SVM From Scratch/SVM From Scratch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "8dd1e060",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfc7e0cd",
   "metadata": {},
   "source": [
    "# Cost Function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90c0d221",
   "metadata": {},
   "source": [
    "### 1- Hinge loss"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65412136",
   "metadata": {},
   "source": [
    "Hinge loss is used in the SVM Classifier to estimate the goodness of the model prediction:"
   ]
  },
  {
   "attachments": {
    "hinge%20loss%201-3.jpg": {
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    }
   },
   "cell_type": "markdown",
   "id": "39d12556",
   "metadata": {},
   "source": [
    "![hinge%20loss%201-3.jpg](attachment:hinge%20loss%201-3.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d743db8",
   "metadata": {},
   "source": [
    "Which is equivalent to:"
   ]
  },
  {
   "attachments": {
    "hinge%20loss%202-2.jpg": {
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    }
   },
   "cell_type": "markdown",
   "id": "eebbbd3c",
   "metadata": {},
   "source": [
    "![hinge%20loss%202-2.jpg](attachment:hinge%20loss%202-2.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 567,
   "id": "e9c64c7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Hinge Loss Visualized\n",
    "predictions = np.arange(-3,3,0.1)\n",
    "L = [1-i if i < 1 else 0 for i in predictions]\n",
    "\n",
    "plt.figure(figsize = (6,6))\n",
    "plt.plot(predictions, L)\n",
    "plt.title('Hinge Loss', fontsize= 20)\n",
    "plt.xlabel('Label*Prediction', fontsize= 15)\n",
    "plt.ylabel('Loss', fontsize= 15)\n",
    "plt.hlines( y = 1, xmax=-3, xmin = 0, linestyles= '--', color = 'red')\n",
    "plt.vlines( x = 0, ymax=0, ymin = 1, linestyles= '--', color = 'red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "533a7360",
   "metadata": {},
   "source": [
    "### 2- Regulatization term"
   ]
  },
  {
   "attachments": {
    "regularization%20component.jpg": {
     "image/jpeg": 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    }
   },
   "cell_type": "markdown",
   "id": "bdd31f03",
   "metadata": {},
   "source": [
    "![regularization%20component.jpg](attachment:regularization%20component.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "208ea0b9",
   "metadata": {},
   "source": [
    "**FINAL COST FUNCTION**"
   ]
  },
  {
   "attachments": {
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     "image/jpeg": 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"
    }
   },
   "cell_type": "markdown",
   "id": "e03f30c7",
   "metadata": {},
   "source": [
    "![final%20cost%20function-3.jpg](attachment:final%20cost%20function-3.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a52a2194",
   "metadata": {},
   "source": [
    "# Gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81832776",
   "metadata": {},
   "source": [
    "**For data points correctly classified**"
   ]
  },
  {
   "attachments": {
    "gradient%202.jpg": {
     "image/jpeg": 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    }
   },
   "cell_type": "markdown",
   "id": "d05ef543",
   "metadata": {},
   "source": [
    "![gradient%202.jpg](attachment:gradient%202.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfce3564",
   "metadata": {},
   "source": [
    "**For data points miss-classified**"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "0c7bd7a6",
   "metadata": {},
   "source": [
    "![gradient%201.jpg](attachment:gradient%201.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23e37e79",
   "metadata": {},
   "source": [
    "# Model Training"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94dbea80",
   "metadata": {},
   "source": [
    "### Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "id": "c779ac72",
   "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>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.974487</td>\n",
       "      <td>3.542517</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.063987</td>\n",
       "      <td>-0.291100</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.760608</td>\n",
       "      <td>4.510147</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.952315</td>\n",
       "      <td>4.527484</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.583514</td>\n",
       "      <td>4.038031</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         X1        X2  class\n",
       "0  3.974487  3.542517      1\n",
       "1  0.063987 -0.291100     -1\n",
       "2  4.760608  4.510147      1\n",
       "3  4.952315  4.527484      1\n",
       "4  4.583514  4.038031      1"
      ]
     },
     "execution_count": 380,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generating the data\n",
    "positive_class = pd.DataFrame(np.random.multivariate_normal([5,5], [[1,0],[0,1]], size = 100), columns= ['X1', 'X2'])\n",
    "positive_class['class'] = +1\n",
    "negative_class = pd.DataFrame(np.random.multivariate_normal([0,0], [[1,0],[0,1]], size = 100), columns= ['X1', 'X2'])\n",
    "negative_class['class'] = -1\n",
    "data = positive_class.append(negative_class).sample(frac=1).reset_index(drop = True)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 548,
   "id": "1a11affa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PfIKdO3ce+XzNmjVs3bqVrq4uZsyYAQQTPP/gBz9g3bp1HDp0iOnTp9PT00N3d3ddZXV39u3bx/79+4EgSebllxPPKxIRaRoFvTLDpw+z+pzVDPYNYhiDfYOsPmc1w6c35xdfd3c3d911F+vXr2dgYICTTjqJL3/5yxP2O/vss1mwYAGvec1rGBwcZMqUKcyePfvI59/5znc47bTTmDZtGkuXLuWOO+5gypQpPPfcc5x33nlMnz6dOXPmcOaZZ7J4cTCpzSc/+cmami43btxIb2/vkezN3t5eTjnllAbvgIhIeqzYXJZX8+bN87Vr107Y/sQTTzBnzpwUSiTl9LcQkaSZ2SPuPq98u2p6IiLSMRT0RESkYyjoiYhIx1DQExGRjqGgJyIiHUNBT0REOoaCnoiIdAwFPRER6RgKehly8803R664ICIijVPQk5p99rOfZd68ebziFa/g4osvTrs4IiKxVV/fRjrSxz/+8XHvpU444QQ++tGP8t3vfpe9e/cmWzARkQaophdmdBSGhqCrK3gfbc6q6UWbN2/m3HPPZdasWfT39/OhD30odL+lS5cye/Zspk+fzty5c3nggQeOfPbwww8zb948pk+fzvHHH88VV1wBBCshFBefnTFjBvPnz+f5559vavnPPfdc3vOe99Df39/U44qItJqCXrnRURgZgY0bwT14HxlpWuA7dOgQixYtYnBwkA0bNvDMM89w4YUXhu47f/58HnvsMbZv38573/tezj//fPbt2wcEAXHp0qXs3LmTp59+mgsuuACAW265hR07drB582bGxsa48cYb6e3tBWDlypUsWrSoKdchIpJHCnrlli+HPXvGb9uzJ9jeBA8//DDPPvss119/PccccwxTpkyJTF4p1tgmTZrElVdeycsvv8yTTz4JQE9PD+vXr2fbtm1MmzaNM84448j2sbEx1q9fT3d3N3PnzmX69OkALFu27MgK6yIinUhBr9ymTbVtr9HmzZsZHBxk0qTq3amf+cxnmDNnDn19fcyYMYMdO3awbds2AG666SaeeuopTj31VObPn38kmC1ZsoSzzz6bCy+8kBNOOIGrrrqKAwcOxCrbokWLmDFjBjNmzGDlypWsXLnyyL9VQxSRdqCgV25goLbtNZo9ezabNm3i4MGDFfd74IEH+NSnPsWdd97Jr3/9a1588UX6+voorn948sknc/vtt/PCCy9w9dVXc95557F79256enq45pprePzxx3nooYe4++67ufXWW2OV7e677+bFF1/kxRdfZNmyZSxbtuzIv1VDFGlQi3MFJB4FvXIrVsDUqeO3TZ0abG+CN73pTbzyla9k2bJl7N69m3379vHggw9O2O+ll15i0qRJzJo1i4MHD/KJT3yCnTt3Hvl8zZo1bN26la6uLmbMmAEEq7L/4Ac/YN26dRw6dIjp06fT09NDd3d3U8pedPDgQfbt28ehQ4c4dOgQ+/btqxrE254eaFJJi3MFJD4FvXLDw7B6NQwOglnwvnp1sL0Juru7ueuuu1i/fj0DAwOcdNJJfPnLX56w39lnn82CBQt4zWtew+DgIFOmTGH27NlHPv/Od77DaaedxrRp01i6dCl33HEHU6ZM4bnnnuO8885j+vTpzJkzhzPPPJPFixcD8MlPfpIFCxY0fA3XXXcdvb29rFy5kjVr1tDb28t1113X8HFzSw80qabFuQISnxWby/Jq3rx5vnbt2gnbn3jiCebMmZNCiaRc2/8thoaCQFducBA2bEi6NJJFXV3BD6JyZnD4cGPHHh0NguemTUE3zIoVTfuR3jIJlNnMHnH3eeXbVdMTaVSLk5+kDbQqVyCslWHJkiCYZrWZPeWWEQU9kUa1OPlJ2kCrcgXCmk2LNcqsNrOn3NSroCfSqBYnP0kbaFWuQLXWhCz2G6bcMqKgJ9KoFic/SRNkIbt2eDjo4z18OHhvxv8fcVoTstbMnnLLSFsHvbwn6bSDw4120udFKx5o0hztnF0b1spQLmvN7Cm3jLRt0JsyZQpjY2MKfClxd/bv388zzzzDMccck3ZxpJO183CB0lYGCFoaSmWxmT3llpG2HbJw4MABtmzZcmSCZknepEmT6OvrY+bMmXR1te3vK8m6Vg4XyJo8Dl9okaghC227nl5PTw+vetWr0i6GSHvJ40N1YCB8HGXWmv2aYXg4+3+PlOnnt4jEk9e+MWXXSgkFPRGJJ699Y8qulRJt26cnIk3WSX1jknuahkxEGqOZZ6RUFsY+1kFBT0TiUd+YFOW1fxcFPRGJS31jUpTX/l3UpyciIrXKQf+u+vRERKQ5cty/q6AnIiITVUpUyXH/roKeiIiMVy1RJcf9u+rTExGR8YaGwqduGxwMVhHJAfXpiYhIZcUmzbCAB9lbm68ObTvhtIiI1KDYpFk+FKFUDhJVqlFNT0REwsfelWp2okpKM7oo6ImINEvcB3kWp/Cq1HTZ7ESVFGd0USKLiEgzhDUPTp06MVjE3S9pSSavJHCu3CSymNkMM/uqmf3CzJ4ws7ekXSYRkariTs2V1Sm8khx7F1WrTCBRJnNBD1gFfMfdTwXeADyRcnlERKqLemBv3Di+GTPFB35FSY69S3FGl0wFPTObDvwecBOAu+939xdTLZSISByVHtil/VbHHRe+T1dX+n18w8NB8+Lhw8F7q5pbU5zRJVNBD/gtYCvwJTP7iZl9wcyOKd/JzEbMbK2Zrd26dWvypRSR1stiskclYQ/ycsVmzbD9Dh3K3TI9dUtxRpdMJbKY2Tzgh8Bb3f1HZrYK2OnuH4v6jhJZRNpQVpM9qhkdDfrmNm0KX4UAgof8bbcd3a+rKwh45XI0+0kW5SWRZQuwxd1/VPj3V4HfTbE8IpKGZiR7pFFTLG0eHBwM32dgYPx+UUvxpN3H16YyFfTc/Tlgs5mdUth0FvB4ikUSkTRUSvaIE8yysLJ33H6rZiR15K0pOE3unqkX8EZgLfAz4JvAb1Taf+7cuS4iGbVmjfvgoLtZ8L5mTbzvDQ66B+Fq/Ku/333q1PHbpk6deNyo7w8ONvXyqopz/WvWxLumSudo5PttCljrITEjU3169VCfnkhGNdIvF/Xd3l4YG5u4f3n/Vw5W9h6ntC9wYCCoDcbtu2yDFRFaIS99eiLSLqL65ZYurd4UF5Xdt317+LnKm0NbOQ6sFU2JjQwVyOq4v4xS0BOR1oh66I6NxetrCwsEcYNZPePA8tJXWC7Fgd55pKAnIq0R96FbzMqME3TiBrNax4HFDWZZnEIsxYHeTZF0Ek5YR1+eXkpkEcmosASLSq+4yRj1JsdUEjfxxSx8P7PGy1CL8ntw2WXNvydJaGESDkpkEZHElSdo7NoVnojS3Z3uAO24iS9ZSBrJ68D9MC28n0pkEZHklffLrVoV3hQXFvAguWSMVvYVNltSTaxJNDumkISjoCciyYnqa6s0e0kSWtVX2ApJBIqkEnZSSMJR0BORZIVlZcYJOq2seVQKZuXnheauRFDrdSURKJKqTaZRcw7r6MvTS4ksIm2iUoJKPQkPzUh4afVsJ/VeV6tnYEkyYacViUmuRBYRybNaEx6alezR6sSVeo/fyAwurSxXhkQlsijoiUj21TqtWLMe2q2ezizq+MVztCKgxdEGGaLK3hSR/Kq1H6tZyR6t7j+Lu9p60jO+ZCFhp0UU9EQk+2pNeGhWsAo7r1kQjJqRTBN3tfU0ZnxpZD7QDFPQE5Hsq7Xm0ayswNLzQnDuYnNkM2ph5dcVRZNHN4369ESkPTU72SOJ5I42SCDJCvXpiUhnaXbzXBKDwrMw40ubU9ATEYkjbj9hI4Po2ziBJCsU9EQkGUkvIdPs88WdNabR6bvaNIEkKxT0RKQ5KgWZpBdfbcX5ypNaurvHrwUI2VxvT8YLm6YlTy9NQyaSAdWmxoq7Xl2ztPJ8la61GdN3tWhark5DxDRkqumJSOOq1XCSXkKmlvNVawYt/3zp0uhrbXR8YFgNdcmSoH8viSbhDqCgJyKNqxZkkl5CJuq4xx03PoB98IOVm0HDglDYIrgQfPbqV4d/tnBhvHKH/Xho5rhAUdATkYJGEj+qBbWkU/HDzjd5MuzcOT6A3Xhj5RpqWBCq5P77w7ffc0+871er+ap/sGEKeiLSeOJHtaCWdCp+2PmOPRYOHBi/X9TkHMXgU2vza7XjVROn5qvZWRqioCcijWcdxglqSaTil9ZWly8Pgm7xfNu3xz9OMfhEBaH+/trKFbcZN85cnEmtJt+mFPREJHzqK4hXqygGmiVLgn/fdlsyQa3WYRHHHRd+zPI5L0trqFE12FWrjg5dqOV41YTN9VnvsRqR9JjKJIWldObppSELIhXESX+vlGpfLcU/iVW8456r0jCFNWvce3omfjZ5svtll1Vesb2//+j+/f1HP48qT6Xj1XPNSQ9fSPJv2kJEDFlIPWg1+lLQE4kQ9+EVFSzMqj/okhx/V+1clcbIRX23vz/6fHHuXzuOqUt6TGWLRAU9rbIg0i7KVxXYtSs8vb58xv5Kq3dXez60emXxWs5VaYWCTZtqL2enrniQ5N+0hbTKgkg7q2U8WXk/XVRiRFSfVZzvRm1Pa1hEPeMEK409bOc+r6THVCYtrPqXp5eaN0U8ukkqTjNVI304tXy30b6iyy4Lv57LLht/jrDmxrBzl/fRlavUJNoGfV6R1KeX7ZeCnohH92eVvyoFpHr7puJ+t9G+oka/X56UEueeTJ48ft/Jk8OPUW+fV1b7BLNarhpEBT316Ym0g6j+p/5+mDateauHN6LRvqJm9DXV0k83OgqXXDJ+QHtPz8QB7qVqeZ4Wm6RLx0dOnar185pEfXoi7azSeLKsrM3WaF9Rpe/H7WOrZSLq5csnBrgDB4IlhcKY1da3l6VliNq5j7JcWPUvTy81b4oUZL1JqtG+okrj4uIet5Ym0rhNxvU2cTZjGaJmSKMPL4H/V1GfnoikrtGHXdj3awlkcR/wa9a4d3dHB6WooBc3YFU6ftLj4ZIel5dQkI0KeurTE5F8q7Wvr3w8Y3k/Z1hfW+kxKz0z44zhq3T8NPr0kh6Xl9D4R/XpiUh7qrWvsNrE15WWE6oU8ErnxazURxZ1/O7udJJYkh6Xl/SCwmUU9ESkedJIiGj2Wn31PHxLA1a1ia+jjn/4cDqJRkmvdZj24PewNs88vdSnJ5IRaQ5qrrevsJY+wrhjH6v1kWVxbstmJ5ZUOl7KfXqpB61GXwp6IhmRxYd5JbVkg0YlrYQFiEqJLpXOm7fVGCqVJQMTdSvoiUhrZSUFP65qSxFVqvFVCuRxVq1o5kM/iSWOapGRHz9RQU99eiLSHGn11dTbj1gpoaKY7LJmTe39XStWTFz8FYJH/+LFQRmheZMGRA1yv/HG6H7FVko5UaUaBT0RaY6kEyKgetJI+b6lwTFqJfXSIF26krlZ8F4tw3J4uHKWZ60BqFpQjwom5WVIaraXtBNVqgmr/uXppeZNkQyJu1J7s5rd4jalhTUB9vRMnFC6WQkVcZJh4jT3xekfqyXxJomm5oys0oD69EQkdc1+IMbtR6y0TFAr+r2iljKqNQDFKXd/fxDAy4+dZr9aBhJrooKeZmQRkeQ0ezaOuMdLYzXw4swvYeWDeNdcaVX7UpMnw7HHwvbtQTPiwoVwyy0dvYKDZmQRkfQ1O8khbj9i0v1MpVOd9fcHQalaGRsp3/79wRJSxcSYz3++9r7IDqGgJyLJaXbwiZtokmSSTXlyzdhY8N7fX3sACit3lPIfDtWmW+tQCnoikpxWBJ84D/ew4HjRRUFtrNlTpoUNIThwYHxNLG4ACit3f3/4vlnJjsy4TAY9M+s2s5+Y2d1pl0VEmqieIQDNPHcxOK5YEfR5tWIcW6NNuOVDFGB8UF+1KvmhIW0kk0EPWAo8kXYhRKQFstDs1uiq5ZXGzjXShBtn3GGaPxzaQOayN83sJOAWYAVwhbsvqrS/sjdFpGaNZHOGrYdXmhlZ7fNKElprrhPkKXvzBuAqIPL/PDMbMbO1ZrZ269atiRVMRHKkVbWxarXERmpiGZ/Cq6USWpYqU0HPzBYBL7j7I5X2c/fV7j7P3efNmjUrodKJSG5UayZsJKEmTmCqtwk361N4tUot08k1KFNBD3gr8C4z2wDcAbzdzNakWyQRyZ1W1sZaGZjSmL80CxrtY61BpoKeu3/E3U9y9yHgQuB+d1+ccrFEJG9aWRtrZWBqtySVuE2WCTbrZiroiYg0RStrY60OTFnIbm2GWposE2zWzWzQc/d/rJa5KSISqtXNhGkHpoSSPhpSS5Nlgs26mQ16IiJ1a7dmwlIJJn00pJYmywT/Xpkbp1crjdMTyYDSCZYHBoJf6O0QYLIoL2P5Ui5nnsbpiUie5KXmESUPTYWl8jKWL6OZqAp6ItKYBNPNmy6PATsvY/ky2sSsoCcijWl1zaOVNbG0A3Y915bRGlSotBN+QijoiUhjWlnzaHVNLM2mwnqvLaM1qLxQ0BORxrSy5tHqmliaTYWNXFujNai89WM2kYKeiDSmlTWPVtfE0mwqTKuWmcd+zCbSkAURya4k0t7TGm6RVkp/XoY8NEhDFkQkf5KoiaWVbJFWLTMvQx5aREFPRLKrnZM20rq2vAx5aBEFPRHJtjg1sbwmZqRRy8zTkIcWUNATkXzr8MSMmrVz7TkGJbKISL51SGKG1EaJLCLSnjo8MUNqo6AnIvnW4YkZUhsFPRHJtw5PzJDaKOiJSL51eGKG1GZS2gUQEWnY8LCCnMSimp6IiHQMBT0RkUbldXB8B1LzpohII4qD44vLBBUHx4OaXDNINT0RkUakvfq61CRW0DOz2WY218ymRXw+08z+pLlFExHJAQ2Oz5WKQc/MXmFmXwE2AA8Dvzazm8ysr2zX3wa+1JoiiohkmAbH50q1mt7VwB8AlwJvBv47sAhYa2Ynt7hsIiLZp8HxuVIt6L0X+Ki7/527r3X3VcAbgF8BD5nZW1peQhGRLNPg+Fyplr05G/hZ6QZ3f87MzgJuA75vZsMEQVBEpDNpcHxuVKvpPQtMaMZ09wPufiHwd8BXgJEWlE1ERKSpqgW9B4AlUR+6++XAnwOXNLFMIiIiLVGtefPzwB+ZWb+7j4Xt4O5/aWYbCRJeREREMqta0Otz9/8R4zhfA05pQnlERERaplrz5vfM7P+a2fFRO5jZOcDjwBVNLZm0ldF1owzdMETXtV0M3TDE6DrNTSgiyasW9M4H3gY8aWZ/ZmZH9jezITP7NvAtggzP01pXTMmz0XWjjNw1wsYdG3GcjTs2MnLXiAKfSDvJyaTbFYOeu38NmAPcBHyaYFD6mWZ2DUHtbg7wTnf/z+6uOXck1PL7lrPnwPi5Cfcc2MPy+zQ3oUhbKE66vXEjuB+ddDuDga/q3JvuvtvdrwTmAjOA+4GPAX8JnObu97a0hJJ7m3aE/x6K2i4iOZOjSbfjTjj9SmA5MAQ8Wtj8B4SM4RMpN9AXPgdh1HYRyZkcTbpdbcLpLjO7HPgFwdyb73H3+cAZQC/wEzP7dNTqCyIAK85awdSe8XMTTu2ZyoqzNDehSFvI0aTb1Wp6jwKfAj4HvNbdvw3g7muBNwGXA+8DfmFmF7SwnJJjw6cPs/qc1Qz2DWIYg32DrD5nNcOna9omkbaQo0m3zd2jPzS7D/iguz9ZYZ9ZwGeAYXfvbn4RK5s3b56vXbs26dOKiEip0dGgD2/TpqCGt2JFqvORmtkj7j5vwvZKQa/GE/wHd3+gKQergYKeiIiUiwp6sRJZ4kgj4ImIiNSiaUFPRDpITgYii5SrNvemiMh4xYHIxXFZxYHIoDXlJPNU0xOR2uRoILJIOQU9EalNjgYii5RT0BOR2uRoILJIOQU9EalNjgYii5RT0BOR2gwPw+rVMDgIZsH76tVKYpFcyFT2ppnNBm4FfhM4DKx291XplkpEJhgeVpCTXMpU0AMOAle6+6NmdizwiJl9z90fT7tgIiKSf5lq3nT3X7n7o4X/fgl4Ajgx3VKJiEi7yFTQK2VmQ8DvAD9q5XlG140ydMMQXdd2MXTDEKPrNLOEiEi7ylrzJgCF9fm+Blzu7jtDPh8BRgAGGkiTHl03yshdI+w5EAy03bhjIyN3BTNLaNkbEZH207RVFprFzHqAu4HvuvtfVdu/kVUWhm4YYuOOjRO2D/YNsuHyDXUdU0RE0tfyVRaawcwMuAl4Ik7Aa9SmHeEzSERtl+ZRs7KIpCFTQQ94K7AEeLuZPVZ4LWzVyQb6wptGo7ZLcxSblTfu2IjjR5qVFfhEpNUyFfTc/f+5u7n76939jYXXPa0634qzVjC1Z/zMElN7prLiLM0s0UrL71t+pB+1aM+BPSy/TxMWi0hrZSroJW349GFWn7Oawb5BDGOwb5DV56xWEkuLqVlZRNKSyezNJA2fPqwgl7CBvoHQBCI1K4tIq3V0TU/SoWZlEUmLgp4kTs3KIpKWzI3Tq1Uj4/RERKQ95WKcnoiISCsp6ImISMdQ0BOpQDPHiLQXBb0M0IO1srTuj2aOEWk/Cnop04O1sjTvj2aOEWk/Cnop04O1sjTvj2aOEWk/Cnop04O1sjTvjyYkF2k/Cnop04O1sjTvj2aOEWk/Cnopq/RgTTKBI6vJNGkGHs0cI9J+NCNLBoyuG2X5fcvZtGMTA30DRx7oI3eNjOvPmtoztSUP3WKySK3nCit3KwJCUucRkfYRNSOLgl5GDd0wFLoSwWDfIBsu35D6ueoNlCIiSdA0ZE2URFNgkgkc9ZxLWacikkcKejVKatxYqxM4SgN3l4X/b1DpXMo6FZE8UtCrUVI1nFYmcJQH7kN+aMI+1c6lrFMRySMFvRolVcNpZeZgWOAG6Lbu2Odq53T+rGayikjjJqVdgLwZ6BsITfpoRQ1n+PThyMDTSEZjVIA+7Ic5fM3h2GUD2i6rsjxBp9h8DeT+2kRENb2aZaGG02i/YrOaJodPH2bD5Rs4fM1hNly+ITQo5K3WpAQdkfamoFejLAxYruXBHBZ06gnc9QSvPE6mrQQdkfamcXo51HVtF87Ev5th45onK42lg/hNk/WOyUtyrGGzVCrzirNWtF1zrki70uD0BmVpVpC4waRZQSfqOP29/UybPC3ynsQNzlkSFeAvesNF3PLTWzQYXyQnNDi9AXGb6ZLqv4rbPNmsprqo/cf2jlW8J3kZ1lD6d1t+33IuesNFE5qv7/nXe9TXJ9IGFPRiiNOHlmT/Vdx+xWYFnbj7l9+TLCT9VBP2d7vlp7ew4qwV4xJ01Ncn0h4U9GKI88BLOusvTuZkVNBZePLCmmqkYceJUnpPspD0U03cv1teaq0iUpnG6cUQZ2xeFmsCYWPpFp68cFzfVJxxaGHH2bV/F2N7xybsWx4EKo01zIK4f7cVZ60I7evLUq1VRKpTTS+GOM10Wa0JlNcIq/VNRfVLlh9n1YJVmW+6jCPu3y0PtVYRqU5BL4Y4D7ys9l+VB7GwGisENZta+iXbJQjU8neL06QsItmmIQtNlKVhDcXylDfJGRY6jGCwbxAgd+PqmiFrfzcRaZzG6WVMEg/aqJpdeeArjjdb8vUldY+ra5fA0S7XIdLpNE4vQ5Ia3hCVpOF4aLNkvf2SeZxuLEy7XIeIRFNNLwVJTc9V63k6abqxMO1yHSKiml6mJDW8odbkmnqTU7I4XKMe7XIdIhJNQS8FSQ1vqCeI1ZOh2EizaJaWHcrqsBMRaR4FvRQkObwhiTT7epcqylr/WVaHnYhI8yjopSDLY9zqqX3Vcz1ZXKw1y38XEWkOJbI0Ud7T3etNZKlH1LJDECSO5PUeikg2KJGlxbLYXFerJGtfUf1khuX6HopItinoNUmrAkaSyR5JZi9GrdxQXvtLu8lTRNqLgl6TtCJgJF17TDJ7sbz/rL+3P3LfuPew0R8IWcsmFZHmU9BrklYEjKSTPZLOXizNLK0k7B6WB6gP/v0HG/qB0A7N0yJSnYJek7QiYCQ9WDqt7MXRdaOha/MVld/DsAB149obG/qBEPUDY+m9S1X7E2kjWkS2ScIWWq2UeRgn0zPO4rXNlsair5UCU39v/4TyhAWoqEzQsB8IYfc+6ofE2N6xIwE5zoK7IpJtGrKQgrhDA5IcQpCmSsMX1py7ZsK1Vtq/XPm8mVH3tHdSb8XaZqVjikj2aMhChsTtq+uUwdJRNdewWl6l/Q0b9++w5uWoe1/cP45am5eVICOSHQp6Kailr64TVuuO6g9dtWBVTftfOu/Sqj8Qou799r3bJ/zAiMooraV5WQkyItmioJeCrExsHFUDSapmUjzPkq8voXdSL/29/bFqtFE14M+/8/NVfyBUuvflPzBWLVjVcHJSFqdbE+lkmUtkMbN3AKuAbuAL7r4y5SI13YqzVoT2KyU5sXF531axBvKln3yJ+395/5E+s2Ymb5QmkBzXexw7X97JgcMHgCBhZGrPVG4797ZY56k34aaWe188/tJ7lx7p7+ud1Bt6PVHJSFquSCRbMlXTM7Nu4HPAAuC1wB+b2WvTLdVRcWtA1fbLQl9dVA3kvl/e15JZUcqb+cb2jh0JeM08TzX13Pu9B/ce+e+xvWOM3DUSe1xgVmr1IhLIVPammb0F+Li7n13490cA3P0vo76TVPZmu2Vc2rVWfafS/bGqg8griVqVvNnnabaocndbN4f80ITtcbNFs/b/g0i7yUv25onA5pJ/bylsS13cvpk89OGMrhudkOlYTaM1k7jNeVmrAUWVOyzghe2fhVq9iByVtT69sCfxhKqomY0AIwADA8k8JOP2zeShD2f5fctjj3MrCpsVpZaB+F3WFRkoirK4YGvUBAFRNb2woJ3GgH8RCZe1mt4WYHbJv08Cni3fyd1Xu/s8d583a9asRAoWt2+mmX04rciiHF03GquZsdTkrsmhTbhx0vCL+4YFiMndk6tmbNZ6D5p9z6KGR4zMHdEq6yI5lLWg92PgZDN7lZlNBi4Evp1ymYD4c2s2aw7OVozvKh6zVvsP7x933lqacMP2haCm9MV3f5FtV22LHGJQ6z1oxT2rNDxCzZYi+ZOpRBYAM1sI3EAwZOGL7l4xWiQ5DVncJr1mrKAelUDRyBRYlZJJqk3FVXreqGnAwpJQ6lkhvXj/osoadQ9acc9EJJ+iElmy1qeHu98D3JN2OcLE7ZuJu1+l4NiKvsFK3119zmoAFn99cdXv1jIRdtS+xRXSYfxYQGBCtmOlsjSyXUQ6T9aaNztGtaa4Sn2D9fZbRR1zsG/wSKCOM/VW3Cbc0XWj7Nq/a8KxDIscCxjVHBrnOlpxz6rRvJoi+aKgl5Jq/WJRgWXhyQvr7reKE6ziTL0VJw2/GNTLm0v7e/srLgMUp1YW1T/aintWiebVFMmfzPXp1SqPSwtBvH6xsObPqL6uuP1Wcfob6+2TLP1e1BCFwb5BgMhriPqsqL+3n21Xbavp+hq9Z1HUhyiSXVF9egp6LRYVQOp9YFZKDDGs7sSZRoXNPBLGMG4797bIWUoguk+v3plMakm8ycJxRaRxeZmRpa1Uav6qd2hDpfF+aTaxxemLg6OrGUQ1j5Z+BsHQBqChIQGtmv9S82qK5I9qei1UrTZXTzNi3BpV0k1scVYzT2vOyVbNf6l5NUWySzW9FFRLoa9ngdjyWlKt526VqNpNt3VPqM0lnfHYqvkvNa+mSP6optdCSSQ6ZCWZolqtp3TAefmQhfLaUTMG94tIZ1NNLwXNmpIs7XPEUV7r6e/tp3dSL0u+voSZ/2sm7/vW+44E50rr9WkYgIi0koJeCyXR/JWlJrZic+2l8y5l+97tjO0dO7Jg7P5D+yt+t9gcm4elmUQkv9S8KU01um6UJV9fUvPSRcXm2DSGAag5VaT9qHkzYe06PVW166pnrT7DWHjyQiD5YQBqThXpLAp6LdCuD9I411VP1qjj3PLTWxoav1it3FGBWs2pIp1FQa8F2vVBGue6KtXIigvGFgecRx2nd1LvuO/U00dZDHR2rbH464sjA7VWZhDpLAp6LdCuD9I41xVWUzOMy+ZddmTB2MMe3jdXDEilk1TvPbi35nKW1kjDlAbYNGZVademb5E8UNBrgTT6pZJ4iMa5rmI2aekSRcf1HsdbB956pJxRfX7d1h1ak7zoGxfVdE1xpkQrBuqwIA2wa/+ultzHdm36FskLBb0WSHLsXJIP0Vquq7SGNrZ3jEu+ecm4sXrlpvZMDV2VAeCQH6rpmuLUqIuBOixIF8vcivvYrk3fInmhoNcCSY6dS/IhGve6wsp04PCByLF6xeMUJ5kOU8s1VatRGzZhfcBpk6c1dM642rXpWyQvJqVdgHZVXDGg1ZJ+iMa5rlrObdi46dIqTaYd97grzloReRzDuHTepROuIan7ONA3EFrb1coMIslQTS/nsri8TS3nDusPDMvurOW4lZYnuu3c2/j8Oz8f+9jNvo9ZmTZOpFMp6OVcFh+iYWXq6ephcvfkcdvCyjl8+jC3/OdbGr6m4pRofo1z8M8P4td4xZUskrqPWZo2TqQTaRqyNpDFabTCygRElrN8/4UnL+Sef70n0WvK4n0UkfpETUOmoCd1a1aQ0GKsItJsmntTmqqZQyWUxi8iSVHQk7o0M1ApjV9EkqKgJ3VpZqDKYgaqiLQnBT2pSzMDVRYzUEWkPSnodYhmz8/ZzEClNH4RSYqCXhuJCmytmJ+z2YGqOK7u8DWHK46n0woFItIIDVloE5XS/pfftzx06qvBvsFxU4BlnYY2iEhcGqfX5oZuGIoMbJt2bApdzscwDl8TvrZdFlW6xjwFbxFpPY3Ta3OVsinbJTtSQxtEpFEKem2iUmBrl+zIdgneIpIeBb02USmwtUt2ZLsEbxFJj/r02kgnTJjcCdcoIo1TIouIiHQMJbKIiEjHU9ATEZGOoaAnuaIZWUSkEZPSLoBIXOUzshSnUwOUzCIisaimJ7mhxWZFpFEKepIbmpFFRBqloCe5kdUZWdTPKJIfCnqSG2EzsgDs2r8rtUDTimWbRKR1FPQkN4rTqfX39o/bPrZ3LLVAo35GkXxR0JNcGT59mGmTp03YnlagUT+jSL4o6EnuZCnQZLWfUUTCKehJ7mQp0GjlB5F8UdDLGWUKZivQtMuyTSKdQqss5Ej5jCQQPOw78SGrJYZEpJLMLy1kZtcD5wD7gaeBS9z9xWrf66SgN3TDEBt3bJywfbBvkA2Xb0i+QCIiGZWHpYW+B7zO3V8PPAV8JOXyZE6WEjhERPIoM0HP3f/B3Q8W/vlD4KQ0y5NFWUrgEBHJo8wEvTLvA+5NuxBZk6UEDhGRPEp0aSEz+z7wmyEfLXf3bxX2WQ4cBCLTEs1sBBgBGBjonFpOMVFDCRwiIvXJTCILgJldBFwKnOXue6rtD52VyCIiIvFkPpHFzN4BXA28K27Ak9bQWEARaVdZWjn9s8ArgO+ZGcAP3f3SdIvUebQ6uYi0s8zU9Nz91e4+293fWHgp4KWg1lUDVCsUkTzJUk1PMqCWsYCqFYpI3mSmpifZUMtYQK0lJyJ5o6An49QyFlAzxIhI3ijoyTi1rBqgGWJEJG/UpycTDJ8+HKtPbsVZK0JXfdAMMSKSVarpSd20lpyI5E2mZmSph2ZkERGRcpmfkUVERKTVFPRERKRjKOiJiEjHUNATEZGOoaAnIiIdQ0FPREQ6hoKeiIh0DAU9ERHpGAp6IiLSMRT0RESkY+R+GjIz2wpsTPCUM4FtCZ4vz3Sv4tF9ik/3Kh7dJxh091nlG3Mf9JJmZmvD5nOTiXSv4tF9ik/3Kh7dp2hq3hQRkY6hoCciIh1DQa92q9MuQI7oXsWj+xSf7lU8uk8R1KcnIiIdQzU9ERHpGAp6dTCz683sF2b2MzP7hpnNSLtMWWJm7zCzJ81svZktS7s8WWVms83sB2b2hJn9i5ktTbtMWWZm3Wb2EzO7O+2yZJmZzTCzrxaeUU+Y2VvSLlOWKOjV53vA69z99cBTwEdSLk9mmFk38DlgAfBa4I/N7LXpliqzDgJXuvsc4AzgT3WvKloKPJF2IXJgFfAddz8VeAO6Z+Mo6NXB3f/B3Q8W/vlD4KQ0y5MxbwLWu/u/uft+4A7g3SmXKZPc/Vfu/mjhv18ieDidmG6pssnMTgLeCXwh7bJkmZlNB34PuAnA3fe7+4upFipjFPQa9z7g3rQLkSEnAptL/r0FPcirMrMh4HeAH6VclKy6AbgKOJxyObLut4CtwJcKTcFfMLNj0i5UlijoRTCz75vZz0Ne7y7ZZzlBE9VoeiXNHAvZphThCsxsGvA14HJ335l2ebLGzBYBL7j7I2mXJQcmAb8L/K27/w6wG1C/eolJaRcgq9z99yt9bmYXAYuAs1zjPkptAWaX/Psk4NmUypJ5ZtZDEPBG3f3raZcno94KvMvMFgJTgOlmtsbdF6dcrizaAmxx92KLwVdR0BtHNb06mNk7gKuBd7n7nrTLkzE/Bk42s1eZ2WTgQuDbKZcpk8zMCPpennD3v0q7PFnl7h9x95PcfYjg/6f7FfDCuftzwGYzO6Ww6Szg8RSLlDmq6dXns8ArgO8Fzy1+6O6XplukbHD3g2b2IeC7QDfwRXf/l5SLlVVvBZYA68zsscK2/+nu96RXJGkD/w0YLfzo/DfgkpTLkymakUVERDqGmjdFRKRjKOiJiEjHUNATEZGOoaAnIiIdQ0FPREQ6hoKeSE6Y2f1m9lMzm1S2/Q/NzM3sD8xscmEVkAfMbK+ZKT1bpISGLIjkhJmdCvwMWFYczF6YwuwJ4CF3/6PCMle/BB4mGIf7dncPmxpOpCOppieSE+7+C+AzwLVmVpzE+1qgD/hwYZ8XgePc/WzgG2mUUyTLFPRE8uUvgDHgf5vZ64E/A65x9yPzm2ouWJFomoZMJEfcfU9hhfVvAvMJ5lX8m1QLJZIjCnoiOePu3zKzR4C5BH12B6t9R0QCat4UyRkzm0ew4KwD/zHd0ojki4KeSI6YWRfwt8A/EySxXGVmv5VuqUTyQ0FPJF8uJajlfRBYCTwD/HWqJRLJEQU9kZwws38HrAD+xt1/5u4vE2RvvtPM3p1u6UTyQYPTRXLCzG4Ffh841d13lmz/JvAG4LXuvtfMFgDHAO8A3g+cX9j1x+6+MdlSi2SLgp5IDpjZ7wH/BLzX3W8v+2yQYOjCX7n7x8xsAzAYcphL3P3mVpdVJMsU9EREpGOoT09ERDqGgp6IiHQMBT0REekYCnoiItIxFPRERKRjKOiJiEjHUNATEZGOoaAnIiIdQ0FPREQ6xv8P67lyyOpaDlwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the data\n",
    "cdict = {1: 'red', -1: 'green'}\n",
    "label = [-1,1]\n",
    "label_dict = {1 : 'class: +1', -1 : 'class: -1' }\n",
    "\n",
    "plt.figure(figsize=(7,6))\n",
    "for g in label:\n",
    "    ix = np.where(data['class'] == g)\n",
    "    plt.scatter(data['X1'].values[ix], data['X2'].values[ix], c = cdict[g], label = label_dict[g])\n",
    "plt.title('Observed data', fontsize = 22)\n",
    "plt.xlabel('X1', fontsize = 15)\n",
    "plt.ylabel('X2', fontsize = 15)\n",
    "plt.legend(loc ='upper left', prop = {'size':12})\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cf6dfd8",
   "metadata": {},
   "source": [
    "#### Helper functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 557,
   "id": "3a8a4102",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to make the prediction\n",
    "def prediction(w, b, X):\n",
    "    '''\n",
    "    w shape (k,1)\n",
    "    X shape (k,)\n",
    "    b shape (1,1)\n",
    "    '''\n",
    "    \n",
    "    return np.dot(w.T, X) + b\n",
    "\n",
    "# Function to calculate the hinge loss\n",
    "def hinge(predictions):\n",
    "    hing_loss = 1 - predictions[0]\n",
    "    hing_loss = max(0, hing_loss)\n",
    "    \n",
    "    return hing_loss\n",
    "    \n",
    "# Function to calculate the gradients \n",
    "def gradients(lambda_reg, w,  X, observed, prediction):\n",
    "    if prediction >=1:\n",
    "        dj_dw = 2*lambda_reg*w\n",
    "        dj_db = 0\n",
    "    else:\n",
    "        dj_dw = 2*lambda_reg*w - np.dot(np.expand_dims(X, axis =1), observed )\n",
    "        dj_db = -observed\n",
    "    \n",
    "    return dj_dw, dj_db"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "738da0e0",
   "metadata": {},
   "source": [
    "#### Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 564,
   "id": "ccb974a6",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "k = data.shape[1] - 1  # number of features, the last column is the class\n",
    "\n",
    "# Initialize w and b\n",
    "w = np.random.normal(size = (k,1))\n",
    "b = np.random.normal()\n",
    "\n",
    "# Hyperparameters\n",
    "n_iter = 500           # number of iterations \n",
    "lambda_reg = 0.00001   # regularization parameter (low lambda --> hard margin SVM)\n",
    "alpha = 0.01           # learning rate\n",
    "\n",
    "Loss = [] # empty list for collecting loss at each iteration \n",
    "\n",
    "# Training loop\n",
    "for i in range(n_iter):\n",
    "    iter_loss = [] # empty list for collecting loss on each row\n",
    "    for row in data.values:\n",
    "        # Extract X , y \n",
    "        X = row[:-1]\n",
    "        y = row[-1]\n",
    "        \n",
    "        # Make prediction\n",
    "        pred = prediction(w, b, X)\n",
    "        pred = y*pred      # multiply prediction by its label\n",
    "        \n",
    "        # Calculateloss on the data point\n",
    "        hinge_loss_row = hinge(pred)\n",
    "        iter_loss.append(hinge_loss_row) # append the loss to the list_loss list\n",
    "\n",
    "        # Calculate the gradients \n",
    "        dj_dw, dj_db = gradients(lambda_reg, w, X, y, pred)\n",
    "\n",
    "        # Update w and b\n",
    "        w -=  alpha * dj_dw\n",
    "        b -=  alpha * dj_db\n",
    "    \n",
    "    # Calculate the total iteration loss: mean of hinge loss + regularization term\n",
    "    hinge_mean = np.mean(iter_loss)\n",
    "    reg_term =  lambda_reg * np.sum(w**2)\n",
    "    Loss.append(hinge_mean + reg_term) # append total cost to the list  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 565,
   "id": "7a2970bd",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plot data and hyperplane\n",
    "# Get an X1 min and max\n",
    "X1min = data['X1'].min()\n",
    "X1max = data['X1'].max()\n",
    "# get an X2 min and max\n",
    "X2min = data['X2'].min()\n",
    "X2max = data['X2'].max()\n",
    "\n",
    "# Hyperplane X2 values\n",
    "X2a_W = (-w[0] * X1min - b) / w[1]\n",
    "X2b_W = (-w[0] * X1max - b) / w[1]\n",
    "\n",
    "# Right support vector X2 values\n",
    "X2a_R = (1 -w[0] * X1min - b) / w[1]\n",
    "X2b_R = (1 -w[0] * X1max - b) / w[1]\n",
    "\n",
    "# Left support vector X2 values\n",
    "X2a_L = (-1 -w[0] * X1min - b) / w[1]\n",
    "X2b_L = (-1 -w[0] * X1max - b) / w[1]\n",
    "\n",
    "##Plot everything\n",
    "plt.figure(figsize=(16,8))\n",
    "# Plot data, hyperplane and margins \n",
    "plt.subplot(1,2,1)\n",
    "plt.plot([X1a, X1b], [X2a_W, X2b_W], label = 'hyperplane w', linestyle= '--', color = 'blue')\n",
    "plt.plot([X1a, X1b], [X2a_R, X2b_R], label = '+1 margin', linestyle= '--', color = 'red')\n",
    "plt.plot([X1a, X1b], [X2a_L, X2b_L], label = '-1 margin', linestyle= '--', color = 'green')\n",
    "for g in label:\n",
    "    ix = np.where(data['class'] == g)\n",
    "    plt.scatter(data['X1'].values[ix], data['X2'].values[ix], c = cdict[g], label = label_dict[g])\n",
    "plt.xlabel('X1')\n",
    "plt.ylabel('X2')\n",
    "plt.legend()\n",
    "plt.title('Observed data, hyperplane & margins', fontsize = 22)\n",
    "plt.xlabel('X1', fontsize = 15)\n",
    "plt.ylabel('X2', fontsize = 15)\n",
    "plt.legend(loc ='upper left', prop = {'size':15})\n",
    "plt.xlim([X1min-1,X1max+1])\n",
    "plt.ylim([X2min-1,X2max+1])\n",
    "\n",
    "# Plot loss value\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(np.arange(1, n_iter+1), Loss)\n",
    "plt.title('Loss', fontsize = 22)\n",
    "plt.xlabel('Iteration', fontsize = 15)\n",
    "plt.ylabel('Loss value', fontsize = 15)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d9b47cbc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2ea5e238",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec50bf3b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f31be2a4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1d269e60",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d0ea16ff",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1b5a59be",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "66e9fbef",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f3217ae8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "574fc084",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0c626eb4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "946f2823",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a4593360",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}