices_01]\n",
    "X_test_1 = X_test[indices_01_t]\n",
    "\n",
    "y_train_1 = y_train[indices_01]\n",
    "y_test_1 = y_test[indices_01_t]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d902334",
   "metadata": {},
   "source": [
    "下面使用编写的梯度下降逻辑回归训练"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 463,
   "id": "bf8acf69",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0]\n",
      "[1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0]\n"
     ]
    }
   ],
   "source": [
    "if __name__ == \"__main__\":\n",
    "    # 实例化和训练逻辑回归模型\n",
    "    model_1 = LogisticRegression()\n",
    "    ls_1, gr_1 = model_1.fit(X_train_1, y_train_1)\n",
    "\n",
    "\n",
    "    print(model_1.predict(X_test_1))\n",
    "    print(y_test_1)\n",
    "    \n",
    "    theta = model_1.get_theta()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 464,
   "id": "1094df79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.02352992, -2.24077983,  2.08131386,  1.89977742]),\n",
       " 2.104288827931714)"
      ]
     },
     "execution_count": 464,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1619b4dd",
   "metadata": {},
   "source": [
    "模型在测试集上分类完全正确！！！"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 465,
   "id": "c78bd14b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(10000, ls, gr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 398,
   "id": "e8792b72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_1.plot_accuracy()  # 绘制准确率曲线"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a74cc7a",
   "metadata": {},
   "source": [
    "使用Sklearn包验证"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 456,
   "id": "00cf077f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coefficients: [[ 0.93436309 -1.35444543  1.58684153  1.50716883]]\n",
      "intercept: [2.25128365]\n",
      "预测结果： [1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "model_s1 = LogisticRegression()\n",
    "model_s1.fit(X_train_1, y_train_1)\n",
    "weights = model_s1.coef_\n",
    "intercept = model_s1.intercept_\n",
    "\n",
    "# 输出参数\n",
    "print(\"coefficients:\", weights)\n",
    "print(\"intercept:\", intercept)\n",
    "print(\"预测结果：\", model_1.predict(X_test_1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bca8eedc",
   "metadata": {},
   "source": [
    "#### 分类器2（setosa vs. virginica)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 400,
   "id": "6591c6db",
   "metadata": {},
   "outputs": [],
   "source": [
    "indices_02 = (y_train == 0) | (y_train == 2)  # 找出类别为0和2的索引\n",
    "indices_02_t = (y_test == 0) | (y_test == 2)\n",
    "\n",
    "X_train_2 = X_train[indices_02]\n",
    "X_test_2 = X_test[indices_02_t]\n",
    "\n",
    "y_train_2 = y_train[indices_02]\n",
    "y_test_2 = y_test[indices_02_t]\n",
    "\n",
    "y_train_2[y_train_2 == 2] = 1\n",
    "y_test_2[y_test_2 == 2]  = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 401,
   "id": "3ea7803b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1]\n",
      "[0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1]\n"
     ]
    }
   ],
   "source": [
    "# 实例化和训练逻辑回归模型\n",
    "model_2 = LogisticRegression()\n",
    "model_2.fit(X_train_2, y_train_2)\n",
    "\n",
    "print(model_2.predict(X_test_2))\n",
    "print(y_test_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb9a2dec",
   "metadata": {},
   "source": [
    "使用sklearn包验证"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 402,
   "id": "4db6316f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coefficients: [[ 0.8224266  -0.7385878   1.33829004  1.39546167]]\n",
      "intercept: [0.71541032]\n",
      "预测结果： [0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1]\n"
     ]
    }
   ],
   "source": [
    "model_s2 = LogisticRegression()\n",
    "model_s2.fit(X_train_2, y_train_2)\n",
    "weights = model_s2.coef_\n",
    "intercept = model_s2.intercept_\n",
    "\n",
    "# 输出参数\n",
    "print(\"coefficients:\", weights)\n",
    "print(\"intercept:\", intercept)\n",
    "print(\"预测结果：\", model_2.predict(X_test_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8afc7a59",
   "metadata": {},
   "source": [
    "#### 分类器3（versicolor vs. virginica）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 403,
   "id": "c21350c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "indices_03 = (y_train == 1) | (y_train == 2)  # 找出类别为0和2的索引\n",
    "indices_03_t = (y_test == 1) | (y_test == 2)\n",
    "\n",
    "X_train_3 = X_train[indices_03]\n",
    "X_test_3 = X_test[indices_03_t]\n",
    "\n",
    "y_train_3 = y_train[indices_03]\n",
    "y_test_3 = y_test[indices_03_t]\n",
    "\n",
    "y_train_3[y_train_3 == 2] = 0\n",
    "y_test_3[y_test_3 == 2]  = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "id": "b4c57d13",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0]\n",
      "[1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "# 实例化和训练逻辑回归模型\n",
    "model_3 = LogisticRegression()\n",
    "model_3.fit(X_train_3, y_train_3)\n",
    "\n",
    "print(model_3.predict(X_test_3))\n",
    "print(y_test_3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be7d1819",
   "metadata": {},
   "source": [
    "使用sklearn包验证"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 405,
   "id": "39abca1c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coefficients: [[-0.25269278  0.57601981 -2.14118478 -2.89522098]]\n",
      "intercept: [3.57649947]\n",
      "预测结果： [1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "model_s3 = LogisticRegression()\n",
    "model_s3.fit(X_train_3, y_train_3)\n",
    "weights = model_s3.coef_\n",
    "intercept = model_s3.intercept_\n",
    "\n",
    "# 输出参数\n",
    "print(\"coefficients:\", weights)\n",
    "print(\"intercept:\", intercept)\n",
    "print(\"预测结果：\", model_3.predict(X_test_3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7def043",
   "metadata": {},
   "source": [
    "三个分类器均已训练完成，接下来用三个分类器进行分类"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 410,
   "id": "60f352c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "p1 = model_1.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 411,
   "id": "0866d288",
   "metadata": {},
   "outputs": [],
   "source": [
    "p2 = model_2.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "id": "3a8b3fdd",
   "metadata": {},
   "outputs": [],
   "source": [
    "p3 = model_3.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "id": "a4130681",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30\n"
     ]
    }
   ],
   "source": [
    "print(X_test.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "id": "bc7a6f6f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1]\n"
     ]
    }
   ],
   "source": [
    "print(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "985feb1a",
   "metadata": {},
   "source": [
    "根据二分类结果进行投票"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "id": "e938c97d",
   "metadata": {},
   "outputs": [],
   "source": [
    "pre = np.zeros(X_test.shape[0])\n",
    "\n",
    "for i in range(X_test.shape[0]):\n",
    "    sp_dict = {'0': 0, '1': 0, '2': 0}\n",
    "    if p1[i] == 0:\n",
    "        sp_dict['0'] += 1\n",
    "    else:\n",
    "        sp_dict['1'] += 1\n",
    "    if p2[i] == 0:\n",
    "        sp_dict['0'] += 1\n",
    "    else:\n",
    "        sp_dict['2'] += 1\n",
    "    if p3[i] == 0:\n",
    "        sp_dict['2'] += 1\n",
    "    else:\n",
    "        sp_dict['1'] += 1\n",
    "    max_key = max(sp_dict, key=sp_dict.get) \n",
    "    pre[i] = (max_key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "id": "1cd6104c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 0., 1., 1., 0., 0., 0., 2., 2., 2., 0., 2., 2., 0., 1.,\n",
       "       1., 2., 2., 0., 1., 1., 2., 1., 2., 0., 0., 2., 2.])"
      ]
     },
     "execution_count": 443,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pre"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "id": "a2a57c59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 0, 1, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 1, 1, 2, 2, 0, 1,\n",
       "       1, 2, 1, 2, 0, 0, 2, 2])"
      ]
     },
     "execution_count": 444,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecc9a099",
   "metadata": {},
   "source": [
    "对比可见，成功通过二分类解决多分类问题，在测试集上分类结果完全正确！！！"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "58b94c81",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}