SGD Classifier.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyM1E4W9suK6NYu9c0qnQLfx",
      "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/ssvakil/Machine-Learning-in-Python-Workshop/blob/master/SGD%20Classifier.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.datasets import fetch_openml\n",
        "data = fetch_openml(\"mnist_784\", version=1)\n",
        "print(data)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "imuME2-qxUkz",
        "outputId": "51ef3dee-d792-418b-9deb-07ddfec2851a"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/datasets/_openml.py:968: FutureWarning: The default value of `parser` will change from `'liac-arff'` to `'auto'` in 1.4. You can set `parser='auto'` to silence this warning. Therefore, an `ImportError` will be raised from 1.4 if the dataset is dense and pandas is not installed. Note that the pandas parser may return different data types. See the Notes Section in fetch_openml's API doc for details.\n",
            "  warn(\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "{'data':        pixel1  pixel2  pixel3  pixel4  pixel5  pixel6  pixel7  pixel8  pixel9  \\\n",
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            "\n",
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            "\n",
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            "0           0.0       0.0       0.0       0.0       0.0  \n",
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            "...         ...       ...       ...       ...       ...  \n",
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            "\n",
            "[70000 rows x 784 columns], 'target': 0        5\n",
            "1        0\n",
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            "        ..\n",
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            "Name: class, Length: 70000, dtype: category\n",
            "Categories (10, object): ['0', '1', '2', '3', ..., '6', '7', '8', '9'], 'frame':        pixel1  pixel2  pixel3  pixel4  pixel5  pixel6  pixel7  pixel8  pixel9  \\\n",
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            "\n",
            "       pixel10  ...  pixel776  pixel777  pixel778  pixel779  pixel780  \\\n",
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            "\n",
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            "...         ...       ...       ...       ...    ...  \n",
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            "69999       0.0       0.0       0.0       0.0      6  \n",
            "\n",
            "[70000 rows x 785 columns], 'categories': None, 'feature_names': ['pixel1', 'pixel2', 'pixel3', 'pixel4', 'pixel5', 'pixel6', 'pixel7', 'pixel8', 'pixel9', 'pixel10', 'pixel11', 'pixel12', 'pixel13', 'pixel14', 'pixel15', 'pixel16', 'pixel17', 'pixel18', 'pixel19', 'pixel20', 'pixel21', 'pixel22', 'pixel23', 'pixel24', 'pixel25', 'pixel26', 'pixel27', 'pixel28', 'pixel29', 'pixel30', 'pixel31', 'pixel32', 'pixel33', 'pixel34', 'pixel35', 'pixel36', 'pixel37', 'pixel38', 'pixel39', 'pixel40', 'pixel41', 'pixel42', 'pixel43', 'pixel44', 'pixel45', 'pixel46', 'pixel47', 'pixel48', 'pixel49', 'pixel50', 'pixel51', 'pixel52', 'pixel53', 'pixel54', 'pixel55', 'pixel56', 'pixel57', 'pixel58', 'pixel59', 'pixel60', 'pixel61', 'pixel62', 'pixel63', 'pixel64', 'pixel65', 'pixel66', 'pixel67', 'pixel68', 'pixel69', 'pixel70', 'pixel71', 'pixel72', 'pixel73', 'pixel74', 'pixel75', 'pixel76', 'pixel77', 'pixel78', 'pixel79', 'pixel80', 'pixel81', 'pixel82', 'pixel83', 'pixel84', 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'pixel335', 'pixel336', 'pixel337', 'pixel338', 'pixel339', 'pixel340', 'pixel341', 'pixel342', 'pixel343', 'pixel344', 'pixel345', 'pixel346', 'pixel347', 'pixel348', 'pixel349', 'pixel350', 'pixel351', 'pixel352', 'pixel353', 'pixel354', 'pixel355', 'pixel356', 'pixel357', 'pixel358', 'pixel359', 'pixel360', 'pixel361', 'pixel362', 'pixel363', 'pixel364', 'pixel365', 'pixel366', 'pixel367', 'pixel368', 'pixel369', 'pixel370', 'pixel371', 'pixel372', 'pixel373', 'pixel374', 'pixel375', 'pixel376', 'pixel377', 'pixel378', 'pixel379', 'pixel380', 'pixel381', 'pixel382', 'pixel383', 'pixel384', 'pixel385', 'pixel386', 'pixel387', 'pixel388', 'pixel389', 'pixel390', 'pixel391', 'pixel392', 'pixel393', 'pixel394', 'pixel395', 'pixel396', 'pixel397', 'pixel398', 'pixel399', 'pixel400', 'pixel401', 'pixel402', 'pixel403', 'pixel404', 'pixel405', 'pixel406', 'pixel407', 'pixel408', 'pixel409', 'pixel410', 'pixel411', 'pixel412', 'pixel413', 'pixel414', 'pixel415', 'pixel416', 'pixel417', 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'pixel501', 'pixel502', 'pixel503', 'pixel504', 'pixel505', 'pixel506', 'pixel507', 'pixel508', 'pixel509', 'pixel510', 'pixel511', 'pixel512', 'pixel513', 'pixel514', 'pixel515', 'pixel516', 'pixel517', 'pixel518', 'pixel519', 'pixel520', 'pixel521', 'pixel522', 'pixel523', 'pixel524', 'pixel525', 'pixel526', 'pixel527', 'pixel528', 'pixel529', 'pixel530', 'pixel531', 'pixel532', 'pixel533', 'pixel534', 'pixel535', 'pixel536', 'pixel537', 'pixel538', 'pixel539', 'pixel540', 'pixel541', 'pixel542', 'pixel543', 'pixel544', 'pixel545', 'pixel546', 'pixel547', 'pixel548', 'pixel549', 'pixel550', 'pixel551', 'pixel552', 'pixel553', 'pixel554', 'pixel555', 'pixel556', 'pixel557', 'pixel558', 'pixel559', 'pixel560', 'pixel561', 'pixel562', 'pixel563', 'pixel564', 'pixel565', 'pixel566', 'pixel567', 'pixel568', 'pixel569', 'pixel570', 'pixel571', 'pixel572', 'pixel573', 'pixel574', 'pixel575', 'pixel576', 'pixel577', 'pixel578', 'pixel579', 'pixel580', 'pixel581', 'pixel582', 'pixel583', 'pixel584', 'pixel585', 'pixel586', 'pixel587', 'pixel588', 'pixel589', 'pixel590', 'pixel591', 'pixel592', 'pixel593', 'pixel594', 'pixel595', 'pixel596', 'pixel597', 'pixel598', 'pixel599', 'pixel600', 'pixel601', 'pixel602', 'pixel603', 'pixel604', 'pixel605', 'pixel606', 'pixel607', 'pixel608', 'pixel609', 'pixel610', 'pixel611', 'pixel612', 'pixel613', 'pixel614', 'pixel615', 'pixel616', 'pixel617', 'pixel618', 'pixel619', 'pixel620', 'pixel621', 'pixel622', 'pixel623', 'pixel624', 'pixel625', 'pixel626', 'pixel627', 'pixel628', 'pixel629', 'pixel630', 'pixel631', 'pixel632', 'pixel633', 'pixel634', 'pixel635', 'pixel636', 'pixel637', 'pixel638', 'pixel639', 'pixel640', 'pixel641', 'pixel642', 'pixel643', 'pixel644', 'pixel645', 'pixel646', 'pixel647', 'pixel648', 'pixel649', 'pixel650', 'pixel651', 'pixel652', 'pixel653', 'pixel654', 'pixel655', 'pixel656', 'pixel657', 'pixel658', 'pixel659', 'pixel660', 'pixel661', 'pixel662', 'pixel663', 'pixel664', 'pixel665', 'pixel666', 'pixel667', 'pixel668', 'pixel669', 'pixel670', 'pixel671', 'pixel672', 'pixel673', 'pixel674', 'pixel675', 'pixel676', 'pixel677', 'pixel678', 'pixel679', 'pixel680', 'pixel681', 'pixel682', 'pixel683', 'pixel684', 'pixel685', 'pixel686', 'pixel687', 'pixel688', 'pixel689', 'pixel690', 'pixel691', 'pixel692', 'pixel693', 'pixel694', 'pixel695', 'pixel696', 'pixel697', 'pixel698', 'pixel699', 'pixel700', 'pixel701', 'pixel702', 'pixel703', 'pixel704', 'pixel705', 'pixel706', 'pixel707', 'pixel708', 'pixel709', 'pixel710', 'pixel711', 'pixel712', 'pixel713', 'pixel714', 'pixel715', 'pixel716', 'pixel717', 'pixel718', 'pixel719', 'pixel720', 'pixel721', 'pixel722', 'pixel723', 'pixel724', 'pixel725', 'pixel726', 'pixel727', 'pixel728', 'pixel729', 'pixel730', 'pixel731', 'pixel732', 'pixel733', 'pixel734', 'pixel735', 'pixel736', 'pixel737', 'pixel738', 'pixel739', 'pixel740', 'pixel741', 'pixel742', 'pixel743', 'pixel744', 'pixel745', 'pixel746', 'pixel747', 'pixel748', 'pixel749', 'pixel750', 'pixel751', 'pixel752', 'pixel753', 'pixel754', 'pixel755', 'pixel756', 'pixel757', 'pixel758', 'pixel759', 'pixel760', 'pixel761', 'pixel762', 'pixel763', 'pixel764', 'pixel765', 'pixel766', 'pixel767', 'pixel768', 'pixel769', 'pixel770', 'pixel771', 'pixel772', 'pixel773', 'pixel774', 'pixel775', 'pixel776', 'pixel777', 'pixel778', 'pixel779', 'pixel780', 'pixel781', 'pixel782', 'pixel783', 'pixel784'], 'target_names': ['class'], 'DESCR': \"**Author**: Yann LeCun, Corinna Cortes, Christopher J.C. Burges  \\n**Source**: [MNIST Website](http://yann.lecun.com/exdb/mnist/) - Date unknown  \\n**Please cite**:  \\n\\nThe MNIST database of handwritten digits with 784 features, raw data available at: http://yann.lecun.com/exdb/mnist/. It can be split in a training set of the first 60,000 examples, and a test set of 10,000 examples  \\n\\nIt is a subset of a larger set available from NIST. The digits have been size-normalized and centered in a fixed-size image. It is a good database for people who want to try learning techniques and pattern recognition methods on real-world data while spending minimal efforts on preprocessing and formatting. The original black and white (bilevel) images from NIST were size normalized to fit in a 20x20 pixel box while preserving their aspect ratio. The resulting images contain grey levels as a result of the anti-aliasing technique used by the normalization algorithm. the images were centered in a 28x28 image by computing the center of mass of the pixels, and translating the image so as to position this point at the center of the 28x28 field.  \\n\\nWith some classification methods (particularly template-based methods, such as SVM and K-nearest neighbors), the error rate improves when the digits are centered by bounding box rather than center of mass. If you do this kind of pre-processing, you should report it in your publications. The MNIST database was constructed from NIST's NIST originally designated SD-3 as their training set and SD-1 as their test set. However, SD-3 is much cleaner and easier to recognize than SD-1. The reason for this can be found on the fact that SD-3 was collected among Census Bureau employees, while SD-1 was collected among high-school students. Drawing sensible conclusions from learning experiments requires that the result be independent of the choice of training set and test among the complete set of samples. Therefore it was necessary to build a new database by mixing NIST's datasets.  \\n\\nThe MNIST training set is composed of 30,000 patterns from SD-3 and 30,000 patterns from SD-1. Our test set was composed of 5,000 patterns from SD-3 and 5,000 patterns from SD-1. The 60,000 pattern training set contained examples from approximately 250 writers. We made sure that the sets of writers of the training set and test set were disjoint. SD-1 contains 58,527 digit images written by 500 different writers. In contrast to SD-3, where blocks of data from each writer appeared in sequence, the data in SD-1 is scrambled. Writer identities for SD-1 is available and we used this information to unscramble the writers. We then split SD-1 in two: characters written by the first 250 writers went into our new training set. The remaining 250 writers were placed in our test set. Thus we had two sets with nearly 30,000 examples each. The new training set was completed with enough examples from SD-3, starting at pattern # 0, to make a full set of 60,000 training patterns. Similarly, the new test set was completed with SD-3 examples starting at pattern # 35,000 to make a full set with 60,000 test patterns. Only a subset of 10,000 test images (5,000 from SD-1 and 5,000 from SD-3) is available on this site. The full 60,000 sample training set is available.\\n\\nDownloaded from openml.org.\", 'details': {'id': '554', 'name': 'mnist_784', 'version': '1', 'description_version': '1', 'format': 'ARFF', 'creator': ['Yann LeCun', 'Corinna Cortes', 'Christopher J.C. Burges'], 'upload_date': '2014-09-29T03:28:38', 'language': 'English', 'licence': 'Public', 'url': 'https://api.openml.org/data/v1/download/52667/mnist_784.arff', 'parquet_url': 'http://openml1.win.tue.nl/dataset554/dataset_554.pq', 'file_id': '52667', 'default_target_attribute': 'class', 'tag': ['AzurePilot', 'OpenML-CC18', 'OpenML100', 'study_1', 'study_123', 'study_41', 'study_99', 'vision'], 'visibility': 'public', 'minio_url': 'http://openml1.win.tue.nl/dataset554/dataset_554.pq', 'status': 'active', 'processing_date': '2020-11-20 20:12:09', 'md5_checksum': '0298d579eb1b86163de7723944c7e495'}, 'url': 'https://www.openml.org/d/554'}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x, y = data[\"data\"], data[\"target\"]\n",
        "print(x.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rM6T4Yse0Tbx",
        "outputId": "0d97e385-3fc5-4358-c1b4-04386c0812d6"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(70000, 784)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "xtrain, xtest, ytrain, ytest = train_test_split(x, y, \n",
        "                                                test_size=0.2,\n",
        "                                                random_state=42)"
      ],
      "metadata": {
        "id": "xNUfuyt6xUoZ"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "image = np.array(xtrain.iloc[0]).reshape(28, 28)\n",
        "plt.imshow(image)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "pPNt9QbQxUpk",
        "outputId": "adb06a77-08c3-44fa-ed9f-ee118b2e7704"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f040a7eb640>"
            ]
          },
          "metadata": {},
          "execution_count": 10
        },
        {
          "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": [
        "from sklearn.linear_model import SGDClassifier\n",
        "model = SGDClassifier()\n",
        "model.fit(xtrain, ytrain)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 75
        },
        "id": "3KcoDJ-SxUs5",
        "outputId": "65998e43-dfb9-418e-89a2-764cd6c83f03"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SGDClassifier()"
            ],
            "text/html": [
              "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 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-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 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-1 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-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 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-1 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-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 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-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 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-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 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-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>SGDClassifier()</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-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SGDClassifier</label><div class=\"sk-toggleable__content\"><pre>SGDClassifier()</pre></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "predictions = model.predict(xtest)\n",
        "print(predictions)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "44ubhupTxUt9",
        "outputId": "60ef880a-8487-4bc6-d67f-4309c29aa1b2"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "['8' '4' '5' ... '2' '7' '1']\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "image = np.array(xtest.iloc[0]).reshape(28, 28)\n",
        "plt.imshow(image)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "T0NVyMYpxUx0",
        "outputId": "c1a64e0f-9726-4793-9216-5f9bd9e9771a"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f040a73d4b0>"
            ]
          },
          "metadata": {},
          "execution_count": 13
        },
        {
          "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": [
        "image = np.array(xtest.iloc[1]).reshape(28, 28)\n",
        "plt.imshow(image)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "T6V2hOK_xUy1",
        "outputId": "e95a56ae-28c6-47fd-b484-250989cea6f9"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f040a8f4a60>"
            ]
          },
          "metadata": {},
          "execution_count": 14
        },
        {
          "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": [
        "image = np.array(xtest.iloc[1]).reshape(28, 28)\n",
        "plt.imshow(xtest)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "id": "qDkcAitMxU33",
        "outputId": "1f058d06-1374-4ee7-8f15-13fdc0cf7b01"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f039c1d9d20>"
            ]
          },
          "metadata": {},
          "execution_count": 15
        },
        {
          "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": [],
      "metadata": {
        "id": "9fX8AtT7xU47"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "TzQQJdIXxU87"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "FhmWLplCxU99"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}