Нормализация.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# Нормализация (Max-Min Normalization, Min-Max Scaling)\n",
    " – техника преобразования значений признака (Feature), масштабирующая значения таким образом, что они располагаются в диапазоне от 0 до 1. Вычисляется каждый нормализованный элемент признака с помощью формулы.\n",
    " Цель такого преобразования – изменить значения числовых столбцов в наборе данных так, чтобы сохранить различия их диапазонов. В Машинном обучении (Machine Learning) Датасет (Dataset) требует нормализации, когда признаки имеют разные диапазоны и тем самым способствуют искажению восприятия взаимоотношений между Переменными-предикторами (Predictor Variable) и Целевой переменной (Target Variable).\n",
    " Нормализация и SkLearn\n",
    "Нормализовать можно с помощью функции SkLearn. Импортируем MinMaxScaler библиотеки Scikit-learn:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "VJDOCvnnOzQz"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "import sklearn\n",
    "from sklearn.preprocessing import MinMaxScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "J_fEa41kLHng"
   },
   "source": [
    "Библиотеки быстро эволюционируют, потому указывается рабочая версия, с которой работал автор на момент написания статьи. Для быстрого дебаггинга используйте команду для установки явной версии '!pip install [библиотека]==[версия]'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Hu83yksBLIkR",
    "outputId": "1c0aa1c3-acb7-440b-aa5e-ed6c27374ab2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3.4\n",
      "0.24.2\n"
     ]
    }
   ],
   "source": [
    "print(pd.__version__)\n",
    "print(sklearn.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 418
    },
    "id": "ktBbdj3_O_Rm",
    "outputId": "b6b703b0-250d-4e4a-aac5-be66b1e582b8"
   },
   "outputs": [
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       "      <th></th>\n",
       "      <th>Возраст</th>\n",
       "      <th>Работа</th>\n",
       "      <th>Семейный статус</th>\n",
       "      <th>Образование</th>\n",
       "      <th>Кредитный дефолт</th>\n",
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       "      <th>Займ</th>\n",
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       "      <th>День недели</th>\n",
       "      <th>...</th>\n",
       "      <th>Кампания</th>\n",
       "      <th>День</th>\n",
       "      <th>Предыдущий контакт</th>\n",
       "      <th>Доходность</th>\n",
       "      <th>Колебание уровня безработицы</th>\n",
       "      <th>Индекс потребительских цен</th>\n",
       "      <th>Индекс потребительской уверенности</th>\n",
       "      <th>Европейская межбанковская ставка</th>\n",
       "      <th>Количество сотрудников в компании</th>\n",
       "      <th>y</th>\n",
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       "      <th>0</th>\n",
       "      <td>27</td>\n",
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       "      <td>Не женат / не замужем</td>\n",
       "      <td>Университетская степень</td>\n",
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       "      <td>Нет</td>\n",
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       "      <td>Октябрь</td>\n",
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       "      <td>...</td>\n",
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       "      <td>Отсутствует</td>\n",
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       "      <td>5.045</td>\n",
       "      <td>5195.8</td>\n",
       "      <td>Нет</td>\n",
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       "      <th>1</th>\n",
       "      <td>30</td>\n",
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       "      <td>-40.4</td>\n",
       "      <td>5.045</td>\n",
       "      <td>5195.8</td>\n",
       "      <td>Да</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>39</td>\n",
       "      <td>Голубой воротничок</td>\n",
       "      <td>Женат / замужем</td>\n",
       "      <td>Базовое (9 классов)</td>\n",
       "      <td>Нет</td>\n",
       "      <td>Нет</td>\n",
       "      <td>Нет</td>\n",
       "      <td>Городской телефон</td>\n",
       "      <td>Октябрь</td>\n",
       "      <td>Пятница</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>999</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>42</td>\n",
       "      <td>Менеджер</td>\n",
       "      <td>Женат / замужем</td>\n",
       "      <td>Высшая школа</td>\n",
       "      <td>Нет</td>\n",
       "      <td>Да</td>\n",
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       "      <td>0</td>\n",
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       "      <td>5.045</td>\n",
       "      <td>5195.8</td>\n",
       "      <td>Да</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>42</td>\n",
       "      <td>Самозанятый</td>\n",
       "      <td>Женат / замужем</td>\n",
       "      <td>Базовое (4 класса)</td>\n",
       "      <td>Нет</td>\n",
       "      <td>Нет</td>\n",
       "      <td>Нет</td>\n",
       "      <td>Городской телефон</td>\n",
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       "      <td>5195.8</td>\n",
       "      <td>Да</td>\n",
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       "   Возраст              Работа        Семейный статус  \\\n",
       "0       27         Самозанятый  Не женат / не замужем   \n",
       "1       30    Преддприниматель        Женат / замужем   \n",
       "2       39  Голубой воротничок        Женат / замужем   \n",
       "3       42            Менеджер        Женат / замужем   \n",
       "4       42         Самозанятый        Женат / замужем   \n",
       "\n",
       "               Образование Кредитный дефолт Ипотека Займ            Контакт  \\\n",
       "0  Университетская степень              Нет     Нет  Нет  Городской телефон   \n",
       "1  Университетская степень              Нет     Нет  Нет  Городской телефон   \n",
       "2      Базовое (9 классов)              Нет     Нет  Нет  Городской телефон   \n",
       "3             Высшая школа              Нет      Да   Да  Городской телефон   \n",
       "4       Базовое (4 класса)              Нет     Нет  Нет  Городской телефон   \n",
       "\n",
       "     Месяц День недели  ...  Кампания  День  Предыдущий контакт   Доходность  \\\n",
       "0  Октябрь     Пятница  ...         1   999                   0  Отсутствует   \n",
       "1  Октябрь     Пятница  ...         1   999                   0  Отсутствует   \n",
       "2  Октябрь     Пятница  ...         1   999                   0  Отсутствует   \n",
       "3  Октябрь     Пятница  ...         1   999                   0  Отсутствует   \n",
       "4  Октябрь     Пятница  ...         1   999                   0  Отсутствует   \n",
       "\n",
       "  Колебание уровня безработицы  Индекс потребительских цен  \\\n",
       "0                         -0.1                      93.798   \n",
       "1                         -0.1                      93.798   \n",
       "2                         -0.1                      93.798   \n",
       "3                         -0.1                      93.798   \n",
       "4                         -0.1                      93.798   \n",
       "\n",
       "   Индекс потребительской уверенности  Европейская межбанковская ставка  \\\n",
       "0                               -40.4                             5.045   \n",
       "1                               -40.4                             5.045   \n",
       "2                               -40.4                             5.045   \n",
       "3                               -40.4                             5.045   \n",
       "4                               -40.4                             5.045   \n",
       "\n",
       "   Количество сотрудников в компании    y  \n",
       "0                             5195.8  Нет  \n",
       "1                             5195.8   Да  \n",
       "2                             5195.8   Да  \n",
       "3                             5195.8   Да  \n",
       "4                             5195.8   Да  \n",
       "\n",
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      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Импортируем датасет, разделителем  является точка с запятой (sep = ';'):\n",
    "df = pd.read_csv('https://www.dropbox.com/s/62xm9ymoaunnfg6/bank-full.csv?dl=1', sep = ';')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ljtV8IDXP6Bb",
    "outputId": "54fe7d5b-32c0-451c-db46-329e69c8a504"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Возраст                                 int64\n",
       "Работа                                 object\n",
       "Семейный статус                        object\n",
       "Образование                            object\n",
       "Кредитный дефолт                       object\n",
       "Ипотека                                object\n",
       "Займ                                   object\n",
       "Контакт                                object\n",
       "Месяц                                  object\n",
       "День недели                            object\n",
       "Длительность                            int64\n",
       "Кампания                                int64\n",
       "День                                    int64\n",
       "Предыдущий контакт                      int64\n",
       "Доходность                             object\n",
       "Колебание уровня безработицы          float64\n",
       "Индекс потребительских цен            float64\n",
       "Индекс потребительской уверенности    float64\n",
       "Европейская межбанковская ставка      float64\n",
       "Количество сотрудников в компании     float64\n",
       "y                                      object\n",
       "dtype: object"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Определим, какие признаки являются числовыми, чтобы впоследствии их нормализовать:\n",
    "df.dtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для простоты восприятия сузим датасет и создадим его копию, состоящую только из признаков, выраженных числами:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "lTBRQooQQPQY"
   },
   "outputs": [],
   "source": [
    "# Выберем встретившиеся числовые типы\n",
    "numerics = ['int64', 'float64']\n",
    "\n",
    "# Создадим копию датасета\n",
    "newdf = df.select_dtypes(include = numerics)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь приступим непосредственно к нормализации:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "id": "-S9Cz-VhPEt8",
    "outputId": "e11f56a3-c384-4b2d-cd9f-f6d9566e7dcd"
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   "outputs": [
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       "    Возраст  Длительность  Кампания  День  Предыдущий контакт  \\\n",
       "0  0.123457      0.004880       0.0   1.0                 0.0   \n",
       "1  0.160494      0.045344       0.0   1.0                 0.0   \n",
       "2  0.271605      0.054900       0.0   1.0                 0.0   \n",
       "3  0.308642      0.020943       0.0   1.0                 0.0   \n",
       "4  0.308642      0.097194       0.0   1.0                 0.0   \n",
       "\n",
       "   Колебание уровня безработицы  Индекс потребительских цен  \\\n",
       "0                        0.6875                    0.622369   \n",
       "1                        0.6875                    0.622369   \n",
       "2                        0.6875                    0.622369   \n",
       "3                        0.6875                    0.622369   \n",
       "4                        0.6875                    0.622369   \n",
       "\n",
       "   Индекс потребительской уверенности  Европейская межбанковская ставка  \\\n",
       "0                            0.435146                               1.0   \n",
       "1                            0.435146                               1.0   \n",
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       "4                            0.435146                               1.0   \n",
       "\n",
       "   Количество сотрудников в компании  \n",
       "0                           0.877883  \n",
       "1                           0.877883  \n",
       "2                           0.877883  \n",
       "3                           0.877883  \n",
       "4                           0.877883  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Инициализация нормализатора\n",
    "scaler = MinMaxScaler()\n",
    "\n",
    "# Передача датасета и преобразование\n",
    "scaler.fit(newdf)\n",
    "scaled_features = scaler.transform(newdf)\n",
    "\n",
    "# Конвертация в табличный формат\n",
    "df_MinMax = pd.DataFrame(data = scaled_features, \n",
    "columns = [\"Возраст\", \n",
    "          \"Длительность\",\n",
    "          \"Кампания\",\n",
    "          \"День\",\n",
    "          \"Предыдущий контакт\", \n",
    "          \"Колебание уровня безработицы\", \n",
    "          \"Индекс потребительских цен\",\n",
    "          \"Индекс потребительской уверенности\",\n",
    "          \"Европейская межбанковская ставка\",\n",
    "          \"Количество сотрудников в компании\"])\n",
    "\n",
    "df_MinMax.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Результирующий нормализованный датасет приобрел следующий вид и готов к дальнейшей обработке и загрузке в Модель (Model):"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нормализация и стандартизация\n",
    "Стандартизация (Standartization) является разновидностью нормализации с использованием Стандартизованной оценки (Z-Score) и как бы центрирует наблюдения относительно нуля. Расстояние от нуля, то есть Дисперсия случайной величины (Variance) не превышает единицы:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Исходные данные\n",
    "[[0, 0], [0, 0], [1, 1], [1, 1]]\n",
    "\n",
    "# Стандартизованные данные\n",
    "[[-1, -1], [-1, -1], [1, 1], [1, 1]]"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "provenance": []
  },
  "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"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}