Lesson104-SVM Kernels 及手工验证实现Polynomial Kernels.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第104讲 SVM Kernels 及手工验证实现Polynomial Kernels\n",
    "\n",
    "## Python学习：https://www.ixigua.com/home/77346806707?utm_source=xiguastudio\n",
    "\n",
    "## Python源文件及数据下载链接: https://github.com/rayc2020/LessonPythonCode"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SVM algorithms use a set of mathematical functions that are defined as the kernel. The function of kernel is to take data as input and transform it into the required form. Different SVM algorithms use different types of kernel functions. These functions can be different types. For example linear, nonlinear, polynomial, radial basis function (RBF), and sigmoid."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Support Vector Machines perform classification by finding linear decision boundaries that are as far away from the data as possible. They work great with linearly separable data but fail miserably otherwise.\n",
    "\n",
    "To make non-linear data linearly separable (and thus convenient for SVMs) we can add more features to the data since in a higher-dimensional space the probability of the data being linearly separable increases.\n",
    "\n",
    "Two popular types of new features to add are polynomial combinations of existing features (polynomial features) and observation-wise distances from landmarks, i.e. some reference values (similarity features).\n",
    "\n",
    "Actually adding them might slow the model down to the extent of making it useless.\n",
    "\n",
    "The kernel trick is a smart maneuver that takes advantage of some mathematical properties in order to deliver the same results as though we have added additional features without actually adding them.\n",
    "\n",
    "The polynomial and RBF kernels (pretend to) add the polynomial and similarity features, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(filename='D:\\python\\Interview-Prepartion-Data-Science-master\\Lesson104-3.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2826f385308>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import make_circles\n",
    "\n",
    "X, y = make_circles(n_samples=750, factor=0.5, noise=0)\n",
    "plt.scatter(X[:,0], X[:,1], c=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.99407532, -0.10869338],\n",
       "       [-0.4854201 ,  0.87428103],\n",
       "       [ 0.41646062, -0.27669577],\n",
       "       ...,\n",
       "       [-0.87224005,  0.48907801],\n",
       "       [ 0.8681122 ,  0.49636803],\n",
       "       [-0.99407532,  0.10869338]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1,\n",
       "       0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1,\n",
       "       0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1,\n",
       "       0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0,\n",
       "       0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0,\n",
       "       0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1,\n",
       "       0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1,\n",
       "       0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1,\n",
       "       1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1,\n",
       "       0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1,\n",
       "       1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0,\n",
       "       0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0,\n",
       "       0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1,\n",
       "       0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0,\n",
       "       1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0,\n",
       "       1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0,\n",
       "       1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0,\n",
       "       1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0,\n",
       "       0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1,\n",
       "       0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1,\n",
       "       1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0,\n",
       "       1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1,\n",
       "       1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1,\n",
       "       1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0,\n",
       "       0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0,\n",
       "       1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0,\n",
       "       1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1,\n",
       "       0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0,\n",
       "       1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0,\n",
       "       0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1,\n",
       "       1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1,\n",
       "       0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0,\n",
       "       0, 0], dtype=int64)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Split the dataset into train and test\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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,\n",
       "       1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0,\n",
       "       1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0,\n",
       "       1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0,\n",
       "       1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1,\n",
       "       0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0,\n",
       "       0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0,\n",
       "       0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1,\n",
       "       1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0,\n",
       "       1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0,\n",
       "       1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1,\n",
       "       0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0,\n",
       "       1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0,\n",
       "       1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0,\n",
       "       0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0,\n",
       "       1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1,\n",
       "       0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1,\n",
       "       0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1,\n",
       "       1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0,\n",
       "       1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1,\n",
       "       1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1,\n",
       "       0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1,\n",
       "       0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0,\n",
       "       1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1,\n",
       "       0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1], dtype=int64)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.9971589 ,  0.07532681],\n",
       "       [-0.02094242,  0.99978068],\n",
       "       [-0.4890738 , -0.10395585],\n",
       "       ...,\n",
       "       [ 0.5       ,  0.        ],\n",
       "       [ 1.        ,  0.        ],\n",
       "       [-0.49984209,  0.01256505]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1.0, break_ties=False, cache_size=200, class_weight=None, coef0=0.0,\n",
       "    decision_function_shape='ovr', degree=3, gamma='scale', kernel='poly',\n",
       "    max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "    tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "classifier=SVC(kernel=\"poly\")\n",
    "classifier.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6914893617021277"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "y_pred = classifier.predict(X_test)\n",
    "accuracy_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 手工验证实现Polynomial Kernels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.99407532, -0.10869338],\n",
       "       [-0.4854201 ,  0.87428103],\n",
       "       [ 0.41646062, -0.27669577],\n",
       "       ...,\n",
       "       [-0.87224005,  0.48907801],\n",
       "       [ 0.8681122 ,  0.49636803],\n",
       "       [-0.99407532,  0.10869338]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.994075</td>\n",
       "      <td>-0.108693</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.485420</td>\n",
       "      <td>0.874281</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.416461</td>\n",
       "      <td>-0.276696</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.193758</td>\n",
       "      <td>-0.460932</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.356412</td>\n",
       "      <td>-0.934329</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         X1        X2  y\n",
       "0 -0.994075 -0.108693  0\n",
       "1 -0.485420  0.874281  0\n",
       "2  0.416461 -0.276696  1\n",
       "3  0.193758 -0.460932  1\n",
       "4  0.356412 -0.934329  0"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df =pd.DataFrame(X,columns=['X1','X2'])\n",
    "df['y']=pd.DataFrame(y,columns=['y'])\n",
    "df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>y</th>\n",
       "      <th>X1_Square</th>\n",
       "      <th>X2_Square</th>\n",
       "      <th>X1*X2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.994075</td>\n",
       "      <td>-0.108693</td>\n",
       "      <td>0</td>\n",
       "      <td>0.988186</td>\n",
       "      <td>0.011814</td>\n",
       "      <td>0.108049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.485420</td>\n",
       "      <td>0.874281</td>\n",
       "      <td>0</td>\n",
       "      <td>0.235633</td>\n",
       "      <td>0.764367</td>\n",
       "      <td>-0.424394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.416461</td>\n",
       "      <td>-0.276696</td>\n",
       "      <td>1</td>\n",
       "      <td>0.173439</td>\n",
       "      <td>0.076561</td>\n",
       "      <td>-0.115233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.193758</td>\n",
       "      <td>-0.460932</td>\n",
       "      <td>1</td>\n",
       "      <td>0.037542</td>\n",
       "      <td>0.212458</td>\n",
       "      <td>-0.089309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.356412</td>\n",
       "      <td>-0.934329</td>\n",
       "      <td>0</td>\n",
       "      <td>0.127029</td>\n",
       "      <td>0.872971</td>\n",
       "      <td>-0.333006</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         X1        X2  y  X1_Square  X2_Square     X1*X2\n",
       "0 -0.994075 -0.108693  0   0.988186   0.011814  0.108049\n",
       "1 -0.485420  0.874281  0   0.235633   0.764367 -0.424394\n",
       "2  0.416461 -0.276696  1   0.173439   0.076561 -0.115233\n",
       "3  0.193758 -0.460932  1   0.037542   0.212458 -0.089309\n",
       "4  0.356412 -0.934329  0   0.127029   0.872971 -0.333006"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We need to find components for the Polynomical Kernel\n",
    "#X1,X2,X1_square,X2_square,X1*X2\n",
    "df['X1_Square']= df['X1']**2\n",
    "df['X2_Square']= df['X2']**2\n",
    "df['X1*X2'] = (df['X1'] *df['X2'])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Independent and Dependent features\n",
    "XX = df[['X1','X2','X1_Square','X2_Square','X1*X2']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X1_Square</th>\n",
       "      <th>X2_Square</th>\n",
       "      <th>X1*X2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.994075</td>\n",
       "      <td>-0.108693</td>\n",
       "      <td>0.988186</td>\n",
       "      <td>0.011814</td>\n",
       "      <td>0.108049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.485420</td>\n",
       "      <td>0.874281</td>\n",
       "      <td>0.235633</td>\n",
       "      <td>0.764367</td>\n",
       "      <td>-0.424394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.416461</td>\n",
       "      <td>-0.276696</td>\n",
       "      <td>0.173439</td>\n",
       "      <td>0.076561</td>\n",
       "      <td>-0.115233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.193758</td>\n",
       "      <td>-0.460932</td>\n",
       "      <td>0.037542</td>\n",
       "      <td>0.212458</td>\n",
       "      <td>-0.089309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.356412</td>\n",
       "      <td>-0.934329</td>\n",
       "      <td>0.127029</td>\n",
       "      <td>0.872971</td>\n",
       "      <td>-0.333006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>745</th>\n",
       "      <td>0.224192</td>\n",
       "      <td>0.446921</td>\n",
       "      <td>0.050262</td>\n",
       "      <td>0.199738</td>\n",
       "      <td>0.100196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>746</th>\n",
       "      <td>-0.903036</td>\n",
       "      <td>0.429566</td>\n",
       "      <td>0.815473</td>\n",
       "      <td>0.184527</td>\n",
       "      <td>-0.387913</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>747</th>\n",
       "      <td>-0.872240</td>\n",
       "      <td>0.489078</td>\n",
       "      <td>0.760803</td>\n",
       "      <td>0.239197</td>\n",
       "      <td>-0.426593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>748</th>\n",
       "      <td>0.868112</td>\n",
       "      <td>0.496368</td>\n",
       "      <td>0.753619</td>\n",
       "      <td>0.246381</td>\n",
       "      <td>0.430903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>749</th>\n",
       "      <td>-0.994075</td>\n",
       "      <td>0.108693</td>\n",
       "      <td>0.988186</td>\n",
       "      <td>0.011814</td>\n",
       "      <td>-0.108049</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>750 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           X1        X2  X1_Square  X2_Square     X1*X2\n",
       "0   -0.994075 -0.108693   0.988186   0.011814  0.108049\n",
       "1   -0.485420  0.874281   0.235633   0.764367 -0.424394\n",
       "2    0.416461 -0.276696   0.173439   0.076561 -0.115233\n",
       "3    0.193758 -0.460932   0.037542   0.212458 -0.089309\n",
       "4    0.356412 -0.934329   0.127029   0.872971 -0.333006\n",
       "..        ...       ...        ...        ...       ...\n",
       "745  0.224192  0.446921   0.050262   0.199738  0.100196\n",
       "746 -0.903036  0.429566   0.815473   0.184527 -0.387913\n",
       "747 -0.872240  0.489078   0.760803   0.239197 -0.426593\n",
       "748  0.868112  0.496368   0.753619   0.246381  0.430903\n",
       "749 -0.994075  0.108693   0.988186   0.011814 -0.108049\n",
       "\n",
       "[750 rows x 5 columns]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "XX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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    "X_train1, X_test1, y_train1, y_test1 = train_test_split(XX, y, \n",
    "                                                    test_size = 0.25, \n",
    "                                                    random_state = 0)"
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "import plotly.express as px\n",
    "\n",
    "fig = px.scatter_3d(df, x='X1', y='X2', z='X1*X2',\n",
    "              color='y')\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = px.scatter_3d(df, x='X1_Square', y='X2_Square', z='X1*X2',\n",
    "              color='y')\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classifier = SVC(kernel=\"linear\")\n",
    "classifier.fit(X_train1, y_train1)\n",
    "y_pred1 = classifier.predict(X_test1)\n",
    "accuracy_score(y_test1, y_pred1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classifier = SVC(kernel=\"poly\")\n",
    "classifier.fit(X_train1, y_train1)\n",
    "y_pred1 = classifier.predict(X_test1)\n",
    "accuracy_score(y_test1, y_pred1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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