240505_AIML_lecture_ColabGoogle.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyMF2VvLvlBzvVwso++rGFIq",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/chai923/AIML/blob/main/240505_AIML_lecture_ColabGoogle.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Perceptron-based classification model\n",
        "- A linear binary classification\n",
        "- Single-layer network that makes prediction based on weighted input"
      ],
      "metadata": {
        "id": "8tCSeBuoixzY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Advantages of google colab:\n",
        "- libraries are preinstalled\n",
        "- optimized for the best performance\n",
        "- good balance of library version compatibility\n",
        "- fast execution\n",
        "- ability to leverage GPUs\n",
        "\n",
        "Disadvantages of google colab:\n",
        "- sometimes the performance slows down depending on the network overload\n",
        "- loss of information"
      ],
      "metadata": {
        "id": "lngHR7oNgU4A"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt #imshow = 'image show'\n",
        "from sklearn.linear_model import Perceptron\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import accuracy_score\n",
        "\n",
        "%matplotlib inline"
      ],
      "metadata": {
        "id": "VjOLltRhinK6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### About the MNIST dataset\n",
        "- MNIST: modified national institute of standards an technology\n",
        "- It's a large database of handwritten digits used for training various image processing models\n",
        "- considered to be the \"hello world!\" of neural networks (NN)\n",
        "- It consists of black and white only (grayscale) representation of 28x28 pixel bounding box (image)\n",
        "- the dataset is a flattened representation of these images\n",
        "- we have 28x28 pixels = 784 pixels flattened (columns)\n",
        "each pixel has a value from 0 to 255  \n",
        "\n",
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "BoKsoOXqlYrz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df = pd.read_csv('mnist_train.csv')"
      ],
      "metadata": {
        "id": "oOr6KLw6nYqN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df.max().max()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TpoWRrHOndvC",
        "outputId": "8b5d719b-4542-43a2-d6ea-f6cb6ab2847f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "255"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "P6Tfu0DandqX",
        "outputId": "297aa5a2-6d49-4482-eab9-a85298db6bd3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 785)"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df.head()\n",
        "#28x28 is the grapyscale value of the last pixel i.e the most bottom right pixel\n",
        "#0 means the absense of light i.e. black so likely represents the black background"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 236
        },
        "id": "cn9g218LpGiM",
        "outputId": "9dd9932f-19ec-47cc-9846-15c20da0b5be"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   label  1x1  1x2  1x3  1x4  1x5  1x6  1x7  1x8  1x9  ...  28x19  28x20  \\\n",
              "0      5    0    0    0    0    0    0    0    0    0  ...      0      0   \n",
              "1      0    0    0    0    0    0    0    0    0    0  ...      0      0   \n",
              "2      4    0    0    0    0    0    0    0    0    0  ...      0      0   \n",
              "3      1    0    0    0    0    0    0    0    0    0  ...      0      0   \n",
              "4      9    0    0    0    0    0    0    0    0    0  ...      0      0   \n",
              "\n",
              "   28x21  28x22  28x23  28x24  28x25  28x26  28x27  28x28  \n",
              "0      0      0      0      0      0      0      0      0  \n",
              "1      0      0      0      0      0      0      0      0  \n",
              "2      0      0      0      0      0      0      0      0  \n",
              "3      0      0      0      0      0      0      0      0  \n",
              "4      0      0      0      0      0      0      0      0  \n",
              "\n",
              "[5 rows x 785 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-cea33e79-8459-4855-ad1b-647149472191\" class=\"colab-df-container\">\n",
              "    <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",
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              "      <th>1x1</th>\n",
              "      <th>1x2</th>\n",
              "      <th>1x3</th>\n",
              "      <th>1x4</th>\n",
              "      <th>1x5</th>\n",
              "      <th>1x6</th>\n",
              "      <th>1x7</th>\n",
              "      <th>1x8</th>\n",
              "      <th>1x9</th>\n",
              "      <th>...</th>\n",
              "      <th>28x19</th>\n",
              "      <th>28x20</th>\n",
              "      <th>28x21</th>\n",
              "      <th>28x22</th>\n",
              "      <th>28x23</th>\n",
              "      <th>28x24</th>\n",
              "      <th>28x25</th>\n",
              "      <th>28x26</th>\n",
              "      <th>28x27</th>\n",
              "      <th>28x28</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>9</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 785 columns</p>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-cea33e79-8459-4855-ad1b-647149472191')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-cea33e79-8459-4855-ad1b-647149472191 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-cea33e79-8459-4855-ad1b-647149472191');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-d3cb26b9-788c-484d-a5ec-986540c3b389\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-d3cb26b9-788c-484d-a5ec-986540c3b389')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-d3cb26b9-788c-484d-a5ec-986540c3b389 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe"
            }
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(df.iloc[0])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lAVsRHkapGdl",
        "outputId": "6a0dbeab-b7e0-40e3-9ef8-df0822e0ff9d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "label    5\n",
            "1x1      0\n",
            "1x2      0\n",
            "1x3      0\n",
            "1x4      0\n",
            "        ..\n",
            "28x24    0\n",
            "28x25    0\n",
            "28x26    0\n",
            "28x27    0\n",
            "28x28    0\n",
            "Name: 0, Length: 785, dtype: int64\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#split the data\n",
        "x = df.drop(columns = 'label')\n",
        "y = df['label']"
      ],
      "metadata": {
        "id": "9P-k45kmpGZf"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x_train,x_test,y_train,y_test = train_test_split(x,y,test_size=0.2,random_state=4)"
      ],
      "metadata": {
        "id": "jicbW8VMrJVv"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model_per = Perceptron() #default hyperparameters"
      ],
      "metadata": {
        "id": "B2BRvxPxrJTU"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#train the model\n",
        "model_per.fit(x_train,y_train)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 75
        },
        "id": "HMew7I4UrJRM",
        "outputId": "31aad940-e2d8-4901-a7de-54ca404d07e6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Perceptron()"
            ],
            "text/html": [
              "<style>#sk-container-id-4 {color: black;background-color: white;}#sk-container-id-4 pre{padding: 0;}#sk-container-id-4 div.sk-toggleable {background-color: white;}#sk-container-id-4 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-4 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-4 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-4 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-4 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-4 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-4 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-4 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-4 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-4 div.sk-item {position: relative;z-index: 1;}#sk-container-id-4 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-4 div.sk-item::before, #sk-container-id-4 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-4 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-4 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-4 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-4 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-4 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-4 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-4 div.sk-label-container {text-align: center;}#sk-container-id-4 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-4 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Perceptron()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" checked><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">Perceptron</label><div class=\"sk-toggleable__content\"><pre>Perceptron()</pre></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#get the predicted output\n",
        "y_pred = model_per.predict(x_test)\n",
        "y_pred"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Q74F09vxrlgA",
        "outputId": "bc438b3d-9d8c-47d0-8b58-2dd49fe0d117"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 7, 6, ..., 6, 4, 2])"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "accuracy = accuracy_score(y_test,y_pred)\n",
        "print(f'Perceptron model accuracy: {accuracy}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2_Olsc8FrlZ6",
        "outputId": "0d66d316-5a91-4d6f-ecae-71c8d42529c0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Perceptron model accuracy: 0.8745\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "y3eaJKn9rlWY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "This uses just one perceptron, and we can get away with it because the images are poorly rendered (like the '5' in the above image).\n",
        "\n",
        "we'll need more perceptrons as we do higher quality images."
      ],
      "metadata": {
        "id": "ncbyrjYxsmx5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's see how our perceptron model is good at predictions."
      ],
      "metadata": {
        "id": "S_sDNFsQs2Ve"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#get a sample of images: 4 images of the number 5\n",
        "digit = 5 #this is the digit we're trying to evaluate\n",
        "sample_size = 4\n",
        "\n",
        "mask = df['label']==digit\n",
        "#convert the flattened data into a 2d image for plotting purposes aka reshape\n",
        "#28 comes from squareroot of 784 i.e. number of columns this only works when the image is a square vs rectangle though\n",
        "sample_images = df[mask].drop(columns='label',axis=1).head(sample_size).values.reshape(sample_size,28,28) #.values turns it into an array\n",
        "\n",
        "sample_images[0]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rsxmdbpxs6pg",
        "outputId": "7b4f3b6a-2187-404a-b3b4-1d757ae75caf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.imshow(sample_images[0],cmap='gray')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "ZbTUnLCAxLpO",
        "outputId": "912a4fa4-a86f-47b7-e760-9eccd9a21beb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7e24ff620460>"
            ]
          },
          "metadata": {},
          "execution_count": 36
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(plt.imshow(sample_images[1],cmap='gray'))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "EJPqwDvLxZzL",
        "outputId": "d756b2a8-f29b-4a12-e436-0db3d66c2dce"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "AxesImage(size=(28, 28))\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(plt.imshow(sample_images[2],cmap='gray'))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "YKL69_2exZrE",
        "outputId": "c1f9e0e7-5cbe-46a7-fa82-3e0230db0166"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "AxesImage(size=(28, 28))\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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5kVsAgJ2oA1RUVKSLFy/q3XfffaABtm/frkAgEFr8fAQAPByi+kHULVu26MSJEzp9+nTYDzH6fD7dunVL7e3tYa+C2tra5PP5ev29PB6PPB5PNGMAAAaxiF4BOee0ZcsWHT16VKdOnVJOTk7Y/bNmzdLw4cNVUVERuq2urk5NTU1R/YQ+ACBxRfQKqKioSAcPHtTx48eVnJwcel/H6/Vq1KhR8nq9Wr9+vUpKSpSWlqaUlBS98MILysvL4xNwAIAwEQVo3759kqQFCxaE3b5//36tW7dOkvTGG29oyJAhWrlypbq6ulRQUKDf//73MRkWAJA4kpxzznqIzwsGg/J6vdZjDAirVq2KeE9xcXHEe/rz26NlZWUR74nmgynRPI4k1dTURLUPwN0CgYBSUlL6vJ9rwQEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEV8MGAMQFV8MGAAxIBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMRBai0tFSzZ89WcnKyMjIytGzZMtXV1YUds2DBAiUlJYWtTZs2xXRoAMDgF1GAqqqqVFRUpJqaGp08eVK3b9/WokWL1NnZGXbchg0b1NLSElq7du2K6dAAgMFvWCQHl5eXh3194MABZWRkqLa2VvPnzw/d/sgjj8jn88VmQgBAQnqg94ACgYAkKS0tLez2d955R+np6Zo2bZq2b9+uGzdu9Pl7dHV1KRgMhi0AwEPARam7u9t997vfdfPmzQu7/Q9/+IMrLy93Fy5ccH/+85/d2LFj3fLly/v8fXbu3OkksVgsFivBViAQuGdHog7Qpk2b3IQJE1xzc/M9j6uoqHCSXH19fa/337x50wUCgdBqbm42P2ksFovFevB1vwBF9B7QZ7Zs2aITJ07o9OnTGjdu3D2Pzc3NlSTV19dr0qRJd93v8Xjk8XiiGQMAMIhFFCDnnF544QUdPXpUlZWVysnJue+e8+fPS5KysrKiGhAAkJgiClBRUZEOHjyo48ePKzk5Wa2trZIkr9erUaNGqaGhQQcPHtR3vvMdjR49WhcuXNDWrVs1f/58zZgxIy5/AADAIBXJ+z7q4/t8+/fvd84519TU5ObPn+/S0tKcx+NxkydPdi+99NJ9vw/4eYFAwPz7liwWi8V68HW/v/uT/j8sA0YwGJTX67UeAwDwgAKBgFJSUvq8n2vBAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMDLgAOeesRwAAxMD9/j4fcAHq6OiwHgEAEAP3+/s8yQ2wlxw9PT26cuWKkpOTlZSUFHZfMBhUdna2mpublZKSYjShPc7DHZyHOzgPd3Ae7hgI58E5p46ODvn9fg0Z0vfrnGH9ONOXMmTIEI0bN+6ex6SkpDzUT7DPcB7u4DzcwXm4g/Nwh/V58Hq99z1mwH0LDgDwcCBAAAATgypAHo9HO3fulMfjsR7FFOfhDs7DHZyHOzgPdwym8zDgPoQAAHg4DKpXQACAxEGAAAAmCBAAwAQBAgCYGDQB2rt3rx5//HGNHDlSubm5+uijj6xH6nevvvqqkpKSwtbUqVOtx4q706dPa8mSJfL7/UpKStKxY8fC7nfOaceOHcrKytKoUaOUn5+vS5cu2QwbR/c7D+vWrbvr+bF48WKbYeOktLRUs2fPVnJysjIyMrRs2TLV1dWFHXPz5k0VFRVp9OjReuyxx7Ry5Uq1tbUZTRwfX+Y8LFiw4K7nw6ZNm4wm7t2gCNDhw4dVUlKinTt36uOPP9bMmTNVUFCgq1evWo/W75566im1tLSE1l//+lfrkeKus7NTM2fO1N69e3u9f9euXXrzzTf11ltv6cyZM3r00UdVUFCgmzdv9vOk8XW/8yBJixcvDnt+HDp0qB8njL+qqioVFRWppqZGJ0+e1O3bt7Vo0SJ1dnaGjtm6davef/99lZWVqaqqSleuXNGKFSsMp469L3MeJGnDhg1hz4ddu3YZTdwHNwjMmTPHFRUVhb7u7u52fr/flZaWGk7V/3bu3OlmzpxpPYYpSe7o0aOhr3t6epzP53O/+c1vQre1t7c7j8fjDh06ZDBh//jieXDOubVr17qlS5eazGPl6tWrTpKrqqpyzt35bz98+HBXVlYWOuaf//ynk+Sqq6utxoy7L54H55z71re+5X784x/bDfUlDPhXQLdu3VJtba3y8/NDtw0ZMkT5+fmqrq42nMzGpUuX5Pf7NXHiRD3//PNqamqyHslUY2OjWltbw54fXq9Xubm5D+Xzo7KyUhkZGZoyZYo2b96sa9euWY8UV4FAQJKUlpYmSaqtrdXt27fDng9Tp07V+PHjE/r58MXz8Jl33nlH6enpmjZtmrZv364bN25YjNenAXcx0i/65JNP1N3drczMzLDbMzMz9a9//ctoKhu5ubk6cOCApkyZopaWFr322mt65plndPHiRSUnJ1uPZ6K1tVWSen1+fHbfw2Lx4sVasWKFcnJy1NDQoJ/+9KcqLCxUdXW1hg4daj1ezPX09Ki4uFjz5s3TtGnTJN15PowYMUKpqalhxyby86G38yBJP/jBDzRhwgT5/X5duHBBP/nJT1RXV6e//OUvhtOGG/ABwv8UFhaGfj1jxgzl5uZqwoQJOnLkiNavX284GQaCNWvWhH49ffp0zZgxQ5MmTVJlZaUWLlxoOFl8FBUV6eLFiw/F+6D30td52LhxY+jX06dPV1ZWlhYuXKiGhgZNmjSpv8fs1YD/Flx6erqGDh1616dY2tra5PP5jKYaGFJTU/Xkk0+qvr7eehQznz0HeH7cbeLEiUpPT0/I58eWLVt04sQJffjhh2H/fIvP59OtW7fU3t4ednyiPh/6Og+9yc3NlaQB9XwY8AEaMWKEZs2apYqKitBtPT09qqioUF5enuFk9q5fv66GhgZlZWVZj2ImJydHPp8v7PkRDAZ15syZh/75cfnyZV27di2hnh/OOW3ZskVHjx7VqVOnlJOTE3b/rFmzNHz48LDnQ11dnZqamhLq+XC/89Cb8+fPS9LAej5Yfwriy3j33Xedx+NxBw4ccP/4xz/cxo0bXWpqqmttbbUerV9t27bNVVZWusbGRve3v/3N5efnu/T0dHf16lXr0eKqo6PDnTt3zp07d85Jcrt373bnzp1z//nPf5xzzv3qV79yqamp7vjx4+7ChQtu6dKlLicnx3366afGk8fWvc5DR0eHe/HFF111dbVrbGx0H3zwgfv617/unnjiCXfz5k3r0WNm8+bNzuv1usrKStfS0hJaN27cCB2zadMmN378eHfq1Cl39uxZl5eX5/Ly8gynjr37nYf6+nr385//3J09e9Y1Nja648ePu4kTJ7r58+cbTx5uUATIOed+97vfufHjx7sRI0a4OXPmuJqaGuuR+t3q1atdVlaWGzFihBs7dqxbvXq1q6+vtx4r7j788EMn6a61du1a59ydj2K/8sorLjMz03k8Hrdw4UJXV1dnO3Qc3Os83Lhxwy1atMiNGTPGDR8+3E2YMMFt2LAh4f4nrbc/vyS3f//+0DGffvqp+9GPfuS+8pWvuEceecQtX77ctbS02A0dB/c7D01NTW7+/PkuLS3NeTweN3nyZPfSSy+5QCBgO/gX8M8xAABMDPj3gAAAiYkAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMPF/j/pw/CZ/6kYAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for i in range(sample_size):\n",
        "  plt.imshow(sample_images[i],cmap='gray') #imshow is from matplotlib and it takes numeric picture data and plots the image\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "OskqdZ4ls6yb",
        "outputId": "7db34c31-9c83-4bd8-ade8-1fb95c28ebd4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for i in range(sample_size):\n",
        "  plt.subplot(1,sample_size,i+1)\n",
        "  plt.imshow(sample_images[i],cmap='gray')\n",
        "  plt.axis(\"off\")"
      ],
      "metadata": {
        "id": "bbVGjJB2y5AR",
        "outputId": "fcea6f35-8271-4b95-95d8-96bd802548b9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 144
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 4 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df['label'].value_counts().plot(kind='bar')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 463
        },
        "id": "w704aGzgy_lF",
        "outputId": "5fbcbaa9-d57d-49b3-f736-0d5436b80870"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: xlabel='label'>"
            ]
          },
          "metadata": {},
          "execution_count": 42
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Apples to apples comparison"
      ],
      "metadata": {
        "id": "6Szz8TBpQFFl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "num_samples = 20\n",
        "sample_images = x.head(num_samples).values.reshape(num_samples,28,28)\n",
        "sample_labels = model_per.predict(x.head(num_samples))"
      ],
      "metadata": {
        "id": "p_yxKa_NQEnz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "np.shape(sample_images)"
      ],
      "metadata": {
        "id": "p_nXQ8XySIl3",
        "outputId": "687872b4-cd2f-417e-ce80-ddf9bfd24c21",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(20, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 81
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.shape(sample_labels)"
      ],
      "metadata": {
        "id": "B5nNgx_6UqaQ",
        "outputId": "0aeeaaea-74da-42fe-8531-a5c493a780f4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(20,)"
            ]
          },
          "metadata": {},
          "execution_count": 83
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(num_samples*2,2)) #40 by 2\n",
        "\n",
        "for i in range(num_samples):\n",
        "  plt.subplot(1,num_samples,i+1)\n",
        "  plt.imshow(sample_images[i],cmap='gray')\n",
        "  #add the predicted labels on top of the image\n",
        "  plt.title('Prediction: {}'.format(sample_labels[i]))\n",
        "  plt.axis('off')"
      ],
      "metadata": {
        "id": "qjgJQUpeRmqo",
        "outputId": "ea246703-beca-4773-ff60-2b92b9345de2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 97
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 4000x200 with 20 Axes>"
            ],
            "image/png": 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}