19-Polynomial-Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.141593</td>\n",
       "      <td>-0.950329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-3.078126</td>\n",
       "      <td>-1.011813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-3.014660</td>\n",
       "      <td>-0.927186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.951193</td>\n",
       "      <td>-0.829626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.887727</td>\n",
       "      <td>-0.991364</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          X         y\n",
       "0 -3.141593 -0.950329\n",
       "1 -3.078126 -1.011813\n",
       "2 -3.014660 -0.927186\n",
       "3 -2.951193 -0.829626\n",
       "4 -2.887727 -0.991364"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate the dataset\n",
    "np.random.seed(42)\n",
    "X = np.linspace(-np.pi, np.pi, 100)\n",
    "y = np.cos(X) + np.random.normal(0, 0.1, X.shape)\n",
    "\n",
    "\n",
    "# Convert to DataFrame\n",
    "data = pd.DataFrame({\n",
    "    'X': X,\n",
    "    'y': y\n",
    "})\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = X.reshape(-1,1)\n",
    "poly_transformer = PolynomialFeatures(degree=50)\n",
    "X_poly_sklearn = poly_transformer.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# df_poly_sklearn = pd.DataFrame(X_poly_sklearn, columns=[\"bias\", \"X\", \"X^2\", \"X^3\"])\n",
    "# df_poly_sklearn['y'] = y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# df_poly_sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fitting Linear Regression with polynomial features\n",
    "lin_reg_poly = LinearRegression()\n",
    "lin_reg_poly.fit(X_poly_sklearn, y)\n",
    "\n",
    "# Making predictions\n",
    "y_pred_poly = lin_reg_poly.predict(X_poly_sklearn)\n",
    "\n",
    "# Plotting the results\n",
    "plt.scatter(X, y, c='b', label=\"Data\")\n",
    "plt.plot(X, y_pred_poly, c='g', label=\"Linear Regression with Polynomial Features\")\n",
    "plt.plot(X, np.cos(X), c='r', label=\"True cosine function\")\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('y')\n",
    "plt.title('Linear Regression with Polynomial Features on Cosine Data')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# With 2 features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generating artificial data for Z (sine function with noise)\n",
    "Z = np.sin(X) + np.random.normal(0, 0.1, X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100, 1), (100, 1), (100,))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape, Z.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>X</th>\n",
       "      <th>Z</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.141593</td>\n",
       "      <td>0.139936</td>\n",
       "      <td>-0.950329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-3.078126</td>\n",
       "      <td>0.029039</td>\n",
       "      <td>-1.011813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-3.014660</td>\n",
       "      <td>-0.120629</td>\n",
       "      <td>-0.927186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.951193</td>\n",
       "      <td>-0.253945</td>\n",
       "      <td>-0.829626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.887727</td>\n",
       "      <td>-0.181326</td>\n",
       "      <td>-0.991364</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          X         Z         y\n",
       "0 -3.141593  0.139936 -0.950329\n",
       "1 -3.078126  0.029039 -1.011813\n",
       "2 -3.014660 -0.120629 -0.927186\n",
       "3 -2.951193 -0.253945 -0.829626\n",
       "4 -2.887727 -0.181326 -0.991364"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating a DataFrame for visualization\n",
    "data_2d = pd.DataFrame(data=np.hstack([X, Z, y.reshape(-1,1)]), columns=[\"X\", \"Z\", \"y\"])\n",
    "data_2d.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating polynomial features for X and Z\n",
    "X_2d = data_2d[['X', 'Z']].values\n",
    "\n",
    "poly_transformer_2d = PolynomialFeatures(degree=3)\n",
    "X_poly_2d = poly_transformer_2d.fit_transform(X_2d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['x0', 'x1', 'x0^2', 'x0 x1', 'x1^2', 'x0^3', 'x0^2 x1', 'x0 x1^2', 'x1^3']"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly_transformer_2d.get_feature_names()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\deprecation.py:87: FutureWarning: Function get_feature_names is deprecated; get_feature_names is deprecated in 1.0 and will be removed in 1.2. Please use get_feature_names_out instead.\n",
      "  warnings.warn(msg, category=FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "\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>1</th>\n",
       "      <th>x0</th>\n",
       "      <th>x1</th>\n",
       "      <th>x0 x1</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>-3.141593</td>\n",
       "      <td>0.139936</td>\n",
       "      <td>-0.439620</td>\n",
       "      <td>-0.950329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>-3.078126</td>\n",
       "      <td>0.029039</td>\n",
       "      <td>-0.089387</td>\n",
       "      <td>-1.011813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>-3.014660</td>\n",
       "      <td>-0.120629</td>\n",
       "      <td>0.363657</td>\n",
       "      <td>-0.927186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>-2.951193</td>\n",
       "      <td>-0.253945</td>\n",
       "      <td>0.749441</td>\n",
       "      <td>-0.829626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>-2.887727</td>\n",
       "      <td>-0.181326</td>\n",
       "      <td>0.523619</td>\n",
       "      <td>-0.991364</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     1        x0        x1     x0 x1         y\n",
       "0  1.0 -3.141593  0.139936 -0.439620 -0.950329\n",
       "1  1.0 -3.078126  0.029039 -0.089387 -1.011813\n",
       "2  1.0 -3.014660 -0.120629  0.363657 -0.927186\n",
       "3  1.0 -2.951193 -0.253945  0.749441 -0.829626\n",
       "4  1.0 -2.887727 -0.181326  0.523619 -0.991364"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating polynomial features for X and Z\n",
    "X_2d = data_2d[['X', 'Z']].values\n",
    "poly_transformer_2d = PolynomialFeatures(degree=3, interaction_only=True)\n",
    "X_poly_2d = poly_transformer_2d.fit_transform(X_2d)\n",
    "\n",
    "# Convert the features into a DataFrame for visualization\n",
    "df_poly_2d = pd.DataFrame(X_poly_2d, columns=poly_transformer_2d.get_feature_names())\n",
    "df_poly_2d['y'] = y\n",
    "\n",
    "# Displaying the first few rows of the DataFrame with polynomial features\n",
    "df_poly_2d.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial Regression with Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "\n",
    "# Generating classification data\n",
    "X_class, y_class = make_moons(n_samples=100, noise=0.15, random_state=42)\n",
    "\n",
    "# Plotting the data\n",
    "plt.scatter(X_class[y_class == 0][:, 0], X_class[y_class == 0][:, 1], c='b', label='Class 0')\n",
    "plt.scatter(X_class[y_class == 1][:, 0], X_class[y_class == 1][:, 1], c='r', label='Class 1')\n",
    "plt.xlabel('Feature 1')\n",
    "plt.ylabel('Feature 2')\n",
    "plt.title('Generated Classification Data')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\deprecation.py:87: FutureWarning: Function get_feature_names is deprecated; get_feature_names is deprecated in 1.0 and will be removed in 1.2. Please use get_feature_names_out instead.\n",
      "  warnings.warn(msg, category=FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "<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>X1^2</th>\n",
       "      <th>X1 X2</th>\n",
       "      <th>X2^2</th>\n",
       "      <th>X1^3</th>\n",
       "      <th>X1^2 X2</th>\n",
       "      <th>X1 X2^2</th>\n",
       "      <th>X2^3</th>\n",
       "      <th>X1^4</th>\n",
       "      <th>...</th>\n",
       "      <th>X1^8 X2^12</th>\n",
       "      <th>X1^7 X2^13</th>\n",
       "      <th>X1^6 X2^14</th>\n",
       "      <th>X1^5 X2^15</th>\n",
       "      <th>X1^4 X2^16</th>\n",
       "      <th>X1^3 X2^17</th>\n",
       "      <th>X1^2 X2^18</th>\n",
       "      <th>X1 X2^19</th>\n",
       "      <th>X2^20</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.613838</td>\n",
       "      <td>-0.491151</td>\n",
       "      <td>2.604474</td>\n",
       "      <td>-0.792638</td>\n",
       "      <td>0.241229</td>\n",
       "      <td>4.203200</td>\n",
       "      <td>-1.279190</td>\n",
       "      <td>0.389305</td>\n",
       "      <td>-0.118480</td>\n",
       "      <td>6.783286</td>\n",
       "      <td>...</td>\n",
       "      <td>9.066907e-03</td>\n",
       "      <td>-2.759396e-03</td>\n",
       "      <td>8.397866e-04</td>\n",
       "      <td>-2.555782e-04</td>\n",
       "      <td>7.778193e-05</td>\n",
       "      <td>-2.367193e-05</td>\n",
       "      <td>7.204245e-06</td>\n",
       "      <td>-2.192519e-06</td>\n",
       "      <td>6.672648e-07</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.089847</td>\n",
       "      <td>0.504391</td>\n",
       "      <td>0.008073</td>\n",
       "      <td>0.045318</td>\n",
       "      <td>0.254410</td>\n",
       "      <td>0.000725</td>\n",
       "      <td>0.004072</td>\n",
       "      <td>0.022858</td>\n",
       "      <td>0.128322</td>\n",
       "      <td>0.000065</td>\n",
       "      <td>...</td>\n",
       "      <td>1.151439e-12</td>\n",
       "      <td>6.464028e-12</td>\n",
       "      <td>3.628821e-11</td>\n",
       "      <td>2.037172e-10</td>\n",
       "      <td>1.143642e-09</td>\n",
       "      <td>6.420255e-09</td>\n",
       "      <td>3.604247e-08</td>\n",
       "      <td>2.023377e-07</td>\n",
       "      <td>1.135897e-06</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.747210</td>\n",
       "      <td>-0.369111</td>\n",
       "      <td>0.558323</td>\n",
       "      <td>-0.275804</td>\n",
       "      <td>0.136243</td>\n",
       "      <td>0.417185</td>\n",
       "      <td>-0.206083</td>\n",
       "      <td>0.101802</td>\n",
       "      <td>-0.050289</td>\n",
       "      <td>0.311725</td>\n",
       "      <td>...</td>\n",
       "      <td>6.214835e-07</td>\n",
       "      <td>-3.070039e-07</td>\n",
       "      <td>1.516555e-07</td>\n",
       "      <td>-7.491561e-08</td>\n",
       "      <td>3.700723e-08</td>\n",
       "      <td>-1.828103e-08</td>\n",
       "      <td>9.030566e-09</td>\n",
       "      <td>-4.460969e-09</td>\n",
       "      <td>2.203654e-09</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.101745</td>\n",
       "      <td>0.236856</td>\n",
       "      <td>1.213842</td>\n",
       "      <td>-0.260955</td>\n",
       "      <td>0.056101</td>\n",
       "      <td>-1.337345</td>\n",
       "      <td>0.287506</td>\n",
       "      <td>-0.061809</td>\n",
       "      <td>0.013288</td>\n",
       "      <td>1.473413</td>\n",
       "      <td>...</td>\n",
       "      <td>6.768164e-08</td>\n",
       "      <td>-1.455040e-08</td>\n",
       "      <td>3.128087e-09</td>\n",
       "      <td>-6.724854e-10</td>\n",
       "      <td>1.445729e-10</td>\n",
       "      <td>-3.108071e-11</td>\n",
       "      <td>6.681822e-12</td>\n",
       "      <td>-1.436478e-12</td>\n",
       "      <td>3.088182e-13</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.728715</td>\n",
       "      <td>0.146523</td>\n",
       "      <td>0.531025</td>\n",
       "      <td>-0.106774</td>\n",
       "      <td>0.021469</td>\n",
       "      <td>-0.386966</td>\n",
       "      <td>0.077808</td>\n",
       "      <td>-0.015645</td>\n",
       "      <td>0.003146</td>\n",
       "      <td>0.281987</td>\n",
       "      <td>...</td>\n",
       "      <td>7.786563e-12</td>\n",
       "      <td>-1.565653e-12</td>\n",
       "      <td>3.148077e-13</td>\n",
       "      <td>-6.329874e-14</td>\n",
       "      <td>1.272755e-14</td>\n",
       "      <td>-2.559143e-15</td>\n",
       "      <td>5.145698e-16</td>\n",
       "      <td>-1.034651e-16</td>\n",
       "      <td>2.080385e-17</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 231 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         X1        X2      X1^2     X1 X2      X2^2      X1^3   X1^2 X2  \\\n",
       "0  1.613838 -0.491151  2.604474 -0.792638  0.241229  4.203200 -1.279190   \n",
       "1  0.089847  0.504391  0.008073  0.045318  0.254410  0.000725  0.004072   \n",
       "2  0.747210 -0.369111  0.558323 -0.275804  0.136243  0.417185 -0.206083   \n",
       "3 -1.101745  0.236856  1.213842 -0.260955  0.056101 -1.337345  0.287506   \n",
       "4 -0.728715  0.146523  0.531025 -0.106774  0.021469 -0.386966  0.077808   \n",
       "\n",
       "    X1 X2^2      X2^3      X1^4  ...    X1^8 X2^12    X1^7 X2^13  \\\n",
       "0  0.389305 -0.118480  6.783286  ...  9.066907e-03 -2.759396e-03   \n",
       "1  0.022858  0.128322  0.000065  ...  1.151439e-12  6.464028e-12   \n",
       "2  0.101802 -0.050289  0.311725  ...  6.214835e-07 -3.070039e-07   \n",
       "3 -0.061809  0.013288  1.473413  ...  6.768164e-08 -1.455040e-08   \n",
       "4 -0.015645  0.003146  0.281987  ...  7.786563e-12 -1.565653e-12   \n",
       "\n",
       "     X1^6 X2^14    X1^5 X2^15    X1^4 X2^16    X1^3 X2^17    X1^2 X2^18  \\\n",
       "0  8.397866e-04 -2.555782e-04  7.778193e-05 -2.367193e-05  7.204245e-06   \n",
       "1  3.628821e-11  2.037172e-10  1.143642e-09  6.420255e-09  3.604247e-08   \n",
       "2  1.516555e-07 -7.491561e-08  3.700723e-08 -1.828103e-08  9.030566e-09   \n",
       "3  3.128087e-09 -6.724854e-10  1.445729e-10 -3.108071e-11  6.681822e-12   \n",
       "4  3.148077e-13 -6.329874e-14  1.272755e-14 -2.559143e-15  5.145698e-16   \n",
       "\n",
       "       X1 X2^19         X2^20  y  \n",
       "0 -2.192519e-06  6.672648e-07  1  \n",
       "1  2.023377e-07  1.135897e-06  1  \n",
       "2 -4.460969e-09  2.203654e-09  1  \n",
       "3 -1.436478e-12  3.088182e-13  0  \n",
       "4 -1.034651e-16  2.080385e-17  0  \n",
       "\n",
       "[5 rows x 231 columns]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating polynomial features for the classification data\n",
    "poly_transformer_class = PolynomialFeatures(degree=20, include_bias=False)\n",
    "X_poly_class = poly_transformer_class.fit_transform(X_class)\n",
    "\n",
    "# Convert the features into a DataFrame for visualization\n",
    "df_poly_class = pd.DataFrame(X_poly_class, columns=poly_transformer_class.get_feature_names(['X1', 'X2']))\n",
    "df_poly_class['y'] = y_class\n",
    "\n",
    "# Displaying the first few rows of the DataFrame with polynomial features\n",
    "df_poly_class.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "# Fitting Logistic Regression with polynomial features\n",
    "log_reg_poly = LogisticRegression(solver='lbfgs')\n",
    "log_reg_poly.fit(X_poly_class, y_class)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the decision boundary\n",
    "x1_min, x1_max = X_class[:, 0].min() - 1, X_class[:, 0].max() + 1\n",
    "x2_min, x2_max = X_class[:, 1].min() - 1, X_class[:, 1].max() + 1\n",
    "\n",
    "xx1, xx2 = np.meshgrid(np.linspace(x1_min, x1_max, 100), np.linspace(x2_min, x2_max, 100))\n",
    "X_grid = np.c_[xx1.ravel(), xx2.ravel()]\n",
    "X_grid_poly = poly_transformer_class.transform(X_grid)\n",
    "probs = log_reg_poly.predict_proba(X_grid_poly)[:, 1].reshape(xx1.shape)\n",
    "\n",
    "plt.scatter(X_class[y_class == 0][:, 0], X_class[y_class == 0][:, 1], c='b', label='Class 0')\n",
    "plt.scatter(X_class[y_class == 1][:, 0], X_class[y_class == 1][:, 1], c='r', label='Class 1')\n",
    "plt.contourf(xx1, xx2, probs, levels=[0, 0.5, 1], alpha=0.3, cmap='Greens')\n",
    "plt.contour(xx1, xx2, probs, levels=[0.5], colors='black')\n",
    "plt.xlabel('Feature 1')\n",
    "plt.ylabel('Feature 2')\n",
    "plt.title('Logistic Regression with Polynomial Features')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.9.13"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}