{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "1af2b4c7",
      "metadata": {
        "id": "1af2b4c7"
      },
      "source": [
        "# <a href=\"https://thetahat.ru/courses/ad\">Введение в анализ данных</a>\n",
        "\n",
        "\n",
        "Scikit-learn (или sklearn) — это одна из наиболее популярных библиотек для машинного обучения на языке Python. Она предоставляет множество инструментов для анализа данных и построения моделей, что делает её идеальным выбором как для начинающих, так и для опытных специалистов в области анализа данных и машинного обучения.\n",
        "\n",
        "Давайте погрузимся в возможности данной библиотеки.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "21d3493c",
      "metadata": {
        "id": "21d3493c"
      },
      "outputs": [],
      "source": [
        "!pip install scikit-learn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "0893dfcf",
      "metadata": {
        "id": "0893dfcf"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# обратите внимание, что Scikit-Learn импортируется как sklearn\n",
        "from sklearn import datasets\n",
        "from sklearn.datasets import fetch_openml\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "from sklearn.metrics import accuracy_score\n",
        "\n",
        "# фиксируем seed для воспроизводимости результатов\n",
        "random_state = 42"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b100a538",
      "metadata": {
        "id": "b100a538"
      },
      "source": [
        "## Распознавание рукописных цифр с помощью kNN\n",
        "\n",
        "\n",
        "### 1. Датасет mnist\n",
        "\n",
        "Пакет `sklearn.datasets` позволяет загружать наборы данных из репозитория.\n",
        "\n",
        "Загрузим датасет **MNIST**.\n",
        "\n",
        "Датасет **MNIST** (Modified National Institute of Standards and Technology) — это один из самых известных и широко используемых наборов данных для обучения и тестирования алгоритмов машинного обучения, особенно в области распознавания изображений. Он состоит из рукописных цифр и часто используется для задач классификации.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mnist = fetch_openml(\"mnist_784\")"
      ],
      "metadata": {
        "id": "vy_hd0kYE0qG"
      },
      "id": "vy_hd0kYE0qG",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "id": "15e1d76a",
      "metadata": {
        "id": "15e1d76a"
      },
      "source": [
        "Каждый объект в наборе данных представлен в виде **черно-белого** (в градациях серого) изображения размером **28x28 пикселей**.\n",
        "\n",
        "Каждый пиксель имеет значение в диапазоне от **0 до 255**, где:\n",
        "\n",
        "- **0** соответствует полностью черному цвету (это фон),\n",
        "- **255** — полностью белому (это сама цифра).\n",
        "\n",
        "Таким образом, чем выше значение пикселя, тем светлее он выглядит, приближаясь к белому цвету.\n",
        "\n",
        "Каждое изображение связано с **меткой класса**, представляющей собой одну из цифр от **0 до 9**. Эта метка указывает, какую именно цифру содержит данное изображение.\n",
        "\n",
        "Данные изображений хранятся в переменной `data`, а соответствующие им метки классов — в переменной `target`.\n",
        "\n",
        "Визуализируем данные:"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(15, 3))\n",
        "\n",
        "for i in range(20):\n",
        "    plt.subplot(2, 10, i + 1)\n",
        "    plt.imshow(\n",
        "        np.array(mnist[\"data\"])[i].reshape(28, 28), cmap=\"gray\"\n",
        "    )  # выводим само изображение\n",
        "    plt.title(\n",
        "        f\"Класс = {mnist['target'][i]}\"\n",
        "    )  # выводим истинные и предсказанные метки\n",
        "    plt.axis(\"off\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "d8DderTR_RvW",
        "outputId": "294b8a67-5f10-4e3d-db12-27d8029e9874"
      },
      "id": "d8DderTR_RvW",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x300 with 20 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Размер каждой картинки **28х28**, т.е. на каждый объект **784** признака, что довольно много. Работа с большим количеством признаков может оказаться сложной задачей, имеющей свои особенности, о которых вы узнаете в дальнейшем.\n",
        "\n",
        "Так что сегодня мы ограничимся урезанной версией этого датасета, размер изображений которой составляет **8х8**.\n",
        "\n"
      ],
      "metadata": {
        "id": "eK4w4rnjEz5n"
      },
      "id": "eK4w4rnjEz5n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "97968db8",
      "metadata": {
        "scrolled": true,
        "id": "97968db8"
      },
      "outputs": [],
      "source": [
        "digits = datasets.load_digits()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Данные изображений хранятся в переменной `images`, а соответствующие им метки классов — в переменной `target`.\n",
        "\n",
        "* Каждый объект в наборе данных представлен в виде **черно-белого** (в градациях серого) изображения размером **8x8 пикселей**.\n",
        "Каждый пиксель имеет значение в диапазоне от **0 до 16**, где:\n",
        "\n",
        "  - **0** соответствует полностью черному цвету (это фон),\n",
        "  - **16** — полностью белому (это сама цифра).\n",
        "\n",
        "  Таким образом, чем выше значение пикселя, тем светлее он выглядит, приближаясь к белому цвету.\n",
        "\n",
        "* Каждое изображение связано с **меткой класса**, представляющей собой одну из цифр от **0 до 9**. Эта метка указывает, какую именно цифру содержит данное изображение.\n",
        "\n",
        "Визуализируем данные:"
      ],
      "metadata": {
        "id": "2nbYuocdC-EE"
      },
      "id": "2nbYuocdC-EE"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "daa1fce9",
      "metadata": {
        "id": "daa1fce9",
        "outputId": "44f7b5bc-9606-4a43-ebeb-1bdc642b5802",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x300 with 20 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.figure(figsize=(15, 3))\n",
        "\n",
        "for i in range(20):\n",
        "    plt.subplot(2, 10, i + 1)\n",
        "    plt.imshow(digits[\"images\"][i], cmap=\"gray\")  # выводим само изображение\n",
        "    plt.title(\n",
        "        f\"Класс = {digits['target'][i]}\"\n",
        "    )  # выводим истинные и предсказанные метки\n",
        "    plt.axis(\"off\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Наши данные представлены в виде матриц, а модели машинного обучения, в частности kNN, работают с векторами. Следовательно нам придется преобразовать все матрицы в вектора, т.е. просто растянуть их."
      ],
      "metadata": {
        "id": "h0RLmiNASTPc"
      },
      "id": "h0RLmiNASTPc"
    },
    {
      "cell_type": "markdown",
      "source": [
        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      ],
      "metadata": {
        "id": "kWZ4Vp6DAoxk"
      },
      "id": "kWZ4Vp6DAoxk"
    },
    {
      "cell_type": "markdown",
      "id": "e5655e65",
      "metadata": {
        "id": "e5655e65"
      },
      "source": [
        "Разделим данные и переведем их в вектор."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n_samples = len(digits[\"images\"])\n",
        "X, y = digits[\"images\"].reshape(n_samples, -1), digits[\"target\"]\n",
        "\n",
        "X.shape, y.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "99fGoTIRusNn",
        "outputId": "5168590f-e220-41b0-a091-788aa6ae6b2c"
      },
      "id": "99fGoTIRusNn",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((1797, 64), (1797,))"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "985674e6",
      "metadata": {
        "id": "985674e6"
      },
      "source": [
        "Как мы видим, каждая строка имеет 64 признака, что соответствует общему числу пикселей на картинке 8x8, т.е. матрица изображения растянулась в вектор.\n",
        "\n",
        "Далее нам необходимо датасет разделить на 2 набора данных: тренировочный и тестовый. Тренировочный набор нам нужен непосредственно для обучения модели, тестовый &mdash; для финальной оценки качества модели.\n",
        "\n",
        "Для этого есть готовая функция [train_test_split](https://scikit-learn.org/dev/modules/generated/sklearn.model_selection.train_test_split.html) из модуля `sklearn.model_selection`.\n",
        "\n",
        "`train_test_split(arrays, test_size=None, train_size=None, random_state=None)`\n",
        "- `arrays`: массивы данных для разделения (например, признаки X и целевая переменная y).\n",
        "- `test_size`: размер тестовой выборки. Может быть числом(количество образцов) или долей от общего числа образцов.\n",
        "- `train_size`: размер обучающей выборки. Может быть числом (количество образцов) или долей от общего числа образцов.\n",
        "- `random_state`: устанавливает начальное значение для генератора случайных чисел (повторяемость разделения данных).\n",
        "\n",
        "*Примечание:*  Если параметры в `test_size`,`train_size` передать `None`, то размер тестовой выборки составит 25%.\n",
        "\n",
        "> &#x2757; **Важно:** При обучении модель ничего не должна знать о тестовой выборке.\n",
        "\n",
        "Разделим данные на тренировочную выборку и тестовую."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "03e90624",
      "metadata": {
        "id": "03e90624"
      },
      "outputs": [],
      "source": [
        "X_train, X_test, y_train, y_test = train_test_split(\n",
        "    X, y, train_size=0.7, random_state=random_state\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "13b44ea1",
      "metadata": {
        "id": "13b44ea1"
      },
      "source": [
        "### 2. kNN классификация\n",
        "\n",
        "Обучим нашу первую модель &mdash; kNN-классификатор. Готовая [реализация](https://scikit-learn.org/1.5/modules/generated/sklearn.neighbors.KNeighborsClassifier.html) этой модели уже есть в sklearn-е модуле `sklearn.neighbors`.\n",
        "\n",
        "Создадим экземпляр классификатора:\n",
        "\n",
        "- `n_neighbors`: количество соседей для учитывания при классификации.\n",
        "- `weights`: веса, присваиваемые соседям (`uniform` &mdash; все веса одинаковы, `distance` &mdash; вес зависит от расстояния).\n",
        "- `algorithm`: алгоритм для поиска ближайших соседей (`auto`, `ball_tree`, `kd_tree` `brute`).\n",
        "- `p`: параметр метрики расстояния (1 &mdash; манхэттенское расстояние, 2 &mdash; евклидово расстояние и т.д.).\n",
        "\n",
        "Выберем число соседей `n_neighbors = 5`, остальные параметры оставим по умолчанию.\n",
        "\n",
        "&#x2753; **Вопрос** &#x2753;\n",
        "\n",
        "> Как изменится точность модели, если использовать слишком большое значение $k$ (параметр `n_neighbors`)?\n",
        "\n",
        "<details>\n",
        "  <summary> Кликни для показа ответа </summary>\n",
        "  \n",
        "> Когда параметр $k$ увеличивается, модель начинает учитывать больше ближайших соседей для принятия решения о классе объекта. При большом значении $k$ модель становится менее чувствительной к выбросам, так как решение принимается не только по ближайшим точкам, но и по большему числу соседей. Однако увеличение $k$ также может привести к потере важной локальной информации. Если данные имеют сложную структуру с множеством мелких кластеров, то использование большого числа соседей может сгладить эти особенности и ухудшить точность классификации в таких областях.\n",
        "\n",
        "</details><br/>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "48a01165",
      "metadata": {
        "id": "48a01165"
      },
      "outputs": [],
      "source": [
        "model = KNeighborsClassifier(n_neighbors=5, algorithm=\"brute\")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8a882aff",
      "metadata": {
        "id": "8a882aff"
      },
      "source": [
        "Для обучения *любой* модели в sklearn-е используется метод класса  `fit(X_train, y_train)`.\n",
        "\n",
        "- `X_train`: массив признаков обучающей выборки.\n",
        "- `y_train`: массив меток классов обучающей выборки."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "cb995474",
      "metadata": {
        "id": "cb995474",
        "outputId": "2657d34e-c691-4639-b618-c24bb7530b11",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KNeighborsClassifier()"
            ],
            "text/html": [
              "<style>#sk-container-id-1 {\n",
              "  /* Definition of color scheme common for light and dark mode */\n",
              "  --sklearn-color-text: #000;\n",
              "  --sklearn-color-text-muted: #666;\n",
              "  --sklearn-color-line: gray;\n",
              "  /* Definition of color scheme for unfitted estimators */\n",
              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
              "\n",
              "  /* Specific color for light theme */\n",
              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-icon: #878787;\n",
              "  }\n",
              "}\n",
              "\n",
              "#sk-container-id-1 {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 pre {\n",
              "  padding: 0;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-hidden--visually {\n",
              "  border: 0;\n",
              "  clip: rect(1px 1px 1px 1px);\n",
              "  clip: rect(1px, 1px, 1px, 1px);\n",
              "  height: 1px;\n",
              "  margin: -1px;\n",
              "  overflow: hidden;\n",
              "  padding: 0;\n",
              "  position: absolute;\n",
              "  width: 1px;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-dashed-wrapped {\n",
              "  border: 1px dashed var(--sklearn-color-line);\n",
              "  margin: 0 0.4em 0.5em 0.4em;\n",
              "  box-sizing: border-box;\n",
              "  padding-bottom: 0.4em;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-container {\n",
              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-1 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-1 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: flex;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "  align-items: start;\n",
              "  justify-content: space-between;\n",
              "  gap: 0.5em;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 label.sk-toggleable__label .caption {\n",
              "  font-size: 0.6rem;\n",
              "  font-weight: lighter;\n",
              "  color: var(--sklearn-color-text-muted);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-1 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-1 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-1 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-1 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 0.5em;\n",
              "  text-align: center;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-1 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KNeighborsClassifier()</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 fitted 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 fitted sk-toggleable__label-arrow\"><div><div>KNeighborsClassifier</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.neighbors.KNeighborsClassifier.html\">?<span>Documentation for KNeighborsClassifier</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>KNeighborsClassifier()</pre></div> </div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "model.fit(X_train, y_train)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f918a4e1",
      "metadata": {
        "id": "f918a4e1"
      },
      "source": [
        "&#x2753; **Вопрос** &#x2753;\n",
        "\n",
        "> Что метод `fit` сделал в данном случае? Что есть обучение kNN?\n",
        "\n",
        "<details>\n",
        "  <summary> Кликни для показа ответа </summary>\n",
        "  \n",
        "> В контексте kNN в случае `algorithm=\"brute\"` \"обучением\" называется процесс запоминания всех данных, предоставленных для обучения. То есть модель просто сохраняет все точки данных вместе с их метками классов. Никакие дополнительные вычисления или оптимизации параметров не производятся.\n",
        "\n",
        " >С одной стороны это делает kNN простым и адаптивным, так как, если данные обновляются, новая версия модели создается мгновенно, без необходимости повторного обучения.  Однако, с другой стороны, это замедляет работу модели и снижает его эффективность на сложных задачах, где требуется выявление сложных взаимосвязей в данных.\n",
        "</details><br/>\n",
        "\n",
        "\n",
        "Теперь когда мы обучили модель, мы можем использовать ее для получения предсказаний. Для этого аналогично обучению существует метод `model.predict(X_test) `\n",
        "\n",
        "- `X_test`: массив признаков тестовой выборки."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "95ca79dc",
      "metadata": {
        "id": "95ca79dc"
      },
      "outputs": [],
      "source": [
        "y_pred = model.predict(X_test)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "&#x2753; **Вопрос** &#x2753;\n",
        "\n",
        "> Что метод `predict` сделал в данном случае? Что есть предсказание kNN?\n",
        "\n",
        "<details>\n",
        "  <summary> Кликни для показа ответа </summary>\n",
        "  \n",
        "> Для каждого элемента из тестовой выборки выбираются $k$ ближайших соседей из тренировочной выборки по измеренному расстоянию. Новый объект классифицируется путем голосования среди выбранных $k$.\n",
        "Класс, который встречается чаще всего среди этих соседей, присваивается новому объекту.\n",
        "</details><br/>\n",
        "\n",
        "При работе с большими наборами данных поиск ближайших соседей может занять значительное время. Для ускорения можно использовать специализированные структуры данных:\n",
        "- KD-дерево (`algorithm=\"kd_tree\"`): позволяет быстро находить ближайшие соседи за логарифмическое время,\n",
        "- BallTree (`algorithm=\"ball_tree\"`): еще одна структура данных, которая ускоряет поиск.  \n",
        "\n",
        "\n",
        "\n",
        "\n",
        "&#x2753; **Вопрос** &#x2753;\n",
        "\n",
        "> Почему метод kNN может работать медленно на больших данных?\n",
        "\n",
        "<details>\n",
        "  <summary> Кликни для показа ответа </summary>\n",
        "  \n",
        "> Основная операция метода kNN заключается в вычислении расстояния между каждым новым объектом и всеми объектами обучающей выборки. Для каждой новой точки нужно найти её $k$ ближайших соседей среди всех объектов в наборе данных. Если количество объектов велико, это требует значительных вычислительных ресурсов. Вычислительная сложность поиска ближайшего соседа для одного нового объекта составляет\n",
        "$O(n\\cdot d)$, где $n$ – число объектов в обучающем множестве, а $d$ – размерность пространства признаков.  \n",
        "\n",
        "> Простой подход к поиску ближайших соседей (brute force search) имеет высокую временную сложность $O(n)$.  \n",
        "</details><br/>\n",
        "\n",
        "Посмотрим на результат предсказания."
      ],
      "metadata": {
        "id": "RJ8ntPpvid7I"
      },
      "id": "RJ8ntPpvid7I"
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred.shape, y_pred[:15]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Tjz8nN_BsjuO",
        "outputId": "e671f828-9e95-45a9-c727-6fd5467264ac"
      },
      "id": "Tjz8nN_BsjuO",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((540,), array([6, 9, 3, 7, 2, 1, 5, 2, 5, 2, 1, 9, 4, 0, 4]))"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "86e57382",
      "metadata": {
        "id": "86e57382"
      },
      "source": [
        "У нас есть истинные метки классов `y_test` и предсказанные моделью `y_pred`. Для оценки качества модели осталось только их сравнить.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "&#x2753; **Вопрос** &#x2753;\n",
        "\n",
        "> Если данные распределены неравномерно, например, одна часть плотно сгруппирована, а другая разрежена (см. ниже), как это может повлиять на результаты kNN?\n",
        "\n",
        "![image.png](data:image/png;base64,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)\n",
        "\n",
        "<details>\n",
        "  <summary> Кликни для показа ответа </summary>\n",
        "  \n",
        ">  Как мы помним, наш метод строит предсказания, основываясь на предположении о схожести соседних объектов в метрическом пространстве.\n",
        "\n",
        "> В плотных областях данных в небольшой окрестности каждой точки расположено довольно много объектов, соответственно, принцип схожести будет соблюдаться в том числе и для больших $k$. Это позволит модели быть более устойчивой в этой области данных, менее зависимой от шумов в данных.\n",
        "\n",
        "> Однако, в разреженных областях даже в большой окрестности будет расположено мало объектов, соответственно, для соблюдения принципа схожести необходимо брать небольшие значения $k$, иначе модель может выдавать сильно смещенные предсказания.\n",
        "\n",
        "> В итоге получаем, что не существует значения $k$, которое было бы оптимальным для всего пространства данных.\n",
        "</details><br/>"
      ],
      "metadata": {
        "id": "_GsAcToKgZtZ"
      },
      "id": "_GsAcToKgZtZ"
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 3. Визуализация результатов\n",
        "\n",
        "Давайте посмотрим на то, как предсказанные значения согласуются с реальными."
      ],
      "metadata": {
        "id": "BKqdGMW9gPW6"
      },
      "id": "BKqdGMW9gPW6"
    },
    {
      "cell_type": "code",
      "source": [
        "def get_random_image(X, predicted_labels, real_labels):\n",
        "    \"\"\"Выбирает случайный элемент из выборки и возвращает матрицу изображения,\n",
        "    метки класса, предсказанные моделью, и реальные.\n",
        "\n",
        "    Принимает:\n",
        "    * X - Матрица изображений.\n",
        "    * predicted_labels - Массив предсказанных меток классов.\n",
        "    * real_labels -  Массив реальных меток классов.\n",
        "    Возвращает:\n",
        "    * random_digit_image - Случайное изображение, преобразованное в матрицу размером 8x8.\n",
        "    * random_digit_label - Предсказанная метка класса для выбранного изображения.\n",
        "    * real_label - Реальная метка класса для выбранного изображения.\n",
        "    \"\"\"\n",
        "\n",
        "    random_digit_number = np.random.randint(\n",
        "        1, len(y_test)\n",
        "    )  # выбираем случайный индекс из тестовой выборки\n",
        "    random_digit_image = X[random_digit_number].reshape(\n",
        "        int(np.sqrt(X.shape[1])), int(np.sqrt(X.shape[1]))\n",
        "    )  # преобразуем вектор признаков обратно в матрицу\n",
        "    random_digit_label = predicted_labels[\n",
        "        random_digit_number\n",
        "    ]  # предсказанная метка\n",
        "    real_label = real_labels[random_digit_number]  # реальная метка\n",
        "\n",
        "    return random_digit_image, random_digit_label, real_label"
      ],
      "metadata": {
        "id": "dQEfmooPFuEG"
      },
      "id": "dQEfmooPFuEG",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "6b9a7867",
      "metadata": {
        "id": "6b9a7867",
        "outputId": "44a91910-8c4e-42f2-a37c-eebc1615f16d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1300x600 with 24 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.figure(figsize=(13, 6))\n",
        "\n",
        "for i in range(24):\n",
        "    plt.subplot(3, 8, i + 1)\n",
        "    image, predicted_label, real_label = get_random_image(\n",
        "        X_test, y_pred, y_test\n",
        "    )\n",
        "    plt.imshow(image, cmap=\"gray\")  # выводим само изображение\n",
        "    plt.title(\n",
        "        f\"predicted = {predicted_label} \\n real = {real_label}\"\n",
        "    )  # выводим истинные и предсказанные метки\n",
        "    plt.axis(\"off\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Как вы могли заметить, на тестовой выборке у нас 540 изображений, и сравнивать все вручную будет довольно проблематично. Для оценки качества моделей вводится такое понятие, как *метрика*.\n",
        "\n",
        "Не стоит путать с метрикой в метрическом пространстве, которая используется для поиска ближайших соседей. *Метрика качества* же помогает оценить, насколько правильно эти соседи определяют класс нового объекта.\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "### 4. Метрика и качество модели\n",
        "\n",
        "Первая идея — это просто посчитать долю правильно угаданных объектов. Такой критерий качества называется **accuracy**.\n",
        "Пусть $Y_1, ..., Y_n$ &mdash; истинные значения, а  $\\widehat{Y}_1,...,\\widehat{Y}_n$\n",
        "  — предсказания. Тогда\n",
        "\n",
        "$$Accuracy = \\frac{1}{n} \\sum_{i=1}^{n} I\\{Y_i = \\widehat{Y}_i\\}$$\n",
        "\n",
        "Как вы уже могли догадаться, в sklearn-е есть готовая [реализация](https://scikit-learn.org/1.5/modules/generated/sklearn.metrics.accuracy_score.html) этой метрики в модуле `sklearn.metrics` функция `accuracy_score`.\n",
        "\n",
        "`accuracy_score(y_true, y_pred)`\n",
        "\n",
        "- `y_true`: массив меток класса на тестовом наборе данных\n",
        "- `y_pred`: массив меток класса предсказанный нашей моделью\n",
        "\n",
        "Оценим качество нашей модели по метрике accuracy.\n"
      ],
      "metadata": {
        "id": "PIguAO2kfO1q"
      },
      "id": "PIguAO2kfO1q"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "21070964",
      "metadata": {
        "id": "21070964",
        "outputId": "013734af-30ac-4368-9233-c7b822732b2e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "метрика accuracy = 99.26%\n"
          ]
        }
      ],
      "source": [
        "score = accuracy_score(y_test, y_pred)\n",
        "print(f\"метрика accuracy = {score*100:.2f}%\")"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Число 99% должно нас очень сильно радовать, но все же, перед тем как говорить об эффективности модели, стоит сравнить с каким-то бейзлайном. К примеру, возьмем самый частый класс и присвоим это значение всем элементам тестовой выборки"
      ],
      "metadata": {
        "id": "chbvWVdnjWfa"
      },
      "id": "chbvWVdnjWfa"
    },
    {
      "cell_type": "code",
      "source": [
        "vals, counts = np.unique(y_train, return_counts=True)\n",
        "naive_class = vals[np.argmax(counts)]\n",
        "print(f\"Самый популярный класс - {naive_class}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bOBGolQPjzaX",
        "outputId": "fa2a671a-d7ff-41fb-8f0e-6fd3ad54f3ba"
      },
      "id": "bOBGolQPjzaX",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Самый популярный класс - 1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred = np.full(len(y_test), naive_class)\n",
        "score = accuracy_score(y_test, y_pred)\n",
        "print(f\"метрика accuracy = {score*100:.2f}%\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dhknOn6Rkggu",
        "outputId": "3fcc1c41-fe5b-4120-b97e-8a5ffcd88b04"
      },
      "id": "dhknOn6Rkggu",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "метрика accuracy = 9.26%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "77b30b5a",
      "metadata": {
        "id": "77b30b5a"
      },
      "source": [
        "&#x2753; **Вопрос** &#x2753;\n",
        "\n",
        "> Почему у самого популярного класса точность меньше 10%? Кажется, должно быть не меньше.\n",
        "\n",
        "<details>\n",
        "  <summary> Кликни для показа ответа </summary>\n",
        "  \n",
        "> Тут стоит отметить, что самый популярный класс был определен на тренировочной выборке. Для тестовой же &mdash; самый популярный класс может оказаться совершенно другим, т.к. разбиение случайное.\n",
        "</details><br/>\n",
        "\n",
        "Теперь мы можем утверждать, что модель k-ближайших соседей (kNN) продемонстрировала высокую точность в 99%, значительно превосходя базовый уровень в 9%. Это подтверждает высокую эффективность модели в данном контексте. Однако стоит рассмотреть, как другие современные модели справляются с аналогичными задачами.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "YNPL_iU5Y6Lo"
      },
      "id": "YNPL_iU5Y6Lo"
    },
    {
      "cell_type": "markdown",
      "source": [
        "Подробнее об этом можно почитать [здесь](https://yann.lecun.com/exdb/mnist/).\n",
        "\n",
        "История классификации датасета MNIST отражает эволюцию методов машинного обучения и искусственного интеллекта. От простых линейных классификаторов до глубоких сверточных нейронных сетей — прогресс был значительным. Сегодня MNIST служит скорее отправной точкой для изучения новых идей и технологий, нежели сложной задачей, требующей решения. Тем не менее, современные модели, такие как сверточные нейронные сети (CNN), рекуррентные нейронные сети (RNN) и трансформеры, продолжают совершенствоваться, предлагая все более точные и эффективные решения для разнообразных задач, выходящих далеко за рамки простого распознавания рукописных цифр. И наша цель познакомить вас со всем многообразием этих моделей от самых простых до самых эффективных.\n",
        "\n"
      ],
      "metadata": {
        "id": "r2IntYY76faz"
      },
      "id": "r2IntYY76faz"
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.7"
    },
    "colab": {
      "provenance": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}