unit01-ml-intro/exercises/2_random-weights/exercise_2_random-weights.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d71bce70-9dc3-448b-9f9a-8896e83b6d09",
   "metadata": {},
   "source": [
    "# Exercise 2: Initialize the model parameters with small random numbers instead of 0's"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5b48fc7-4f46-4d5a-8558-cd06892aaa27",
   "metadata": {},
   "source": [
    "## 1) Installing Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "be1f5a9a-b3ee-424b-ab02-4371f49bd786",
   "metadata": {},
   "outputs": [],
   "source": [
    "# !conda install numpy pandas matplotlib --yes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "79dd2077-ba5c-4ab5-95fc-6ee4d8a9f811",
   "metadata": {},
   "outputs": [],
   "source": [
    "# !conda install watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bc4fa295-5c62-4888-bcf8-d07d6a7afc47",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.9.7\n",
      "IPython version      : 8.0.1\n",
      "\n",
      "numpy     : 1.22.1\n",
      "pandas    : 1.4.0\n",
      "matplotlib: 3.5.1\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -v -p numpy,pandas,matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9549676-2fa5-41a7-bbb9-ce03f5797c34",
   "metadata": {},
   "source": [
    "## 2) Loading the Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f609024c-3eae-4ad5-8cb8-b95b403b7606",
   "metadata": {},
   "outputs": [
    {
     "data": {
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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>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.77</td>\n",
       "      <td>-1.14</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.33</td>\n",
       "      <td>1.44</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.91</td>\n",
       "      <td>-3.07</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.37</td>\n",
       "      <td>-1.91</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.63</td>\n",
       "      <td>-1.53</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.39</td>\n",
       "      <td>-1.99</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.49</td>\n",
       "      <td>-2.74</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-0.68</td>\n",
       "      <td>-1.52</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-0.10</td>\n",
       "      <td>-3.43</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-0.05</td>\n",
       "      <td>-1.95</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>3.88</td>\n",
       "      <td>0.65</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.73</td>\n",
       "      <td>2.97</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.83</td>\n",
       "      <td>3.94</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1.59</td>\n",
       "      <td>1.25</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.14</td>\n",
       "      <td>3.91</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.73</td>\n",
       "      <td>2.80</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.31</td>\n",
       "      <td>1.85</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.56</td>\n",
       "      <td>3.85</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.23</td>\n",
       "      <td>2.54</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.33</td>\n",
       "      <td>2.03</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "      x1    x2  label\n",
       "0   0.77 -1.14      0\n",
       "1  -0.33  1.44      0\n",
       "2   0.91 -3.07      0\n",
       "3  -0.37 -1.91      0\n",
       "4  -0.63 -1.53      0\n",
       "5   0.39 -1.99      0\n",
       "6  -0.49 -2.74      0\n",
       "7  -0.68 -1.52      0\n",
       "8  -0.10 -3.43      0\n",
       "9  -0.05 -1.95      0\n",
       "10  3.88  0.65      1\n",
       "11  0.73  2.97      1\n",
       "12  0.83  3.94      1\n",
       "13  1.59  1.25      1\n",
       "14  1.14  3.91      1\n",
       "15  1.73  2.80      1\n",
       "16  1.31  1.85      1\n",
       "17  1.56  3.85      1\n",
       "18  1.23  2.54      1\n",
       "19  1.33  2.03      1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv(\"perceptron_toydata-truncated.txt\", sep=\"\\t\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "319546d0-e9ed-4542-873e-395edc05ef2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = df[[\"x1\", \"x2\"]].values\n",
    "y_train = df[\"label\"].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "71792068-9926-41bb-81c0-2a46f6e956fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.77, -1.14],\n",
       "       [-0.33,  1.44],\n",
       "       [ 0.91, -3.07],\n",
       "       [-0.37, -1.91],\n",
       "       [-0.63, -1.53],\n",
       "       [ 0.39, -1.99],\n",
       "       [-0.49, -2.74],\n",
       "       [-0.68, -1.52],\n",
       "       [-0.1 , -3.43],\n",
       "       [-0.05, -1.95],\n",
       "       [ 3.88,  0.65],\n",
       "       [ 0.73,  2.97],\n",
       "       [ 0.83,  3.94],\n",
       "       [ 1.59,  1.25],\n",
       "       [ 1.14,  3.91],\n",
       "       [ 1.73,  2.8 ],\n",
       "       [ 1.31,  1.85],\n",
       "       [ 1.56,  3.85],\n",
       "       [ 1.23,  2.54],\n",
       "       [ 1.33,  2.03]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f2571853-0be0-48b2-9985-8a6021d01276",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 2)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3a5e5ffb-1bca-4f1b-b4cf-a78be1b07753",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "68bfbbf9-4fed-4111-8391-15f2b338d8b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20,)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b6800df4-98f6-401e-bb6c-9964c3b6e3cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10, 10])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.bincount(y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc4663a6-e8a7-472e-b9b0-c64f546a85e9",
   "metadata": {},
   "source": [
    "## 3) Visualizing the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "36a879c3-0c84-4476-a79a-f41d897c696a",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "bd31bb2e-5699-43d4-8874-38e9307ce853",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(\n",
    "    X_train[y_train == 0, 0],\n",
    "    X_train[y_train == 0, 1],\n",
    "    marker=\"D\",\n",
    "    markersize=10,\n",
    "    linestyle=\"\",\n",
    "    label=\"Class 0\",\n",
    ")\n",
    "\n",
    "plt.plot(\n",
    "    X_train[y_train == 1, 0],\n",
    "    X_train[y_train == 1, 1],\n",
    "    marker=\"^\",\n",
    "    markersize=13,\n",
    "    linestyle=\"\",\n",
    "    label=\"Class 1\",\n",
    ")\n",
    "\n",
    "plt.legend(loc=2)\n",
    "\n",
    "plt.xlim([-5, 5])\n",
    "plt.ylim([-5, 5])\n",
    "\n",
    "plt.xlabel(\"Feature $x_1$\", fontsize=12)\n",
    "plt.ylabel(\"Feature $x_2$\", fontsize=12)\n",
    "\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db50db02-3696-4f86-b149-74baabeec6c4",
   "metadata": {},
   "source": [
    "## 4) Implementing the Perceptron"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8f3b0412-fd38-47d4-9fd3-c1603fbc00b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.44171353268653823"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "random.uniform(-0.5, 0.5)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "90c6ae5d-6e69-4f3b-a160-3fdb96b467ac",
   "metadata": {},
   "source": [
    "# <font color='red'>Exercise\n",
    "\n",
    "<font color='red'>Modify the Perceptron class below such that it initializes the weights and bias unit using small random numbers. You can use `random.uniform(-0.5, 0.5)` from Python's [random](https://docs.python.org/3/library/random.html) standard library for this. To make the results reproducible when you run the code multiple times, we already added `random.seed(123)` to the `__init__` constructor below.</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "62d20409-bac5-45be-967e-a2260eb715f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Perceptron:\n",
    "    def __init__(self, num_features):\n",
    "        random.seed(123)\n",
    "        self.num_features = num_features\n",
    "        self.weights = [0.0 for _ in range(num_features)]\n",
    "        self.bias = 0.0\n",
    "\n",
    "    def forward(self, x):\n",
    "        weighted_sum_z = self.bias\n",
    "        for i, _ in enumerate(self.weights):\n",
    "            weighted_sum_z += x[i] * self.weights[i]\n",
    "\n",
    "        if weighted_sum_z > 0.0:\n",
    "            prediction = 1\n",
    "        else:\n",
    "            prediction = 0\n",
    "\n",
    "        return prediction\n",
    "\n",
    "    def update(self, x, true_y):\n",
    "        prediction = self.forward(x)\n",
    "        error = true_y - prediction\n",
    "\n",
    "        # update\n",
    "        self.bias += error\n",
    "        for i, _ in enumerate(self.weights):\n",
    "            self.weights[i] += error * x[i]\n",
    "\n",
    "        return error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f488858e-7315-4343-9133-03ec98fbc6f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(model, all_x, all_y, epochs):\n",
    "\n",
    "    for epoch in range(epochs):\n",
    "        error_count = 0\n",
    "\n",
    "        for x, y in zip(all_x, all_y):\n",
    "            error = model.update(x, y)\n",
    "            error_count += abs(error)\n",
    "\n",
    "        print(f\"Epoch {epoch+1} errors {error_count}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "036bd985-5ac3-48cb-ac1f-0b466d8b51f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 errors 1\n",
      "Epoch 2 errors 3\n",
      "Epoch 3 errors 1\n",
      "Epoch 4 errors 0\n",
      "Epoch 5 errors 0\n"
     ]
    }
   ],
   "source": [
    "ppn = Perceptron(num_features=2)\n",
    "\n",
    "train(model=ppn, all_x=X_train, all_y=y_train, epochs=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26690d7f-e842-4558-80d9-a587b8db6017",
   "metadata": {},
   "source": [
    "# <font color='red'>Exercise\n",
    "\n",
    "<font color='red'>What do you observe, does the perceptron train better or worse?</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb0d5821-7c8d-46b5-9e7d-02e72cac2acc",
   "metadata": {},
   "source": [
    "## 5) Evaluating the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "d910ddbb-798f-47ab-8aab-e2dba4aa4005",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_accuracy(model, all_x, all_y):\n",
    "\n",
    "    correct = 0.0\n",
    "\n",
    "    for x, y in zip(all_x, all_y):\n",
    "        prediction = model.forward(x)\n",
    "        correct += int(prediction == y)\n",
    "\n",
    "    return correct / len(all_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "27538c8d-61bc-47b0-8289-b6aab4aa16ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_acc = compute_accuracy(ppn, X_train, y_train)\n",
    "train_acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "5a4ecf35-4745-43a8-8ea8-14f71cba5b59",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 100.0%\n"
     ]
    }
   ],
   "source": [
    "print(f\"Accuracy: {train_acc*100}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbcd412a-02c0-4d2c-835e-4b01368f53f8",
   "metadata": {},
   "source": [
    "## 6) Optional: Visualizing the Decision Boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a76bb67c-358c-4e91-a5c7-5456333827aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wxPe0mE9M5HvGsAyYDEwCfmtm45Lbv1DIokTCFjQcYhEKkFjMp3N/5jYt5lOx8g2GUe7+dXefB1wA3GZmTYUuSiQK+gqH2ISCe2I96J6rvEHinojND5e+JimqfIPhLWb2FgB3fxH4KHA1ML7QhYlEQW/hEJtQANjyCOzpZThuxx546CvQlV9nvURboGAws9T/FV8CDk2vmFyX+WPJ7SIVqWc4xCoUAB69IfvZQooW86k4Qc8YHjazoe7+pLu/kv6Eu3e6+x1FqE0kMlLhMPqIIfEKhe1rYVcfw1K1mE/FCRoM64Hfmdmo1AYzO93MNKuWxMa0sXX87roZ8QkFgJYboWNf3/tpMZ+KEigY3P0a4BYS4XC+ma0E7gLuK2JtIhImTbYXW/l0Pq8GXgfuBF4Cxrj794pSlYiET5PtxVbQzuefAy3APcAngA8DM4pXloiEbiCT7UlCmU46GHQSveeBz7v7fwOY2QvAA2bW4O43F606EQnPQCbbk4QynXQwaB/DtalQSD5+Cng/MKdYhYmIlLUynnSw35PoufsO4LQC1iIiUjnKeNLBAc2umrzBTURE0pX5pIOadltEpNDKfNJBBYOISCH1MengiLY1pa8pTwoGEZFC6mPSwXHPL4r8pIOBg8HMzjSzxWb2YPJxo5npXgYRkXR9TDpY0/F65CcdDHqD2+UkpsR4Hjg9uXkvcEOR6hIRKT8BJh0c1LUv8pMOBj1juBI4w93nA13JbX8C3l2MokREylKFTDoYNBiGkZgfCbpn1KoBDhS8IhGRclRBkw4GDYZVwHU9tn0ReKyw5YiIlKkKmnQw6FxJlwMPmtkcYJiZPUdiptWPFq0yEZFyUkGTDgYNhleBqcmf40hcVvqDu3flfJWISFwEnHSwpaWFpqam4tYyQH0GQ3K953bgCHf/A/CHolclIiKh6bOPwd07gc3AiOKXIyIiYQt6KelO4Bdm9gNgO2nd7u7+aCELMrOzgB8A1cBtySGyIiJSIkGD4QvJP+f12O7A8YUqJnnZ6mbgTBIBtMbMHnD3Zwt1DBERyS1QMLj7mGIXkvReYIu7vwBgZsuBjwEKBhGREgkUDGb2b7095+7/u3DlMJruG+kgcdZwSpZ65gJzAUaOHElLS0sBS+if9vb2SNQRNrVDN7VFN7VFt3Joi6CXko7p8fho4APAvYUtB8uy7bDbCN39VuBWgMbGRo/C0K9yGIJWCmqHbmqLbmqLbuXQFkEvJV3Sc1uyk/iCAtezncwQqgf+WuBjiIhIDgNZj+HXwMcLVEfKGuAEMxtjZoOB84EHCnwMERHJIWgfQ8+RR28FLiSzP2DA3P2gmf0L8CsSw1Vvd/dnCnkMERHJLWgfwxYS1/pTfQB7gD8CFxe6IHd/CHio0O8rIiLBBO1j0BKgIiIxEXQFt6t72f6lwpYjIiJhC3om0Nu9Cl8vVCEiIhINOS8lmdmM5K/VZjadzPsMjgfeKFZhIiISjr76GBYn/6wFbk/b7iTWaLi8GEWJiEh4cgZDao4kM1vm7p8tTUkiIhKmoKOSPmtmI0lMcldH2iUld7+91xeKiEjZCXqD28eBO4DngZOAZ4DxwG/JvMQkIiJlLuiopBuAS9z9ZODN5J9zgbVFq0xEREIRNBiOdfcVPbYtBdTvICJSYYIGw9+SfQwA28zsfwJjScxnJCIiFSRoMCwC3p/8fSHwGLAB+L/FKEpERMITKBjc/d/d/Z7k78uA/wFMcfdvFLM4Eclt9dZdnDr/UVZv3RV2KVJB+jU5nrv/xd03FboYEQlu9dZdzF7Syo7X9jJ7SavCQQomcDCY2ZlmttjMHkw+bkybMkNESigVCns7OgHY29GpcJCCCTq76uXALSTuYzg9uXkviWGsIlJCPUMhReEghRL0jOFK4Ax3nw90Jbf9CXh3MYoSkex6C4UUhYMUQtBgGEb3Mp6e/LMGOFDwikQkq75CIUXhIAMVNBhWAdf12PZFEsNWRaTIgoZCisJBBiJoMFwOnGdm24BhZvYcMAvQCm4iJXDNio2BQyFlb0cn16zYWKSKpJLlDAYzOxrA3V8GpgL/BFwIXAyc4u6vFL1CkSJavXUXjTespPFbKyP97XrBrIkMqclvooEhNdUsmDWxSBVJJevrjGFz6hd3d+A6d1/h7k+6e1eO14lE3uqtu2j+8Rp2tR9g15sHaL59TWTDYdrYOhY3NwYOhyE11SxubmTa2LoiVyaVqK9gsB6Pm4pUh0hJpULhwMHu7zcHOrsqIhwUCjJQfQWD9/G8SNnJFgop5R4OCgUphL6CYZCZTTezGcm7nDMe685nKTe5QiGlXMNBoSCF0lcw/I3ECm2Lkz9tPR7fVtTqRAooSCiklFs4KBSkkHIGg7s3uPuYHD/Hl6pQkYHIJxRSyiUcRh8xRKEgBdWv2VVFys01KzbmFQopBzq7In0vwLSxdfzuuhkKBSkoBYPEwoJZExk8KP9/7oOrq3QvgMSOgkFiYdrYOpZcMjWvcBhcXcWSz01l2ti6vBbESe27qS2/O5VFokLBILGRTzj0DIWgC+Kk77tw7b68+ye0IptEgYJBYiVIOGQLhSAL4vTc90AXeU1kpxXZJCoUDBI7ucIhVyikZAuHgS6eoxXZJEoUDBJL2cIhSCikpH9wD3TxHK3IJlETmWAwswVm9icz22hm95rZEWHXJJUtFQ51QwdT97bBgUMhZW9HJ823r6H5x2v6vXiOVmSTKIpMMAArgfHuPpHErK5fDbkeiYFpY+to/fqZtH7jzLxCIeVAZ1fg+yN6fshrRTaJqsgEg7v/2t0PJh8+CdSHWY/EU38WxMlHavEcrcgmUWaJZRaixcweBH7m7nf08vxcYC7AyJEjpyxfvryU5WXV3t7O0KFDwy4jdOXeDpvaOlm4dh8HirTayOAquGpKLbc9tZ+2ffn/vzei1vhe01uLUFlxlfu/i0KKSltMnz59rbs3ZnuupMFgZo8AR2d56np3vz+5z/VAI/AJD1BcY2Ojt7a2FrbQfmhpaaGpqSnsMkJXCe2Qz7f5wdVVYAS6nJQ+0V2+Zww9X19uKuHfRaFEpS3MrNdgKOmlJHc/w93HZ/lJhcLFwDnAp4OEgkgx5LMgzpLPTWXJJVPzXjxHK7JJlEWmj8HMzgKuBc519z1h1yPxls+COP1dPEcrsklURSYYgB8Cw4CVZrbezH4UdkESb/ksiNPfxXO0IptEUWSCwd3Hufsx7j4p+XNp2DWJ5LMgTs99B1cR6ENdK7JJ1EQmGESiKp8FcdL3vWpKbeAPda3IJlGiYBAJIJ8FcVL7vmdEsI7l9NdpRTaJgkFhFyAi3VKhIhImnTGIiEgGBYNIFlowR+JMwSDSgxbMkbhTMIik0YI5IgoGkUO0YI5IgoJBBC2YI5JOwSCxpwVzRDIpGCTWtGCOyOEUDBJr/VmxLbUKW1RpqK0MlIJBYm3BrImB10RIGVJTzYJZE4tU0cBoqK0UgoJBYq2SFszRUFspFAWDxF4lLJijobZSSAoGEcp7wRwNtZVCUzCIJJXjgjkaaivFoGAQSVNOC+ZoqK0Ui4JBpIdyWTCnEofaSjQoGESyyGfFtpRS3z9QaUNtJToUDCIFEMb9A5U01FaiRcEgMkC93T+wqS2/yzz9UQlDbSV6FAwiA5Dr/oGFa/dF4sxBoSD5UjCI9FNfo4IOdBH6ZSWFgvSHgkGkH6J4/0A5DbWVaFMwiOQpyvcPlMtQW4k2BYNInqJ+/0B/htqKpFMwiORJ9w9IpVMwiORJ9w9IpVMwiPSD7h+QSqZgEOmnvsJhcBUKBSlLCgaRAch1/8BVU2oVClKWFAwiA9Tb/QPvGZFfB7VIVCgYRApA9w9IJRkUdgEilSJ1/4BIuYvcGYOZXW1mbmb6yiUiEoJIBYOZHQOcCfwl7FpEROIqUsEALAS+AnjYhYiIxJW5R+Mz2MzOBT7o7leY2Tag0d2zzjpmZnOBuQAjR46csnz58tIV2ov29naGDh0adhmhUzt0U1t0U1t0i0pbTJ8+fa27N2Z7rqTBYGaPAEdneep64GvAh9x9d1/BkK6xsdFbW1sLW2g/tLS00NTUFHYZoVM7dFNbdFNbdItKW5hZr8FQ0lFJ7n5Gtu1mNgEYA2wwM4B6YJ2ZvdfdXylhiSIisReJ4aru/hRwVOpxPmcMIiJSWFHrfBYRkZBF4oyhJ3dvCLsGEZG40hmDiIhkUDCIiEgGBYOIiGRQMIiISAYFg4iIZFAwiIhIBgWDiIhkUDCIiEgGBYOIiGRQMIiISAYFg4iIZFAwiIhIBgWDiIhkUDCIiEgGBYOIiGRQMIiISAZz97BrGBAz2wn8Oew6gDpAS5GqHdKpLbqpLbpFpS2Oc/d3Znui7IMhKsys1d0bw64jbGqHbmqLbmqLbuXQFrqUJCIiGRQMIiKSQcFQOLeGXUBEqB26qS26qS26Rb4t1McgIiIZdMYgIiIZFAwiIpJBwVBgZna1mbmZ1YVdS1jMbIGZ/cnMNprZvWZ2RNg1lZqZnWVmz5nZFjO7Lux6wmJmx5jZY2a2ycyeMbMrwq4pbGZWbWZ/NLNfhF1LbxQMBWRmxwBnAn8Ju5aQrQTGu/tEYDPw1ZDrKSkzqwZuBj4CnAhcYGYnhltVaA4CX3b39wDvA/45xm2RcgWwKewiclEwFNZC4CtArHv03f3X7n4w+fBJoD7MekLwXmCLu7/g7geA5cDHQq4pFO7+sruvS/7+BokPxNHhVhUeM6sH/hG4LexaclEwFIiZnQvscPcNYdcSMZ8Dfhl2ESU2Gngp7fF2YvxhmGJmDcDJwO9DLiVM3yfx5bEr5DpyGhR2AeXEzB4Bjs7y1PXA14APlbai8ORqC3e/P7nP9SQuJdxZytoiwLJsi/VZpJkNBe4BrnT318OuJwxmdg7wN3dfa2ZNIZeTk4IhD+5+RrbtZjYBGANsMDNIXDpZZ2bvdfdXSlhiyfTWFilmdjFwDvBBj9/NMtuBY9Ie1wN/DamW0JlZDYlQuNPdfx52PSE6FTjXzM4GaoG3m9kd7v6ZkOs6jG5wKwIz2wY0unsUZlAsOTM7C7gJ+IC77wy7nlIzs0EkOt0/COwA1gAXuvszoRYWAkt8U1oK/Le7XxlyOZGRPGO42t3PCbmUrNTHIMXwQ2AYsNLM1pvZj8IuqJSSHe//AvyKRGfrXXEMhaRTgYuAGcl/C+uT35glwnTGICIiGXTGICIiGRQMIiKSQcEgIiIZFAwiIpJBwSAiIhkUDCIikkHBILFgZtvMbK+Ztaf9jCrAe+a8A1ykHCkYJE4+6u5D035Cm6YieXe0SCQpGCTWzGyUmd1jZjvN7EUz+2KP568zs61m9oaZPWtm5yW3/wQ4FngwefbxleR2N7Nxaa9fYmY3JH/fZmbXmtlG4E0zG9TX8bPU+x9mdm/a4wVm9pvkfEQiBaFvLRJbZlYFPAjcD1xAYrK7R8zsOXf/VXK3rcBpwCvALOAOMxvn7heZ2WnA5939kTwOewGJ+fh3kZh6ua/j9/TvwFYzm0Ri4ZuzgPe7e0ceNYjkpDMGiZP7zOy15M99wFTgne7+b+5+wN1fABYB56de4O4r3P2v7t7l7j8DniexEE9//R93f8nd9wY5fk/u3kZiTv9lJFbGO9vdd5vZcDP7Q/LsZfwA6hPRGYPEysfTv92b2T8Bo8zstbR9qoEn0vb5LPAloCG5aSgwkPW80xfwOa6v4/fij8A3gU+7e+r99pA4E1kwgNpEAAWDxNtLwIvufkK2J83sOBLf4D8I/Je7d5rZeroX4sk2A+Ue4K1pj48msT5DSvprch6/l5omALeQmMr6c8BPAZKXknYm1wMRGRBdSpI4+wPwerJDeIiZVZvZeDObmnz+bSQ+yHcCmNklQPplmleB43u853rgwuR7nQV8YADHz2Bmo0n0SVwKXAZMiPpKYFKeFAwSW+7eCXwUmAS8SKJD+DZgePL5Z4HvAf9FIgQmAL9Le4sbga8n+yyuTm67IvmerwGfBu7r7/HTmdnbgYeAm9z9AXffQ+Ky0bfz/e8W6YvWYxCpIGa2BPiuuz8ddi1SvnTGIFIhzOwh4EPAIjNrDrkcKWM6YxARkQw6YxARkQwKBhERyaBgEBGRDAoGERHJoGAQEZEMCgYREcmgYBARkQwKBhERyfD/AfD0U8YNJmmzAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(\n",
    "    X_train[y_train == 0, 0],\n",
    "    X_train[y_train == 0, 1],\n",
    "    marker=\"D\",\n",
    "    markersize=10,\n",
    "    linestyle=\"\",\n",
    "    label=\"Class 0\",\n",
    ")\n",
    "\n",
    "plt.plot(\n",
    "    X_train[y_train == 1, 0],\n",
    "    X_train[y_train == 1, 1],\n",
    "    marker=\"^\",\n",
    "    markersize=13,\n",
    "    linestyle=\"\",\n",
    "    label=\"Class 1\",\n",
    ")\n",
    "\n",
    "plt.legend(loc=2)\n",
    "\n",
    "plt.xlim([-5, 5])\n",
    "plt.ylim([-5, 5])\n",
    "\n",
    "plt.xlabel(\"Feature $x_1$\", fontsize=12)\n",
    "plt.ylabel(\"Feature $x_2$\", fontsize=12)\n",
    "\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "5d9f1813-d232-4a7d-aebc-cfd5303fae48",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_boundary(model):\n",
    "\n",
    "    w1, w2 = model.weights[0], model.weights[1]\n",
    "    b = model.bias\n",
    "\n",
    "    x1_min = -20\n",
    "    x2_min = (-(w1 * x1_min) - b) / w2\n",
    "\n",
    "    x1_max = 20\n",
    "    x2_max = (-(w1 * x1_max) - b) / w2\n",
    "\n",
    "    return x1_min, x1_max, x2_min, x2_max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "2d71b5df-dd8d-41d5-b6fd-640d6f40d5a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1_min, x1_max, x2_min, x2_max = plot_boundary(ppn)\n",
    "\n",
    "\n",
    "plt.plot(\n",
    "    X_train[y_train == 0, 0],\n",
    "    X_train[y_train == 0, 1],\n",
    "    marker=\"D\",\n",
    "    markersize=10,\n",
    "    linestyle=\"\",\n",
    "    label=\"Class 0\",\n",
    ")\n",
    "\n",
    "plt.plot(\n",
    "    X_train[y_train == 1, 0],\n",
    "    X_train[y_train == 1, 1],\n",
    "    marker=\"^\",\n",
    "    markersize=13,\n",
    "    linestyle=\"\",\n",
    "    label=\"Class 1\",\n",
    ")\n",
    "\n",
    "plt.plot([x1_min, x1_max], [x2_min, x2_max], color=\"k\")\n",
    "\n",
    "plt.legend(loc=2)\n",
    "\n",
    "plt.xlim([-5, 5])\n",
    "plt.ylim([-5, 5])\n",
    "\n",
    "plt.xlabel(\"Feature $x_1$\", fontsize=12)\n",
    "plt.ylabel(\"Feature $x_2$\", fontsize=12)\n",
    "\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}