统计学习方法/支持向量机/Experiment-SVM/SVM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SVM 实战\n",
    "## 实战一：利用自定义SMO算法训练\n",
    "### 步骤一：导入相应库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 步骤二：数据获取及特征标准化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "#获取数据\n",
    "dataset = pd.read_csv('./Social_Network_Ads.csv')\n",
    "x = dataset.iloc[:, [2, 3]].values\n",
    "x = x.astype(float)\n",
    "y = dataset.iloc[:, 4].values\n",
    "\n",
    "#将0替换为-1\n",
    "for i in range(len(y)):\n",
    "    if y[i]==0:\n",
    "        y[i]=-1\n",
    "\n",
    "# 数据集划分\n",
    "train_data, test_data, train_label, test_label = train_test_split(x, y, test_size = 0.25, random_state = 61)\n",
    "\n",
    "#特征标准化\n",
    "sc = StandardScaler()\n",
    "train_data = sc.fit_transform(train_data)\n",
    "test_data = sc.transform(test_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 步骤三：SMO算法定义\n",
    "- 该算法理解可参考李航《统计学习方法》SMO算法部分\n",
    "- 也可参考博客：https://www.cnblogs.com/zgqcn/p/15092351.html\n",
    "- 代码注释以书本为准"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "class smo:\n",
    "    def __init__(self, max_iter=100, kernel='linear'):\n",
    "        '''\n",
    "        input:max_iter(int):最大训练轮数\n",
    "              kernel(str):核函数，等于'linear'表示线性，等于'poly'表示多项式\n",
    "        '''\n",
    "        self.max_iter = max_iter\n",
    "        self._kernel = kernel\n",
    "         \n",
    "    # 初始化模型\n",
    "    def init_args(self, features, labels):\n",
    "        self.m, self.n = features.shape                  # 特征数据的行列数量\n",
    "        self.X = features                                # 输入数据\n",
    "        self.Y = labels                                  # 标签\n",
    "        self.b = 0.0                                     # 初始化 b\n",
    "                                                         # 将Ei保存在一个列表里\n",
    "        self.alpha = np.ones(self.m)                     # alpha的数量等于训练数据的数量\n",
    "        self.E = [self._E(i) for i in range(self.m)]     # 记录每个训练数据的误差                                           \n",
    "        self.C = 1.0                                     # 错误惩罚参数\n",
    "   \n",
    "    # kkt条件    \n",
    "    # 根据课本(7.111)- (7.113)定义\n",
    "    def _KKT(self, i):\n",
    "        y_g = self._g(i) * self.Y[i]\n",
    "        if self.alpha[i] == 0:\n",
    "            return y_g >= 1\n",
    "        elif 0 < self.alpha[i] < self.C:\n",
    "            return y_g == 1\n",
    "        else:\n",
    "            return y_g <= 1\n",
    "\n",
    "    # g(x)预测值，输入xi\n",
    "    # 根据课本(7.104)定义\n",
    "    def _g(self, i):                                 \n",
    "        r = self.b\n",
    "        for j in range(self.m):\n",
    "            r += self.alpha[j] * self.Y[j] * self.kernel(self.X[i], self.X[j])\n",
    "        return r\n",
    "\n",
    "    # 核函数,多项式添加二次项即可\n",
    "    def kernel(self, x1, x2):\n",
    "        if self._kernel == 'linear':\n",
    "            return sum([x1[k] * x2[k] for k in range(self.n)])\n",
    "        elif self._kernel == 'poly':\n",
    "            return (sum([x1[k] * x2[k] for k in range(self.n)]) + 1)**2    \n",
    "        return 0\n",
    "\n",
    "    # E（x）为g(x)对输入x的预测值和y的差\n",
    "    # 根据课本(7.105)定义\n",
    "    def _E(self, i):\n",
    "        return self._g(i) - self.Y[i]\n",
    "\n",
    "    # 初始alpha，选择2个alpha参数\n",
    "    def _init_alpha(self):\n",
    "        # 外层循环首先遍历所有满足0<a<C的样本点，检验是否满足KKT\n",
    "        index_list = [i for i in range(self.m) if 0 < self.alpha[i] < self.C]\n",
    "        # 否则遍历整个训练集\n",
    "        non_satisfy_list = [i for i in range(self.m) if i not in index_list]\n",
    "        index_list.extend(non_satisfy_list)\n",
    "        for i in index_list:\n",
    "            if self._KKT(i):\n",
    "                continue\n",
    "            E1 = self.E[i]\n",
    "            # 如果E1是正的，选择最小的Ej作为E2；如果E1是负的，选择最大的Ej作为E2\n",
    "            # 参考书本p147\n",
    "            if E1 >= 0:\n",
    "                j = min(range(self.m), key=lambda x: self.E[x])\n",
    "            else:\n",
    "                j = max(range(self.m), key=lambda x: self.E[x])\n",
    "            return i, j\n",
    "\n",
    "    # 根据约束条件裁剪\n",
    "    # 根据课本(7.108)定义\n",
    "    def _compare(self, _alpha, L, H):\n",
    "        if _alpha > H:\n",
    "            return H\n",
    "        elif _alpha < L:\n",
    "            return L\n",
    "        else:\n",
    "            return _alpha\n",
    "\n",
    "    #训练\n",
    "    def fit(self, features, labels):\n",
    "        '''\n",
    "        input:features(ndarray):特征\n",
    "              label(ndarray):标签\n",
    "        '''\n",
    "        self.init_args(features, labels)\n",
    "        for t in range(self.max_iter):\n",
    "            i1, i2 = self._init_alpha()\n",
    "            # 边界，根据课本p145的公式定义\n",
    "            if self.Y[i1] == self.Y[i2]:\n",
    "                L = max(0, self.alpha[i1] + self.alpha[i2] - self.C)\n",
    "                H = min(self.C, self.alpha[i1] + self.alpha[i2])\n",
    "            else:\n",
    "                L = max(0, self.alpha[i2] - self.alpha[i1])\n",
    "                H = min(self.C, self.C + self.alpha[i2] - self.alpha[i1])\n",
    "            E1 = self.E[i1]\n",
    "            E2 = self.E[i2]\n",
    "            # eta = K11 + K22 - 2K12，根据课本(7.107)定义\n",
    "            eta = self.kernel(self.X[i1], self.X[i1]) + self.kernel(self.X[i2], self.X[i2]) - 2 * self.kernel(self.X[i1], self.X[i2])\n",
    "            if eta <= 0:\n",
    "                continue\n",
    "            alpha2_new_unc = self.alpha[i2] + self.Y[i2] * (E2 - E1) / eta  # 根据课本(7.106)定义\n",
    "            alpha2_new = self._compare(alpha2_new_unc, L, H)                # 根据课本(7.108)定义\n",
    "            alpha1_new = self.alpha[i1] + self.Y[i1] * self.Y[i2] * (self.alpha[i2] - alpha2_new) # 根据课本(7.109)定义\n",
    "            b1_new = -E1 - self.Y[i1] * self.kernel(self.X[i1], self.X[i1]) * (alpha1_new-self.alpha[i1]) - self.Y[i2] * self.kernel(self.X[i2], self.X[i1]) * (alpha2_new-self.alpha[i2])+ self.b  # 根据课本(7.115)定义 \n",
    "            b2_new = -E2 - self.Y[i1] * self.kernel(self.X[i1], self.X[i2]) * (alpha1_new-self.alpha[i1]) - self.Y[i2] * self.kernel(self.X[i2], self.X[i2]) * (alpha2_new-self.alpha[i2])+ self.b  # 根据课本(7.116)定义 \n",
    "            if 0 < alpha1_new < self.C:    # 根据书本p148的约束条件\n",
    "                b_new = b1_new\n",
    "            elif 0 < alpha2_new < self.C:\n",
    "                b_new = b2_new\n",
    "            else:\n",
    "                # 选择中点\n",
    "                b_new = (b1_new + b2_new) / 2\n",
    "            # 更新参数\n",
    "            self.alpha[i1] = alpha1_new\n",
    "            self.alpha[i2] = alpha2_new\n",
    "            self.b = b_new\n",
    "            self.E[i1] = self._E(i1)   # 根据课本(7.117)定义\n",
    "            self.E[i2] = self._E(i2)     \n",
    "\n",
    "      \n",
    "    def predict(self, data):\n",
    "        '''\n",
    "        input:data(ndarray):单个样本\n",
    "        output:预测为正样本返回+1，负样本返回-1\n",
    "        '''\n",
    "        r = self.b\n",
    "        for i in range(self.m):\n",
    "            r += self.alpha[i] * self.Y[i] * self.kernel(data, self.X[i])\n",
    "        if r > 0:\n",
    "            return 1\n",
    "        else:\n",
    "            return -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 步骤四：模型训练"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "classifier = smo()\n",
    "classifier.fit(train_data, train_label)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 步骤五：模型测试"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predict：-1 \t True：-1\n",
      "Predict：-1 \t True：-1\n",
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      "Predict：-1 \t True：1\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(test_data)):\n",
    "    y_pred = classifier.predict(test_data[i])\n",
    "    print('Predict：{} \\t True：{}'.format(y_pred, test_label[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 实战二：SVM Model for Social Network Ads\n",
    "> 本实战利用`sklearn.svm.SVC`库进行SVM  \n",
    "\n",
    "- SVM、SVC、SVR 三者的关系：\n",
    "    - SVM = Support Vector Machine 是支持向量\n",
    "    - SVC = Support Vector Classification 就是支持向量机用于分类，\n",
    "    - SVR= Support Vector Regression 就是支持向量机用于回归分析\n",
    "- sklearn中的算法\n",
    "    - svm.LinearSVC Linear Support Vector Classification.\n",
    "    - svm.LinearSVR Linear Support Vector Regression.\n",
    "    - svm.NuSVC Nu-Support Vector Classification.\n",
    "    - svm.NuSVR Nu Support Vector Regression.\n",
    "    - svm.OneClassSVM Unsupervised Outlier Detection.\n",
    "    - svm.SVC C-Support Vector Classification.\n",
    "    - svm.SVR Epsilon-Support Vector Regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 步骤1：导入相关库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # 线性代数\n",
    "import matplotlib.pyplot as plt # 绘图\n",
    "import pandas as pd # 数据预处理"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 步骤2：数据导入及预处理"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 数据集获取\n",
    "dataset = pd.read_csv('./Social_Network_Ads.csv')\n",
    "X = dataset.iloc[:, [2, 3]].values\n",
    "X = X.astype(float)\n",
    "y = dataset.iloc[:, 4].values\n",
    "\n",
    "# 数据集划分\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.25, random_state = 0)\n",
    "\n",
    "# 数据特征化\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "sc = StandardScaler()\n",
    "X_train = sc.fit_transform(X_train)\n",
    "X_test = sc.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 步骤3：定义`线性`SVM模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "  decision_function_shape='ovr', degree=3, gamma='auto_deprecated',\n",
       "  kernel='linear', max_iter=-1, probability=False, random_state=0,\n",
       "  shrinking=True, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 使用线性核函数性将 SVM 对训练集进行拟合\n",
    "from sklearn.svm import SVC\n",
    "classifier = SVC(kernel='linear',random_state=0)\n",
    "classifier.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 步骤3.1：利用已训练`线性`SVM模型测试"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = classifier.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 步骤3.2：计算混淆矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[66  2]\n",
      " [ 8 24]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "cm = confusion_matrix(y_test, y_pred)\n",
    "print(cm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 步骤3.3：训练结果可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "*c* argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with *x* & *y*.  Please use the *color* keyword-argument or provide a 2-D array with a single row if you intend to specify the same RGB or RGBA value for all points.\n",
      "*c* argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with *x* & *y*.  Please use the *color* keyword-argument or provide a 2-D array with a single row if you intend to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
      "image/png": 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TrvfSo718Z1uXaypokDLVrWNauJx3HV0JFJNCGHWJ4yD9eKs1BbJaDVvU9JsG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\nrQenT3evZT89hl6ocVTuDHJNv527Kgy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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "X_set, y_set = X_train, y_train\n",
    "\n",
    "# 坐标向量中生成坐标矩阵\n",
    "X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 1, stop = X_set[:, 0].max() + 1, step = 0.01), # x轴\n",
    "                     np.arange(start = X_set[:, 1].min() - 1, stop = X_set[:, 1].max() + 1, step = 0.01)) # y轴\n",
    "\n",
    "# 绘制等高线图\n",
    "plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape), # 对坐标矩阵每个点进进行预测\n",
    "             alpha = 0.2, cmap = ListedColormap(('red', 'green')))\n",
    "plt.xlim(X1.min(), X1.max())\n",
    "plt.ylim(X2.min(), X2.max())\n",
    "\n",
    "for i, j in enumerate(np.unique(y_set)):  # np.unique去除重复数据\n",
    "    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],\n",
    "                c = ListedColormap(('red', 'green'))(i), label = j)\n",
    "    \n",
    "plt.title('SVM (Training set)')\n",
    "plt.xlabel('Age')\n",
    "plt.ylabel('Estimated Salary')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 步骤3.4：测试结果可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "*c* argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with *x* & *y*.  Please use the *color* keyword-argument or provide a 2-D array with a single row if you intend to specify the same RGB or RGBA value for all points.\n",
      "*c* argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with *x* & *y*.  Please use the *color* keyword-argument or provide a 2-D array with a single row if you intend to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
      "image/png": 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dhI9NiBLb4tCEJM8M69xs4VLZYN6UHj8J4FLgAPBZ4CfASzijgSKhqreraq2q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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "X_set, y_set = X_test, y_test\n",
    "X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 1, stop = X_set[:, 0].max() + 1, step = 0.01),\n",
    "                     np.arange(start = X_set[:, 1].min() - 1, stop = X_set[:, 1].max() + 1, step = 0.01))\n",
    "plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),\n",
    "             alpha = 0.2, cmap = ListedColormap(('red', 'green')))\n",
    "plt.xlim(X1.min(), X1.max())\n",
    "plt.ylim(X2.min(), X2.max())\n",
    "for i, j in enumerate(np.unique(y_set)):\n",
    "    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],\n",
    "                c = ListedColormap(('red', 'green'))(i), label = j)\n",
    "plt.title('SVM (Test set)')\n",
    "plt.xlabel('Age')\n",
    "plt.ylabel('Estimated Salary')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 正如我们所看到的，由于这个分类器的线性特性，模型做出了一些不正确的预测（根据混淆矩阵和图表，有 10 个错误的预测）。 \n",
    "- 现在让我们尝试使用不同的内核类型，看看它是否能做出更好的预测"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 步骤4：定义`非线性`SVM模型\n",
    "- 核函数利用高斯核函数`RBF`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "  decision_function_shape='ovr', degree=3, gamma='auto_deprecated',\n",
       "  kernel='rbf', max_iter=-1, probability=False, random_state=0,\n",
       "  shrinking=True, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "classifier = SVC(kernel='rbf',random_state=0)\n",
    "classifier.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 步骤4.1：利用已训练非`线性SVM`模型测试"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = classifier.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 步骤4.2：计算混淆矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[64  4]\n",
      " [ 3 29]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "cm = confusion_matrix(y_test, y_pred)\n",
    "print(cm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 步骤4.3：训练结果可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "*c* argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with *x* & *y*.  Please use the *color* keyword-argument or provide a 2-D array with a single row if you intend to specify the same RGB or RGBA value for all points.\n",
      "*c* argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with *x* & *y*.  Please use the *color* keyword-argument or provide a 2-D array with a single row if you intend to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
      "image/png": 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nAvOAsZm/FwMnxS9alePm/si6OpJkp4dC3LvX3V1zyCFOfEDE+Tp9uvv7ZxT3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\n5lIuo+bmfGPlVdI7bHC4IIb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1+gs/g5TGJuZ1XJzXxStOvIKopx4O+15ZzpCtr7B/zGi2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\nrNxRrQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "X_set, y_set = X_train, y_train\n",
    "X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 1, stop = X_set[:, 0].max() + 1, step = 0.01),\n",
    "                     np.arange(start = X_set[:, 1].min() - 1, stop = X_set[:, 1].max() + 1, step = 0.01))\n",
    "plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),\n",
    "             alpha = 0.2, cmap = ListedColormap(('red', 'green')))\n",
    "plt.xlim(X1.min(), X1.max())\n",
    "plt.ylim(X2.min(), X2.max())\n",
    "for i, j in enumerate(np.unique(y_set)):\n",
    "    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],\n",
    "                c = ListedColormap(('red', 'green'))(i), label = j)\n",
    "plt.title('SVM (Training set)')\n",
    "plt.xlabel('Age')\n",
    "plt.ylabel('Estimated Salary')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 步骤4.4：测试结果可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "*c* argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with *x* & *y*.  Please use the *color* keyword-argument or provide a 2-D array with a single row if you intend to specify the same RGB or RGBA value for all points.\n",
      "*c* argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with *x* & *y*.  Please use the *color* keyword-argument or provide a 2-D array with a single row if you intend to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
      "image/png": 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4PD93LBsytMWhKSHmrC9bK8gU8rMUxN+IyCDwKNAPbMt9D6oPeLOIHCciM4CL\nceYcZIPl+5uY5dcKMibPz1IQHwdOUtXfhfnBqnpYRK4E7sFJA/2yqj4e5mekWpRbHLplF0X1WSaY\nSnZwMyZkfgLA08ArUXy4qm4BsrtsYRTLILhVKNde63QvvPba2DGrZEqLK0W3VDKA/duYiPkJAJ8E\n/ktEfga8mj+oqv87slKZyXOrUA4fnvg6q2S8xXlXbskAJkF+AsAXgf8EfgF4rKhlUqOSisMqGXdh\n3JX77YbL2uJ/Ean1LR2j4icATFfVj0ZeEhMOv8sT519rJgp6V15JN1xbmzPjt3gpCEsG8K33qV46\nf9zJwcPO73Bw/yCdP3ZabBYESvMzD6A3NxnrGBF5ff4r8pKZyXHLLpo2DaZPH38sX8kEXYjshhvg\n9NNh6VLn+w0ll3OqDkFTdL264fKVf97Bg3D//fGlgW6pzeG2rr6u0co/7+Dhg3T12aTKcvy0AFbk\nvheuJKXA8eEXxwTmlV3kdSxIX/cNN8Bdd409HhkZe3z11cGvJWx+B3bd1viv5K680m64mPZEaB/Z\nRNPZF0T+OXF7fr/779vruBlTNgCo6nFxFMSEyKtCKT7W1hasr3vjRu/jaQsAlQzsBk3RTXE33LI3\nL4v18+LQMKuBwf0Tf98Ns6yLsxzPLiAROSf3/UK3r/iKaCITtK+71C5bEa1vP2lxrr1UaTdcHAZq\nd3/gjpYOZk4b//ueOW0mHS02jlJOqRbAO3Gyf9zW/VHA4/bPVI3Zs53Ny92O++G1zy6M3QGnZc5B\nJcEuaBpoJd1wMf1O2p++CWbXx/JZccsP9FoWUOU8A4Cq/mPux+tU9ZnC50TEuoVqgUhlx4tdeOH4\nMQAvaZhzUEm6ZRhpoH674WK06uIbE/vsqLWe0GoV/iT4yQL6tssxH3/1JvXc7v5LHS929dVw0UVO\nSwDGvrtJes5BJWsvefXf++3XT5sazf4xwXm2AETkD4G3AnOK+vzrgZnu7zIVSXpHsDAmIV199fgB\nX68drpKec1DJwK5X11apAOdHQv/e7SObYOGiyD/HVJ9SYwAnAm3AUYwfB9gHXB5hmbIhDYuABU13\njOucYfGbbllqcHuyenvhuuvGTwS77rqxckVk2+ZumF1v+wEbV372BH6Hqv4kpvKUVFN7AsexF6wf\nUdyVJt2yCVour3+bOXOgrm5y13XuubB3r/s5f/CDyq7Dry1baB/ZZHsBG889gf1MBPtTEXkcZ1ew\nfwdOBv5OVW8PuYzZkpZFwKKYhFTJOeMKFpW0uNxaMdOnw8svj1XilbbY3Cr/UsdDUKsTv0x4/HRq\nvkdVh3C6g54FTgA+EWWhMiHuHcGCLvkQVZk6O53KVHWsUo2ibJXMA3DbpauubuKqqinew/lTPc4G\n8LU48cuEx08AyM9eeS/wLVWN7pYlS+LcESzOirYScU7OqrTF1drqdMX19Tnf9+2r7P3FAbf43zqv\nPprc/N0MccbyqyI5t6kdfgLA90TkCWAJ8AMRORo4WOY9ppw494KNs6KtRJzdYF6T2/xOequkxeYW\ncIeHJ86vmDYNPhF+Y7q95wpYuIjmo20jeFOan7WArhaRG4G9qjosIq8A74u+aBkQ0yJgqRlvKBbn\nWvhBJ71Vkt3kFnBfey3YILJP7T1XWNaP8a3UWkBrCh6eq6rDAKr6MmC7gVWTuMcb/IqzGyzopLdK\nWmxegXVoaHy3UtjBPzfhq5Zn/JpwleoCurjg5+LbifMjKIuJSpwVbSWi7AYr7oP36uqpJAgWjwt4\nlTOBgLttczftI5vK9vvP3djLSae3cdr8Fk46vY25G1OQDGASU6oLSDx+dnts0izo8sZRiqIbzC3l\nc/p0p8+9MJMnqiAY92S4gQG6tZ+msy8o2e8/d2Mvi9Z0MvWAU64jdg2yaI2TyrrnwhT8X0hQVreU\nLBUA1ONnt8cm7eIab0iDBPvggdgDbvvTN8GSpeNSPt0qtE/c0DVa+edNPXCQeTd0ZToAZHlLyVIB\n4BQRGcK526/L/Uzusa0FZNKrVB98VLNui8W1y1cu42fVaatGj3lVaMe9/iArd008x4zd2d45q9SW\nkrUeADzHAFR1qqrWq+psVZ2W+zn/eLrX+4xJXFoHvUM2WvkXZfx4VWh//x73P/dDTbX1e6lUlreU\nDLi8oTEplNZB7xCVSvf0qrh2zB5huG7872W4bia7rq6d30uh3qd6advQRsutLbRtaKP3KfcBb6+t\nI7OwpaQFAFN74pxkl4D2nisA73RP7wqtke03ruXVeY2oCK/Ocx7XYv9/vhtscP8gio52g7kFgSxv\nKelnMThjqk+NDnqPVv4lVvjsaOkYNwYAYxXanhNaa7LCL1ZJv36Wt5RMJACIyJ8D64Bm4HRV7U+i\nHMZUjdzSzlC68ofwKrRqTo2stF8/q1tKJtUCeAy4EPhiQp9vJiOt6/zXuoGB0aWd/a7uGbRCq/bU\nyIZZDQzun7jMSBb69SuRyBiAqg6o6q+S+GwzSXGuKJrGpasT1P70TRVV/mEo1YUShN+B2aCy3K9f\nCRsDMBO53emXWlE0zFZAGrbKTIuBAddJXmFz6+qJIjUyzlZFlvv1K1F2S8hJn1jk+0Cjy1NrVfW7\nudfcB3y81BiAiKwGVgMsbGxcsj3O7RKzqLgCBieFsrjyzxNx1sYJS1q2ykxavs/fJc+/WJC++uJK\nGZw75RlTZzD06sSF8hpnNdKzYnL/Dm0b2ly7ZYKc0/gTZEvISVHVd4V0nvXAenD2BA7jnKYErzv9\nKVPcN0UPe3JVWpeujtHtPdfzANthydJxM3zdBL2r9urqOWLqEcycNtM1k2iysjzhKq1sHoAZz6ui\nHRlxFlQrNH16+JOrMjKL10u+8l91+S1lK38I3lfvVfkOvTrE2rPW0jirEUFonNXI2rPWBupCyfKE\nq7RKJACIyJ+KyE7gHcBmEbkniXIYF14V7Zw5zuBvoSi6DzMwi9fLts3do5W/X0HvqktVyq0ntNKz\nooe+y/voWdETuP/cBmbTJ6ksoO+o6nxVPUJVG1T1vCTKkSl+M2u8KmDViZuiHz4c/raSNT6L10t7\nzxV0a3/F+/gGvasuVSmHnbHTekJr6K0KE4xlAWVBJZk1XksZX3ON+7mj6Juv0Vm8XvzM7vVSatav\nH17ZMkAkGTtZnXCVVpFlAUVh6eLF2n/bbUkXI3phT7gKI7PGsnMiEaTyz4tixq5l7NSW2LOAzCRF\nkQcfRmZN3LtcBVUFs5bDqPwhmrtqy9jJBssCSptSE64mK4zMmmrqm49z1vIkhVX5R8UydrLBAkDa\nRJEHH1Zmjd9N0ZMWRRANUdorf7CMnaywLqC0aWhw72sPkgef5k3ho5DiyWTVUPmDLaWQFRYA0iaq\nvvYsZdZ4BdH6emcwO6EgOLqLl8dGLpMV1bLNlrFT+6wLKG2qqa89rdy6vKZPh5dfTmxcoNwuXpNV\nyc5XxhSzAJBGUfS1R7XEchqXbnYLonV1EyeyxTQuEGW3T1TLNptssC6gLIhqieU0L91c3OW1dEIK\ntMOtqygsFeziNVmWrmmCsBZAFkSVFRN3tk2Q1sYUj//qXseDKtjFK8oBX0vXNEFYAMiCqLJi4sy2\nCZrb77aUdanjAcW1i5ela5ogLABkQVRLLMe5dHPQ1kaj295EJY4H0N5zReS7eOXZAmsmCAsAWRDV\nEstRndetqydoayOmZabbe65wdvHysZZ/WMJettlkhw0CZ0FUE8GiOK/XwHJ9PezdO/H1flsbMUyG\nG83zL7OFozFpYauBmnTxWnW0vh4OHZo4QS4lcySimuRlTBi8VgO1LiCTLl5dOvv2pXaCXFSTvIyJ\nmnUBmXQptRZSCpezqJa1fYxxYy0Aky5VtCewVf6m2lkLwKRLlaxcapW/qQUWAEz6pLCrp9CnetYA\nVvmb6mddQMZU4FM9a9jNkFX+piZYADDGp9t7rrfK39QUCwDG+PQA2zlj+VVJF8OY0FgAMMaH/KBv\n89HNCZfEmPBYADCmjNFZvtb1Y2qMBQBjSrBZvqaWWQAwxoOle5pal0gAEJHPiMgTIvKoiHxHRI5K\nohzGeNm2udsyfkzNS6oFsBU4SVVPBn4N2Pq5JlW6tZ+msy9IuhjGRCqRAKCq/6Gqh3MPfwrMT6Ic\nxrjJ9/vHsaOXMUlKwxjAXwOeG7uKyGoR6ReR/hf37ImxWCaLbI0fkyWRrQUkIt8H3DZcXauq3829\nZi1wGLjD6zyquh5YD86GMBEU1RjAKn+TPZEFAFV9V6nnReQyoA04V6tpWzJTmwYGAKv8TbYkshqo\niJwPrAHeqaqvJFEGYwq1P30TLFyUdDGMiVVSYwBfAGYDW0XkYRGx2y6TGNvM3WRVIi0AVT0hic81\nppht5m6yLA1ZQMYkYnSmr1X+JqMsAJhsGhhgN0O2vLPJNAsAJpPan76JprMvsOWdTaZZADCZYzN9\njXFYADCZYmv7GzPGAoDJjNt7rgds0NeYPAsAJhO2be7mAbbbnb8xBSwAmNq3ZQvd2m+VvzFFLACY\nmtc+ssnSPY1xYQHA1LR8xo+lexozkQUAU7NseWdjSrMAYGqSVf7GlGcBwNQcq/yN8aeqAsBzL21P\nuggm5azyN8a/qgoAzJhBe88Vo6s4GlPIKn9jKlNVAeANc45h1eW3sJuh0T92Y6BgaWer/I3xTapp\nO14ReRGoxX6gNwC/S7oQEajV64LavbZavS6o3Wvzc12LVPXo4oNVFQBqlYj0q+rSpMsRtlq9Lqjd\na6vV64LavbYg11VVXUDGGGPCYwHAGGMyygJAOqxPugARqdXrgtq9tlq9Lqjda5v0ddkYgDHGZJS1\nAIwxJqMsABhjTEZZAEgJEfmMiDwhIo+KyHdE5KikyxQGEflzEXlcREZEpOpT8ETkfBH5lYg8JSJX\nJ12esIjIl0XkBRF5LOmyhElEFojIvSLyy9z/w5rZGEJEZorIgyLySO7arq30HBYA0mMrcJKqngz8\nGvhkwuUJy2PAhcCPki5IUCIyFegCWoHFwAoRWZxsqULzVeD8pAsRgcPAx1R1MfB2oKOG/s1eBc5R\n1VOAtwHni8jbKzmBBYCUUNX/UNXDuYc/BeYnWZ6wqOqAqv4q6XKE5HTgKVX9jaoeAr4BvC/hMoVC\nVX8E/HfS5Qibqv5WVR/K/bwPGADmJVuqcKhjf+7h9NxXRVk9FgDS6a+B3qQLYSaYB+woeLyTGqlM\nskBEjgVOBX6WcFFCIyJTReRh4AVgq6pWdG3TIimVcSUi3wcaXZ5aq6rfzb1mLU6z9Y44yxaEn+sy\nJkkiMgv4NvARVR1KujxhUdVh4G25McPviMhJqup7HMcCQIxU9V2lnheRy4A24Fytogka5a6rhuwC\nFhQ8np87ZlJMRKbjVP53qOrGpMsTBVV9SUTuxRnH8R0ArAsoJUTkfGANcIGqvpJ0eYyrPuDNInKc\niMwALgY2JVwmU4KICPAlYEBVP5d0ecIkIkfnswVFpA54N/BEJeewAJAeXwBmA1tF5GERqYmF7UXk\nT0VkJ/AOYLOI3JN0mSYrN0h/JXAPzmDiN1X18WRLFQ4R2QD8BDhRRHaKyIeSLlNIzgAuBc7J/V09\nLCLLki5USI4B7hWRR3FuTraqak8lJ7ClIIwxJqOsBWCMMRllAcAYYzLKAoAxxmSUBQBjjMkoCwDG\nGJNRFgCM8UlElouIisgfJl0WY8JgAcAY/1YA9+e+G1P1LAAY40NuLZkzgQ/hzABGRKaIyP/L7eOw\nVUS2iMhFueeWiMgPRWSbiNwjIsckWHxjXFkAMMaf9wH/rqq/Bn4vIktw9jk4FmdvgEtxZjvn1575\nPHCRqi4Bvgx0JlFoY0qxxeCM8WcFcFPu52/kHk8DvqWqI8BgbjEugBOBk3CW9QCYCvw23uIaU54F\nAGPKEJHXA+cA/0NEFKdCV+A7Xm8BHlfVd8RURGMmxbqAjCnvIuA2VV2kqseq6gLgGZwdtP4sNxbQ\nAJyde/2vgKNFZLRLSETemkTBjSnFAoAx5a1g4t3+t3E2wdkJ/BK4HXgI2JvbLvIi4NMi8gjwMPA/\nYyutMT7ZaqDGBCAis1R1v4j8AfAgcIaqDiZdLmP8sDEAY4LpyW3KMQP4lFX+pppYC8AYYzLKxgCM\nMSajLAAYY0xGWQAwxpiMsgBgjDEZZQHAGGMy6v8DlFlLWaiIz1YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "X_set, y_set = X_test, y_test\n",
    "X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 1, stop = X_set[:, 0].max() + 1, step = 0.01),\n",
    "                     np.arange(start = X_set[:, 1].min() - 1, stop = X_set[:, 1].max() + 1, step = 0.01))\n",
    "plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),\n",
    "             alpha = 0.2, cmap = ListedColormap(('red', 'green')))\n",
    "plt.xlim(X1.min(), X1.max())\n",
    "plt.ylim(X2.min(), X2.max())\n",
    "for i, j in enumerate(np.unique(y_set)):\n",
    "    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],\n",
    "                c = ListedColormap(('red', 'green'))(i), label = j)\n",
    "plt.title('SVM (Test set)')\n",
    "plt.xlabel('Age')\n",
    "plt.ylabel('Estimated Salary')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 正如我们从上图中观察到的，内核为 rbf 的分类器做出了更好的预测，只有 7 个错误的预测\n",
    "- 因此，与 Logistic 回归和 K-NN 相比，这仍然是一个更好的模型，可以对因变量进行有用的预测"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 实战参考\n",
    "- [SVM Model for Social Network Ads](https://www.kaggle.com/farhanmd29/svm-model-for-social-network-ads)\n",
    "- [序列最小优化算法（smo算法）](https://www.cnblogs.com/lsm-boke/p/12317200.html)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:keras]",
   "language": "python",
   "name": "conda-env-keras-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}