perceptron_tensor.ipynb

{
 "cells": [
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## 1) Installing Libraries",
   "id": "777ff721e76088ae"
  },
  {
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-09-02T09:07:29.994168Z",
     "start_time": "2024-09-02T09:07:23.095259Z"
    }
   },
   "cell_type": "code",
   "source": "!conda install numpy pandas matplotlib --yes",
   "id": "initial_id",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Channels:\r\n",
      " - defaults\r\n",
      " - conda-forge\r\n",
      "Platform: osx-arm64\r\n",
      "Collecting package metadata (repodata.json): done\r\n",
      "Solving environment: done\r\n",
      "\r\n",
      "\r\n",
      "==> WARNING: A newer version of conda exists. <==\r\n",
      "    current version: 24.3.0\r\n",
      "    latest version: 24.7.1\r\n",
      "\r\n",
      "Please update conda by running\r\n",
      "\r\n",
      "    $ conda update -n base -c conda-forge conda\r\n",
      "\r\n",
      "\r\n",
      "\r\n",
      "# All requested packages already installed.\r\n",
      "\r\n"
     ]
    }
   ],
   "execution_count": 1
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:07:33.302429Z",
     "start_time": "2024-09-02T09:07:32.810985Z"
    }
   },
   "cell_type": "code",
   "source": "!pip install torch",
   "id": "9c53ff7441412ea1",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: torch in /Users/vinodkiran/miniforge3/envs/dl-course/lib/python3.9/site-packages (2.4.0)\r\n",
      "Requirement already satisfied: filelock in /Users/vinodkiran/miniforge3/envs/dl-course/lib/python3.9/site-packages (from torch) (3.15.4)\r\n",
      "Requirement already satisfied: typing-extensions>=4.8.0 in /Users/vinodkiran/miniforge3/envs/dl-course/lib/python3.9/site-packages (from torch) (4.11.0)\r\n",
      "Requirement already satisfied: sympy in /Users/vinodkiran/miniforge3/envs/dl-course/lib/python3.9/site-packages (from torch) (1.13.2)\r\n",
      "Requirement already satisfied: networkx in /Users/vinodkiran/miniforge3/envs/dl-course/lib/python3.9/site-packages (from torch) (3.2.1)\r\n",
      "Requirement already satisfied: jinja2 in /Users/vinodkiran/miniforge3/envs/dl-course/lib/python3.9/site-packages (from torch) (3.1.4)\r\n",
      "Requirement already satisfied: fsspec in /Users/vinodkiran/miniforge3/envs/dl-course/lib/python3.9/site-packages (from torch) (2024.6.1)\r\n",
      "Requirement already satisfied: MarkupSafe>=2.0 in /Users/vinodkiran/miniforge3/envs/dl-course/lib/python3.9/site-packages (from jinja2->torch) (2.1.3)\r\n",
      "Requirement already satisfied: mpmath<1.4,>=1.1.0 in /Users/vinodkiran/miniforge3/envs/dl-course/lib/python3.9/site-packages (from sympy->torch) (1.3.0)\r\n"
     ]
    }
   ],
   "execution_count": 2
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:07:43.077382Z",
     "start_time": "2024-09-02T09:07:36.205181Z"
    }
   },
   "cell_type": "code",
   "source": "!conda install watermark --yes",
   "id": "113d49cae29fa963",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Channels:\r\n",
      " - defaults\r\n",
      " - conda-forge\r\n",
      "Platform: osx-arm64\r\n",
      "Collecting package metadata (repodata.json): done\r\n",
      "Solving environment: done\r\n",
      "\r\n",
      "\r\n",
      "==> WARNING: A newer version of conda exists. <==\r\n",
      "    current version: 24.3.0\r\n",
      "    latest version: 24.7.1\r\n",
      "\r\n",
      "Please update conda by running\r\n",
      "\r\n",
      "    $ conda update -n base -c conda-forge conda\r\n",
      "\r\n",
      "\r\n",
      "\r\n",
      "# All requested packages already installed.\r\n",
      "\r\n"
     ]
    }
   ],
   "execution_count": 3
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:07:50.140095Z",
     "start_time": "2024-09-02T09:07:49.106180Z"
    }
   },
   "cell_type": "code",
   "source": [
    "%load_ext watermark\n",
    "%watermark -v -p numpy,pandas,matplotlib,torch"
   ],
   "id": "a78d3b952808a7b2",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.9.19\n",
      "IPython version      : 8.15.0\n",
      "\n",
      "numpy     : 1.26.4\n",
      "pandas    : 2.2.2\n",
      "matplotlib: 3.8.4\n",
      "torch     : 2.4.0\n",
      "\n"
     ]
    }
   ],
   "execution_count": 4
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "### 2) Loading the Dataset",
   "id": "6bd9dd8e7cd3809c"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:08:46.033038Z",
     "start_time": "2024-09-02T09:08:46.020238Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv(\"./data/perceptron_toydata-truncated.txt\", sep=\"\\t\")\n",
    "df"
   ],
   "id": "86bb216344440a8e",
   "outputs": [
    {
     "data": {
      "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"
      ],
      "text/html": [
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       "      <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",
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       "    <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",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.63</td>\n",
       "      <td>-1.53</td>\n",
       "      <td>0</td>\n",
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       "    <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",
       "</table>\n",
       "</div>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 7
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:18:04.740298Z",
     "start_time": "2024-09-02T09:18:04.737285Z"
    }
   },
   "cell_type": "code",
   "source": [
    "X_train = df[[\"x1\", \"x2\"]].values\n",
    "Y_train = df[\"label\"].values"
   ],
   "id": "78ab7ca931e0cf15",
   "outputs": [],
   "execution_count": 31
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:18:06.100099Z",
     "start_time": "2024-09-02T09:18:06.097583Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import torch\n",
    "\n",
    "X_train = torch.from_numpy(X_train)\n",
    "Y_train = torch.from_numpy(Y_train)"
   ],
   "id": "72dc633798c3d86d",
   "outputs": [],
   "execution_count": 32
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:19:26.104171Z",
     "start_time": "2024-09-02T09:19:26.100999Z"
    }
   },
   "cell_type": "code",
   "source": [
    "X_train = X_train.to(torch.float32)\n",
    "X_train"
   ],
   "id": "1b2175eda1a17790",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ 0.7700, -1.1400],\n",
       "        [-0.3300,  1.4400],\n",
       "        [ 0.9100, -3.0700],\n",
       "        [-0.3700, -1.9100],\n",
       "        [-0.6300, -1.5300],\n",
       "        [ 0.3900, -1.9900],\n",
       "        [-0.4900, -2.7400],\n",
       "        [-0.6800, -1.5200],\n",
       "        [-0.1000, -3.4300],\n",
       "        [-0.0500, -1.9500],\n",
       "        [ 3.8800,  0.6500],\n",
       "        [ 0.7300,  2.9700],\n",
       "        [ 0.8300,  3.9400],\n",
       "        [ 1.5900,  1.2500],\n",
       "        [ 1.1400,  3.9100],\n",
       "        [ 1.7300,  2.8000],\n",
       "        [ 1.3100,  1.8500],\n",
       "        [ 1.5600,  3.8500],\n",
       "        [ 1.2300,  2.5400],\n",
       "        [ 1.3300,  2.0300]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 36
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:19:43.214683Z",
     "start_time": "2024-09-02T09:19:43.211542Z"
    }
   },
   "cell_type": "code",
   "source": [
    "X_train.shape\n",
    "X_train.dtype"
   ],
   "id": "9a3a8a33a935f463",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.float32"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 39
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:20:17.478913Z",
     "start_time": "2024-09-02T09:20:17.475344Z"
    }
   },
   "cell_type": "code",
   "source": [
    "Y_train = Y_train.to(torch.float32)\n",
    "Y_train.dtype"
   ],
   "id": "80dde1b5f7a61824",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.float32"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 41
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "### 3) Visualizing the dataset",
   "id": "e3f3b80807b515c"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:20:21.669838Z",
     "start_time": "2024-09-02T09:20:21.600925Z"
    }
   },
   "cell_type": "code",
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\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",
    "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",
    "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()"
   ],
   "id": "93742ed54ab08b31",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 42
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 4) Implementing the Perceptron\n",
    "![](images/perceptron-sketch.png)"
   ],
   "id": "85f583dec7230b86"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:20:26.428114Z",
     "start_time": "2024-09-02T09:20:26.424327Z"
    }
   },
   "cell_type": "code",
   "source": [
    "class Perceptron:\n",
    "    def __init__(self, num_features):\n",
    "        self.num_features = num_features\n",
    "        self.weights = torch.zeros(num_features)\n",
    "        self.bias = torch.tensor(0.)"
   ],
   "id": "9895f329aa421fc9",
   "outputs": [],
   "execution_count": 43
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:20:28.091536Z",
     "start_time": "2024-09-02T09:20:28.088871Z"
    }
   },
   "cell_type": "code",
   "source": "ppn = Perceptron(num_features=2)\n",
   "id": "f30a58554a6379b8",
   "outputs": [],
   "execution_count": 44
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:20:29.424740Z",
     "start_time": "2024-09-02T09:20:29.420259Z"
    }
   },
   "cell_type": "code",
   "source": "ppn.weights",
   "id": "6bf110310be2a507",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 0.])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 45
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:20:31.125122Z",
     "start_time": "2024-09-02T09:20:31.121277Z"
    }
   },
   "cell_type": "code",
   "source": "ppn.bias",
   "id": "df73f6b47d005406",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 46
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "![](images/computing-z.png)",
   "id": "b9b8c411140597e8"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:07.272069Z",
     "start_time": "2024-09-02T09:27:07.267442Z"
    }
   },
   "cell_type": "code",
   "source": [
    "class Perceptron:\n",
    "    def __init__(self, num_features):\n",
    "        self.num_features = num_features\n",
    "        self.weights = torch.zeros(num_features)\n",
    "        self.bias = torch.tensor(0.)\n",
    "\n",
    "    def forward(self, x):\n",
    "        weighted_sum_z = torch.dot(x, self.weights) + self.bias\n",
    "        prediction = torch.where(weighted_sum_z > 0, 1.0, 0.0 )\n",
    "        if weighted_sum_z > 0.:\n",
    "            prediction = torch.tensor(1.)\n",
    "        else:\n",
    "            prediction = torch.tensor(0.)\n",
    "\n",
    "        return prediction\n",
    "    "
   ],
   "id": "bf235dfaa5a6ebc6",
   "outputs": [],
   "execution_count": 64
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:09.495973Z",
     "start_time": "2024-09-02T09:27:09.492232Z"
    }
   },
   "cell_type": "code",
   "source": [
    "ppn = Perceptron(num_features=2)\n",
    "\n",
    "x = torch.tensor([1.1, 2.1])\n",
    "ppn.forward(x)"
   ],
   "id": "671793cecdab4fea",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 65
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "![](images/perceptron-algo-sketch.png)\n",
   "id": "b4b13520034e6bf6"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:11.533196Z",
     "start_time": "2024-09-02T09:27:11.528719Z"
    }
   },
   "cell_type": "code",
   "source": [
    "class Perceptron:\n",
    "    def __init__(self, num_features):\n",
    "        self.num_features = num_features\n",
    "        self.weights = torch.zeros(num_features)\n",
    "        self.bias = torch.tensor(0.)\n",
    "\n",
    "    def forward(self, x):\n",
    "        weighted_sum_z = torch.dot(x, self.weights) + self.bias\n",
    "        prediction = torch.where(weighted_sum_z > 0, 1.0, 0.0)\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",
    "        self.weights += error * x\n",
    "\n",
    "        return error"
   ],
   "id": "8e1d5d03c410de36",
   "outputs": [],
   "execution_count": 66
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:13.629356Z",
     "start_time": "2024-09-02T09:27:13.624798Z"
    }
   },
   "cell_type": "code",
   "source": [
    "ppn = Perceptron(num_features=2)\n",
    "\n",
    "x = torch.tensor([1.1, 2.1])\n",
    "ppn.update(x, true_y=1)"
   ],
   "id": "a990d3b6d6be648",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(1.)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 67
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:15.504357Z",
     "start_time": "2024-09-02T09:27:15.500853Z"
    }
   },
   "cell_type": "code",
   "source": [
    "print(\"Model parameters:\")\n",
    "print(\"  Weights:\", ppn.weights)\n",
    "print(\"  Bias:\", ppn.bias)"
   ],
   "id": "55c7529039225f84",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model parameters:\n",
      "  Weights: tensor([1.1000, 2.1000])\n",
      "  Bias: tensor(1.)\n"
     ]
    }
   ],
   "execution_count": 68
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:17.454501Z",
     "start_time": "2024-09-02T09:27:17.450036Z"
    }
   },
   "cell_type": "code",
   "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}\")"
   ],
   "id": "6e407759d1de3e7d",
   "outputs": [],
   "execution_count": 69
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:19.290414Z",
     "start_time": "2024-09-02T09:27:19.285511Z"
    }
   },
   "cell_type": "code",
   "source": [
    "ppn = Perceptron(num_features=2)\n",
    "\n",
    "train(model=ppn, all_x=X_train, all_y=Y_train, epochs=5)"
   ],
   "id": "62533c7056ab9513",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 errors 1.0\n",
      "Epoch 2 errors 3.0\n",
      "Epoch 3 errors 1.0\n",
      "Epoch 4 errors 0.0\n",
      "Epoch 5 errors 0.0\n"
     ]
    }
   ],
   "execution_count": 70
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "### 5) Evaluating the results",
   "id": "713b41f892302809"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:21.242244Z",
     "start_time": "2024-09-02T09:27:21.239154Z"
    }
   },
   "cell_type": "code",
   "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)"
   ],
   "id": "3581c7a966ea8e26",
   "outputs": [],
   "execution_count": 71
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:23.279280Z",
     "start_time": "2024-09-02T09:27:23.274322Z"
    }
   },
   "cell_type": "code",
   "source": [
    "train_acc = compute_accuracy(ppn, X_train, Y_train)\n",
    "train_acc"
   ],
   "id": "cebeb461547a440",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 72
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:24.941909Z",
     "start_time": "2024-09-02T09:27:24.939008Z"
    }
   },
   "cell_type": "code",
   "source": "print(f\"Accuracy: {train_acc*100}%\")",
   "id": "84fc69133a30038f",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 100.0%\n"
     ]
    }
   ],
   "execution_count": 73
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "### 6) Visualizing the Decision Boundary",
   "id": "5a9d0269e33dcbde"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:47.644658Z",
     "start_time": "2024-09-02T09:27:47.580362Z"
    }
   },
   "cell_type": "code",
   "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()"
   ],
   "id": "fdf01f2bb73156d",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 74
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:51.114001Z",
     "start_time": "2024-09-02T09:27:51.110846Z"
    }
   },
   "cell_type": "code",
   "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"
   ],
   "id": "8f5ad478f3ee245",
   "outputs": [],
   "execution_count": 75
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-02T09:27:53.509487Z",
     "start_time": "2024-09-02T09:27:53.442331Z"
    }
   },
   "cell_type": "code",
   "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()"
   ],
   "id": "9f7497b9c4a92edf",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 76
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}