Digit_Recognizer_kaggle.ipynb

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      "name": "Digit_Recognizer_kaggle.ipynb",
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        "   **contents**\n",
        "\n",
        "\n",
        "\n",
        "1.   Importing Libraries\n",
        "2.   Getting The Dataset\n",
        "   \n",
        "3.   Splitting Dataset into Data and Labels\n",
        "\n",
        "\n",
        "\n",
        "4.   Binary Classifier\n",
        "\n",
        "5.   Evaluating Training set\n",
        "6.   Error Analysis\n",
        "7.   Image Representation of confusion-matrix\n",
        "\n",
        "8.   Visualizing predictions\n",
        "9.   Submission\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      },
      "source": [
        "# **Importing Libraries**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yWa0bjMdTdjj"
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q_k-xFYo9_Up"
      },
      "source": [
        "# **Getting** **the** **Dataset**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9MI6ZOD9Thfl"
      },
      "source": [
        "train_data=pd.read_csv('train_digit_new.csv')\n",
        "test_data=pd.read_csv('test_digit_new.csv')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 439
        },
        "id": "KwYGNSSgUAzF",
        "outputId": "5946d3b1-179b-4e53-c474-5cc94f944fce"
      },
      "source": [
        "train_data"
      ],
      "execution_count": null,
      "outputs": [
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          "output_type": "execute_result",
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              "      <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>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>41995</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>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>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>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",
              "      <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>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>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>41996</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>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>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>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",
              "      <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>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>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>41997</th>\n",
              "      <td>7</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",
              "      <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>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>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",
              "      <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>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>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>41998</th>\n",
              "      <td>6</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",
              "      <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>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>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",
              "      <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>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>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>41999</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>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>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>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",
              "      <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>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>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>42000 rows × 785 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "       label  pixel0  pixel1  pixel2  ...  pixel780  pixel781  pixel782  pixel783\n",
              "0          1       0       0       0  ...         0         0         0         0\n",
              "1          0       0       0       0  ...         0         0         0         0\n",
              "2          1       0       0       0  ...         0         0         0         0\n",
              "3          4       0       0       0  ...         0         0         0         0\n",
              "4          0       0       0       0  ...         0         0         0         0\n",
              "...      ...     ...     ...     ...  ...       ...       ...       ...       ...\n",
              "41995      0       0       0       0  ...         0         0         0         0\n",
              "41996      1       0       0       0  ...         0         0         0         0\n",
              "41997      7       0       0       0  ...         0         0         0         0\n",
              "41998      6       0       0       0  ...         0         0         0         0\n",
              "41999      9       0       0       0  ...         0         0         0         0\n",
              "\n",
              "[42000 rows x 785 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 346
        },
        "id": "ctt9Kbgz1gzb",
        "outputId": "48a5bb3d-9d14-4379-d95b-e6f3fcfacf67"
      },
      "source": [
        "train_data.describe()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>label</th>\n",
              "      <th>pixel0</th>\n",
              "      <th>pixel1</th>\n",
              "      <th>pixel2</th>\n",
              "      <th>pixel3</th>\n",
              "      <th>pixel4</th>\n",
              "      <th>pixel5</th>\n",
              "      <th>pixel6</th>\n",
              "      <th>pixel7</th>\n",
              "      <th>pixel8</th>\n",
              "      <th>pixel9</th>\n",
              "      <th>pixel10</th>\n",
              "      <th>pixel11</th>\n",
              "      <th>pixel12</th>\n",
              "      <th>pixel13</th>\n",
              "      <th>pixel14</th>\n",
              "      <th>pixel15</th>\n",
              "      <th>pixel16</th>\n",
              "      <th>pixel17</th>\n",
              "      <th>pixel18</th>\n",
              "      <th>pixel19</th>\n",
              "      <th>pixel20</th>\n",
              "      <th>pixel21</th>\n",
              "      <th>pixel22</th>\n",
              "      <th>pixel23</th>\n",
              "      <th>pixel24</th>\n",
              "      <th>pixel25</th>\n",
              "      <th>pixel26</th>\n",
              "      <th>pixel27</th>\n",
              "      <th>pixel28</th>\n",
              "      <th>pixel29</th>\n",
              "      <th>pixel30</th>\n",
              "      <th>pixel31</th>\n",
              "      <th>pixel32</th>\n",
              "      <th>pixel33</th>\n",
              "      <th>pixel34</th>\n",
              "      <th>pixel35</th>\n",
              "      <th>pixel36</th>\n",
              "      <th>pixel37</th>\n",
              "      <th>pixel38</th>\n",
              "      <th>...</th>\n",
              "      <th>pixel744</th>\n",
              "      <th>pixel745</th>\n",
              "      <th>pixel746</th>\n",
              "      <th>pixel747</th>\n",
              "      <th>pixel748</th>\n",
              "      <th>pixel749</th>\n",
              "      <th>pixel750</th>\n",
              "      <th>pixel751</th>\n",
              "      <th>pixel752</th>\n",
              "      <th>pixel753</th>\n",
              "      <th>pixel754</th>\n",
              "      <th>pixel755</th>\n",
              "      <th>pixel756</th>\n",
              "      <th>pixel757</th>\n",
              "      <th>pixel758</th>\n",
              "      <th>pixel759</th>\n",
              "      <th>pixel760</th>\n",
              "      <th>pixel761</th>\n",
              "      <th>pixel762</th>\n",
              "      <th>pixel763</th>\n",
              "      <th>pixel764</th>\n",
              "      <th>pixel765</th>\n",
              "      <th>pixel766</th>\n",
              "      <th>pixel767</th>\n",
              "      <th>pixel768</th>\n",
              "      <th>pixel769</th>\n",
              "      <th>pixel770</th>\n",
              "      <th>pixel771</th>\n",
              "      <th>pixel772</th>\n",
              "      <th>pixel773</th>\n",
              "      <th>pixel774</th>\n",
              "      <th>pixel775</th>\n",
              "      <th>pixel776</th>\n",
              "      <th>pixel777</th>\n",
              "      <th>pixel778</th>\n",
              "      <th>pixel779</th>\n",
              "      <th>pixel780</th>\n",
              "      <th>pixel781</th>\n",
              "      <th>pixel782</th>\n",
              "      <th>pixel783</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.00000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.00000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.00000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.000000</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "      <td>42000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>4.456643</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.00300</td>\n",
              "      <td>0.011190</td>\n",
              "      <td>0.005143</td>\n",
              "      <td>0.000214</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000381</td>\n",
              "      <td>0.001310</td>\n",
              "      <td>0.010548</td>\n",
              "      <td>0.027262</td>\n",
              "      <td>0.050905</td>\n",
              "      <td>0.066405</td>\n",
              "      <td>0.129571</td>\n",
              "      <td>...</td>\n",
              "      <td>3.772524</td>\n",
              "      <td>2.748905</td>\n",
              "      <td>1.796452</td>\n",
              "      <td>1.089905</td>\n",
              "      <td>0.563190</td>\n",
              "      <td>0.239571</td>\n",
              "      <td>0.093524</td>\n",
              "      <td>0.024833</td>\n",
              "      <td>0.000857</td>\n",
              "      <td>0.001405</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.006143</td>\n",
              "      <td>0.035833</td>\n",
              "      <td>0.082357</td>\n",
              "      <td>0.114905</td>\n",
              "      <td>0.178714</td>\n",
              "      <td>0.301452</td>\n",
              "      <td>0.413643</td>\n",
              "      <td>0.513667</td>\n",
              "      <td>0.558833</td>\n",
              "      <td>0.677857</td>\n",
              "      <td>0.60281</td>\n",
              "      <td>0.489238</td>\n",
              "      <td>0.340214</td>\n",
              "      <td>0.219286</td>\n",
              "      <td>0.117095</td>\n",
              "      <td>0.059024</td>\n",
              "      <td>0.02019</td>\n",
              "      <td>0.017238</td>\n",
              "      <td>0.002857</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>2.887730</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.56812</td>\n",
              "      <td>1.626927</td>\n",
              "      <td>1.053972</td>\n",
              "      <td>0.043916</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.078072</td>\n",
              "      <td>0.232634</td>\n",
              "      <td>1.131661</td>\n",
              "      <td>2.310396</td>\n",
              "      <td>3.121847</td>\n",
              "      <td>3.259128</td>\n",
              "      <td>4.992894</td>\n",
              "      <td>...</td>\n",
              "      <td>26.957829</td>\n",
              "      <td>22.879248</td>\n",
              "      <td>18.595109</td>\n",
              "      <td>14.434439</td>\n",
              "      <td>10.517823</td>\n",
              "      <td>6.469315</td>\n",
              "      <td>3.976306</td>\n",
              "      <td>1.846016</td>\n",
              "      <td>0.139556</td>\n",
              "      <td>0.287891</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.949803</td>\n",
              "      <td>2.350859</td>\n",
              "      <td>3.934280</td>\n",
              "      <td>4.543583</td>\n",
              "      <td>5.856772</td>\n",
              "      <td>7.219742</td>\n",
              "      <td>8.928286</td>\n",
              "      <td>10.004069</td>\n",
              "      <td>10.129595</td>\n",
              "      <td>11.254931</td>\n",
              "      <td>10.69603</td>\n",
              "      <td>9.480066</td>\n",
              "      <td>7.950251</td>\n",
              "      <td>6.312890</td>\n",
              "      <td>4.633819</td>\n",
              "      <td>3.274488</td>\n",
              "      <td>1.75987</td>\n",
              "      <td>1.894498</td>\n",
              "      <td>0.414264</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>2.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>4.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>7.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>9.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>116.00000</td>\n",
              "      <td>254.000000</td>\n",
              "      <td>216.000000</td>\n",
              "      <td>9.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>47.000000</td>\n",
              "      <td>157.000000</td>\n",
              "      <td>254.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>243.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>253.000000</td>\n",
              "      <td>28.000000</td>\n",
              "      <td>59.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>177.000000</td>\n",
              "      <td>231.000000</td>\n",
              "      <td>253.000000</td>\n",
              "      <td>254.000000</td>\n",
              "      <td>254.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>255.00000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>255.000000</td>\n",
              "      <td>254.000000</td>\n",
              "      <td>254.000000</td>\n",
              "      <td>253.000000</td>\n",
              "      <td>253.00000</td>\n",
              "      <td>254.000000</td>\n",
              "      <td>62.000000</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>8 rows × 785 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "              label   pixel0   pixel1  ...  pixel781  pixel782  pixel783\n",
              "count  42000.000000  42000.0  42000.0  ...   42000.0   42000.0   42000.0\n",
              "mean       4.456643      0.0      0.0  ...       0.0       0.0       0.0\n",
              "std        2.887730      0.0      0.0  ...       0.0       0.0       0.0\n",
              "min        0.000000      0.0      0.0  ...       0.0       0.0       0.0\n",
              "25%        2.000000      0.0      0.0  ...       0.0       0.0       0.0\n",
              "50%        4.000000      0.0      0.0  ...       0.0       0.0       0.0\n",
              "75%        7.000000      0.0      0.0  ...       0.0       0.0       0.0\n",
              "max        9.000000      0.0      0.0  ...       0.0       0.0       0.0\n",
              "\n",
              "[8 rows x 785 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y5pQgZEC-hBL"
      },
      "source": [
        " Since there are no missing values so there is no need to handle the missing values"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7bD4-Kfw-rF_"
      },
      "source": [
        "# **Splitting into Data and Labels**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YAGQzGvbUTuG"
      },
      "source": [
        "X=train_data.drop(['label'],axis=1)\n",
        "Y=train_data['label'].copy()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "auPoSawu4NoD"
      },
      "source": [
        "X=X.to_numpy()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LQK5eKCU_Gke"
      },
      "source": [
        "# **Binary Classifier**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_zf43o8L22-f"
      },
      "source": [
        "some_digit=X[3]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aFjBDsWW_RYG"
      },
      "source": [
        "# Image"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "MAqDUF3qZAxB",
        "outputId": "836eaeda-925e-4625-bcbe-1cdeb1f4a605"
      },
      "source": [
        "some_digit_shaped=some_digit.reshape(28,28)\n",
        "plt.imshow(some_digit_shaped,cmap=\"binary\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0qHY_NODUvtV",
        "outputId": "971a4370-f73d-4315-a053-0737e487c91c"
      },
      "source": [
        "from sklearn.linear_model import SGDClassifier\n",
        "sgd=SGDClassifier()\n",
        "sgd.fit(X,Y)\n",
        "sgd.predict([some_digit])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([4])"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vF1iaVhj_ct0"
      },
      "source": [
        "**Note** - The SGDClassifier correctly predicted the digit"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "m8k6ppSpZZTb",
        "outputId": "a8107db0-f7cb-4eea-b01b-fe7050c21293"
      },
      "source": [
        "sgd.classes_"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "k8DnwXKpb9YS",
        "outputId": "d0ecaf30-6fcb-45cb-dd5a-40f658143539"
      },
      "source": [
        "sgd.decision_function([some_digit])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ -2422.49689509, -40335.65304826,    862.4010922 ,\n",
              "        -15014.56978145,   2602.63101706,  -6570.78763758,\n",
              "         -5411.62059677, -34767.37257818,  -5550.10893223,\n",
              "         -8866.493502  ]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pCP2v8j5Ok1q"
      },
      "source": [
        "### *The classifier is fairly confident about is predictions and the classifier(class 4) is largely positive with a score of 2602.6310*"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NFp9GbFfC6JW"
      },
      "source": [
        "## **Evaluating training set**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CRKaikPDbBEp",
        "outputId": "a8e776a5-820a-435b-f7ae-854fa32e8bf7"
      },
      "source": [
        "from sklearn.model_selection import cross_val_score\n",
        "cross_val_score(sgd,X,Y,cv=3,scoring='accuracy')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.86642857, 0.86928571, 0.87292857])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "etUfWWWFPhpG"
      },
      "source": [
        "# **Error Analysis**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "waj90DQCCW0n",
        "outputId": "19978693-7b5a-4a17-b480-781ee9eb0cd8"
      },
      "source": [
        "from sklearn.metrics import accuracy_score,confusion_matrix\n",
        "train_pred=sgd.predict(X)\n",
        "train_cm=confusion_matrix(train_pred,Y)\n",
        "print(train_cm)\n",
        "print(\" \")\n",
        "accuracy_score(train_pred,Y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[4084    0   63   29   24   74   68   22   42   45]\n",
            " [   0 4622   76   52   31   23   19   30  111   51]\n",
            " [   1    4 3661  117   20   16   43   47   14    9]\n",
            " [   1    6   22 3233    1   46    1    5   23   13]\n",
            " [   1    1   37    2 3688   24   29   29    6   70]\n",
            " [  14    6   26  481   18 3327  174   19  141  114]\n",
            " [   2    0   16    5    5   22 3696    1    9    0]\n",
            " [   1    2   19   16   15   26    0 4030    4  218]\n",
            " [  26   43  251  377  151  221  107  140 3708  376]\n",
            " [   2    0    6   39  119   16    0   78    5 3292]]\n",
            " \n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8890714285714286"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bsHh6faCIL9s"
      },
      "source": [
        "**Accuracy on Training Set is : 88.9%**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ge2wzpAbJqmj"
      },
      "source": [
        "## **Image Representation of confusion-matrix**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 275
        },
        "id": "TZGbBulOlnCE",
        "outputId": "6acebb2b-9be6-404e-cfa1-fcece2483079"
      },
      "source": [
        "plt.matshow(train_cm,cmap=plt.cm.gray)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPoAAAECCAYAAADXWsr9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAK2ElEQVR4nO3dz4td9RnH8c8nM4maSVFDu9CMNrMoFhFKZCxqxIURbOsvhC4sKNTNbFoTRRDtxn9ARBdFGGLdGHQRswgaUgvqoggxYyLEZCxKYmNMxJQQNQadmczTxb3SJBO95zbnO+eePO8XCJnr8evDZd6cc2/O/V5HhABc2JY0PQCA8ggdSIDQgQQIHUiA0IEECB1IoLHQbf/G9r9sf2z7iabmqMr2Vbbfsr3P9l7bG5qeqQrbQ7Z3236t6VmqsH2Z7c22P7Q9bfumpmfqxfaj3d+JD2y/bPvipmc6WyOh2x6S9FdJv5V0raQ/2L62iVn6MCfpsYi4VtKNkv7UgpklaYOk6aaH6MNzkrZHxC8l/UoDPrvtVZLWSxqPiOskDUm6v9mpFmrqjP5rSR9HxP6ImJH0iqR7G5qlkog4EhG7un/+Wp1fwFXNTvXjbI9KulPSxqZnqcL2pZJulfSCJEXETEQcb3aqSoYlXWJ7WNJySYcbnmeBpkJfJenT034+pAGP5nS2V0taI2lHs5P09KykxyXNNz1IRWOSjkp6sftyY6PtkaaH+jER8ZmkpyUdlHRE0pcR8UazUy3Em3F9sr1C0quSHomIr5qe54fYvkvSFxHxXtOz9GFY0vWSno+INZK+kTTQ79/Yvlydq9ExSVdKGrH9QLNTLdRU6J9Juuq0n0e7jw0020vViXxTRGxpep4e1kq6x/Yn6rw0us32S82O1NMhSYci4vsrpc3qhD/Ibpd0ICKORsSspC2Sbm54pgWaCn2npF/YHrO9TJ03L7Y2NEsltq3Oa8fpiHim6Xl6iYgnI2I0Ilar8/y+GREDd6Y5XUR8LulT29d0H1onaV+DI1VxUNKNtpd3f0fWaQDfQBxu4n8aEXO2/yzp7+q8S/m3iNjbxCx9WCvpQUl7bL/ffewvEbGtwZkuRA9L2tQ9AeyX9FDD8/yoiNhhe7OkXer8zcxuSZPNTrWQ+ZgqcOHjzTggAUIHEiB0IAFCBxIgdCCBxkO3PdH0DP1o27wSMy+GQZ+38dAlDfQTdA5tm1di5sUw0PMOQugACityw8zKlStjdHS00rHHjh3TypUrKx27Z8+e8xkLSCEifPZjRW6BHR0d1euvv177uldffXXta35vaGioyLrz8235hOj/lHouSt6FWep57ty+3h4/9Dxw6Q4kQOhAAoQOJEDoQAKEDiRQKfS27cEO4Ew9Q2/pHuwATlPljN66PdgBnKlK6K3egx1AjW/G2Z6wPWV76tixY3UtC6AGVUKvtAd7RExGxHhEjFe9dx3A4qgSeuv2YAdwpp4famnpHuwATlPp02vdLyngiwqAluLOOCABQgcSIHQgAUIHEiB0IIEim0PaLrI5WMk9x5YuXVpk3ZJ7xvFNuOWV+r2QpLm5udrXnJ+fP+fmkJzRgQQIHUiA0IEECB1IgNCBBAgdSIDQgQQIHUiA0IEECB1IgNCBBAgdSIDQgQQIHUiA0IEECB1IgNCBBAgdSIDQgQQIHUiA0IEECB1IoFXbPZf07rvvFln3lltuKbKuJM3OzhZZt9Q20kuWtO+8UnK77lLY7hlIitCBBAgdSIDQgQQIHUiA0IEECB1IoGfotq+y/Zbtfbb32t6wGIMBqM9whWPmJD0WEbts/0TSe7b/ERH7Cs8GoCY9z+gRcSQidnX//LWkaUmrSg8GoD59vUa3vVrSGkk7SgwDoIwql+6SJNsrJL0q6ZGI+Ooc/35C0kSNswGoSaXQbS9VJ/JNEbHlXMdExKSkye7xrftQC3Ahq/KuuyW9IGk6Ip4pPxKAulV5jb5W0oOSbrP9fvef3xWeC0CNel66R8Q/JS34fCuA9uDOOCABQgcSIHQgAUIHEiB0IAF2ge3q3C5Qv61btxZZV5LuvvvuIuuW2q21jTuqlvq9kMrttssusEBShA4kQOhAAoQOJEDoQAKEDiRA6EAChA4kQOhAAoQOJEDoQAKEDiRA6EAChA4kQOhAAoQOJEDoQAKEDiRA6EAChA4kQOhAAoQOJMB2z11t3OJ4amqqyLo33HBDkXXbqNSWzJI0NDRU+5qnTp1iu2cgK0IHEiB0IAFCBxIgdCABQgcSIHQggcqh2x6yvdv2ayUHAlC/fs7oGyRNlxoEQDmVQrc9KulOSRvLjgOghKpn9GclPS6p3P2cAIrpGbrtuyR9ERHv9ThuwvaU7TI3YAP4v1U5o6+VdI/tTyS9Iuk22y+dfVBETEbEeESM1zwjgPPUM/SIeDIiRiNitaT7Jb0ZEQ8UnwxAbfh7dCCB4X4Ojoi3Jb1dZBIAxXBGBxIgdCABQgcSIHQgAUIHEmAX2C57wcaZtbjiiiuKrCtJhw8fLrLu9u3bi6x73333FVlXkr799tsi6y5btqzIulKZHWZnZ2c1Pz/PLrBARoQOJEDoQAKEDiRA6EAChA4kQOhAAoQOJEDoQAKEDiRA6EAChA4kQOhAAoQOJEDoQAKEDiRA6EAChA4kQOhAAoQOJEDoQALsAosFSu2Iu3PnziLrStL4ON/W/b2IYBdYICNCBxIgdCABQgcSIHQgAUIHEiB0IIFKodu+zPZm2x/anrZ9U+nBANRnuOJxz0naHhG/t71M0vKCMwGoWc/QbV8q6VZJf5SkiJiRNFN2LAB1qnLpPibpqKQXbe+2vdH2SOG5ANSoSujDkq6X9HxErJH0jaQnzj7I9oTtKdtTNc8I4DxVCf2QpEMRsaP782Z1wj9DRExGxHhE8OkCYMD0DD0iPpf0qe1rug+tk7Sv6FQAalX1XfeHJW3qvuO+X9JD5UYCULdKoUfE+5K4JAdaijvjgAQIHUiA0IEECB1IgNCBBAgdSIDtnrtKbXFc4vktrY3PxYEDB4qsOzY2VmRdSVqxYkXta548eVKnTp1iu2cgI0IHEiB0IAFCBxIgdCABQgcSIHQgAUIHEiB0IAFCBxIgdCABQgcSIHQgAUIHEiB0IAFCBxIgdCABQgcSIHQgAUIHEiB0IIFiu8CW2Em01O6kkjQyMlJk3YsuuqjIupJ04sSJIusOD1f9kt3+fPfdd0XWlaQlS8qcs955550i60rSHXfcUfuax48f1+zsLLvAAhkROpAAoQMJEDqQAKEDCRA6kAChAwlUCt32o7b32v7A9su2Ly49GID69Azd9ipJ6yWNR8R1koYk3V96MAD1qXrpPizpEtvDkpZLOlxuJAB16xl6RHwm6WlJByUdkfRlRLxRejAA9aly6X65pHsljUm6UtKI7QfOcdyE7SnbU/WPCeB8VLl0v13SgYg4GhGzkrZIuvnsgyJiMiLGI2K87iEBnJ8qoR+UdKPt5e58fGydpOmyYwGoU5XX6DskbZa0S9Ke7n8zWXguADWq9MHjiHhK0lOFZwFQCHfGAQkQOpAAoQMJEDqQAKEDCRA6kECx7Z5rX7SlSm1DLJXblnlmZqbIuiWVei7m5uaKrCtJ27Ztq33N9evX66OPPmK7ZyAjQgcSIHQgAUIHEiB0IAFCBxIgdCABQgcSIHQgAUIHEiB0IAFCBxIgdCABQgcSIHQgAUIHEiB0IAFCBxIgdCABQgcSIHQggVK7wB6V9O+Kh/9U0n9qH6Kcts0rMfNiGJR5fx4RPzv7wSKh98P2VESMNzpEH9o2r8TMi2HQ5+XSHUiA0IEEBiH0yaYH6FPb5pWYeTEM9LyNv0YHUN4gnNEBFEboQAKEDiRA6EAChA4k8F+FZqlDDYnjgAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PoVyQXoyQNXK"
      },
      "source": [
        "### ***The matrix looks good since most images are on the main diagonal i.e. they are classified correctly.***"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yDR2xgBkgXvL"
      },
      "source": [
        "test_data=test_data.values\n",
        "pred=sgd.predict(test_data)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0WqoNltkHxEp"
      },
      "source": [
        "# **Visualizing predictions**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 589
        },
        "id": "x6qfMuYBGqKx",
        "outputId": "c6464884-72af-41c8-b500-2c96717fab88"
      },
      "source": [
        "# visualise predictions\n",
        "plt.figure(figsize=(10,10))\n",
        "for i in range(25):\n",
        "    plt.subplot(5,5,i+1)\n",
        "    plt.xticks([])\n",
        "    plt.yticks([])\n",
        "    plt.grid(False)\n",
        "    one_image = test_data[i].reshape(28,28)\n",
        "    plt.imshow(one_image, cmap=plt.cm.binary)\n",
        "    plt.xlabel(pred[i])\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 25 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LGfUT91KH9qb"
      },
      "source": [
        "# **Submission**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 419
        },
        "id": "PmTjdrLaxlNQ",
        "outputId": "11ea7a92-a12e-4fba-9eb4-e86787892fd8"
      },
      "source": [
        "y_pred = pd.Series(pred,name=\"Predictions\")\n",
        "submission = pd.concat([pd.Series(range(1,28001),name = \"ImageId\"),y_pred],axis = 1)\n",
        "\n",
        "submission.to_csv(\"mnist_submission.csv\",index=False)\n",
        "submission"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>ImageId</th>\n",
              "      <th>Predictions</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27995</th>\n",
              "      <td>27996</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27996</th>\n",
              "      <td>27997</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27997</th>\n",
              "      <td>27998</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27998</th>\n",
              "      <td>27999</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27999</th>\n",
              "      <td>28000</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>28000 rows × 2 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "       ImageId  Predictions\n",
              "0            1            2\n",
              "1            2            0\n",
              "2            3            8\n",
              "3            4            7\n",
              "4            5            3\n",
              "...        ...          ...\n",
              "27995    27996            9\n",
              "27996    27997            7\n",
              "27997    27998            3\n",
              "27998    27999            9\n",
              "27999    28000            2\n",
              "\n",
              "[28000 rows x 2 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZKARHu1LRHtT"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}