Sprint 8 - 2 (1).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "288fdfa9",
   "metadata": {},
   "source": [
    "# SPRINT 8: Algoritmos de aprendizaje no supervisado - Agrupación"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9daf7be4",
   "metadata": {},
   "source": [
    "## Objetivos:\n",
    "- Limpieza e interpretación de datos\n",
    "- Preprocesado\n",
    "- Encontrar número de clusters óptimos\n",
    "- Creación de modelos no supervisados (k-means y clustering jerárquico)\n",
    "- Interpretación de resultados"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "83887de1",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ï»¿status_id</th>\n",
       "      <th>status_type</th>\n",
       "      <th>status_published</th>\n",
       "      <th>num_reactions</th>\n",
       "      <th>num_comments</th>\n",
       "      <th>num_shares</th>\n",
       "      <th>num_likes</th>\n",
       "      <th>num_loves</th>\n",
       "      <th>num_wows</th>\n",
       "      <th>num_hahas</th>\n",
       "      <th>num_sads</th>\n",
       "      <th>num_angrys</th>\n",
       "      <th>Column1</th>\n",
       "      <th>Column2</th>\n",
       "      <th>Column3</th>\n",
       "      <th>Column4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>246675545449582_1649696485147474</td>\n",
       "      <td>video</td>\n",
       "      <td>4/22/2018 6:00</td>\n",
       "      <td>529</td>\n",
       "      <td>512</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <th>1</th>\n",
       "      <td>246675545449582_1649426988507757</td>\n",
       "      <td>photo</td>\n",
       "      <td>4/21/2018 22:45</td>\n",
       "      <td>150</td>\n",
       "      <td>0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <th>2</th>\n",
       "      <td>246675545449582_1648730588577397</td>\n",
       "      <td>video</td>\n",
       "      <td>4/21/2018 6:17</td>\n",
       "      <td>227</td>\n",
       "      <td>236</td>\n",
       "      <td>57</td>\n",
       "      <td>204</td>\n",
       "      <td>21</td>\n",
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       "      <th>3</th>\n",
       "      <td>246675545449582_1648576705259452</td>\n",
       "      <td>photo</td>\n",
       "      <td>4/21/2018 2:29</td>\n",
       "      <td>111</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>111</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>246675545449582_1645700502213739</td>\n",
       "      <td>photo</td>\n",
       "      <td>4/18/2018 3:22</td>\n",
       "      <td>213</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>204</td>\n",
       "      <td>9</td>\n",
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       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>7045</th>\n",
       "      <td>1050855161656896_1061863470556065</td>\n",
       "      <td>photo</td>\n",
       "      <td>9/24/2016 2:58</td>\n",
       "      <td>89</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>89</td>\n",
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       "      <th>7046</th>\n",
       "      <td>1050855161656896_1061334757275603</td>\n",
       "      <td>photo</td>\n",
       "      <td>9/23/2016 11:19</td>\n",
       "      <td>16</td>\n",
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       "      <td>14</td>\n",
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       "      <th>7047</th>\n",
       "      <td>1050855161656896_1060126464063099</td>\n",
       "      <td>photo</td>\n",
       "      <td>9/21/2016 23:03</td>\n",
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       "      <th>7048</th>\n",
       "      <td>1050855161656896_1058663487542730</td>\n",
       "      <td>photo</td>\n",
       "      <td>9/20/2016 0:43</td>\n",
       "      <td>351</td>\n",
       "      <td>12</td>\n",
       "      <td>22</td>\n",
       "      <td>349</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>7049</th>\n",
       "      <td>1050855161656896_1050858841656528</td>\n",
       "      <td>photo</td>\n",
       "      <td>9/10/2016 10:30</td>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "<p>7050 rows × 16 columns</p>\n",
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       "                           ï»¿status_id status_type status_published  \\\n",
       "0      246675545449582_1649696485147474       video   4/22/2018 6:00   \n",
       "1      246675545449582_1649426988507757       photo  4/21/2018 22:45   \n",
       "2      246675545449582_1648730588577397       video   4/21/2018 6:17   \n",
       "3      246675545449582_1648576705259452       photo   4/21/2018 2:29   \n",
       "4      246675545449582_1645700502213739       photo   4/18/2018 3:22   \n",
       "...                                 ...         ...              ...   \n",
       "7045  1050855161656896_1061863470556065       photo   9/24/2016 2:58   \n",
       "7046  1050855161656896_1061334757275603       photo  9/23/2016 11:19   \n",
       "7047  1050855161656896_1060126464063099       photo  9/21/2016 23:03   \n",
       "7048  1050855161656896_1058663487542730       photo   9/20/2016 0:43   \n",
       "7049  1050855161656896_1050858841656528       photo  9/10/2016 10:30   \n",
       "\n",
       "      num_reactions  num_comments  num_shares  num_likes  num_loves  num_wows  \\\n",
       "0               529           512         262        432         92         3   \n",
       "1               150             0           0        150          0         0   \n",
       "2               227           236          57        204         21         1   \n",
       "3               111             0           0        111          0         0   \n",
       "4               213             0           0        204          9         0   \n",
       "...             ...           ...         ...        ...        ...       ...   \n",
       "7045             89             0           0         89          0         0   \n",
       "7046             16             0           0         14          1         0   \n",
       "7047              2             0           0          1          1         0   \n",
       "7048            351            12          22        349          2         0   \n",
       "7049             17             0           0         17          0         0   \n",
       "\n",
       "      num_hahas  num_sads  num_angrys  Column1  Column2  Column3  Column4  \n",
       "0             1         1           0      NaN      NaN      NaN      NaN  \n",
       "1             0         0           0      NaN      NaN      NaN      NaN  \n",
       "2             1         0           0      NaN      NaN      NaN      NaN  \n",
       "3             0         0           0      NaN      NaN      NaN      NaN  \n",
       "4             0         0           0      NaN      NaN      NaN      NaN  \n",
       "...         ...       ...         ...      ...      ...      ...      ...  \n",
       "7045          0         0           0      NaN      NaN      NaN      NaN  \n",
       "7046          1         0           0      NaN      NaN      NaN      NaN  \n",
       "7047          0         0           0      NaN      NaN      NaN      NaN  \n",
       "7048          0         0           0      NaN      NaN      NaN      NaN  \n",
       "7049          0         0           0      NaN      NaN      NaN      NaN  \n",
       "\n",
       "[7050 rows x 16 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn import preprocessing\n",
    "from sklearn.model_selection import train_test_split\n",
    "from scipy import stats\n",
    "\n",
    "df=pd.read_csv('Publicacions Facebook Thailandia.csv', sep=',', encoding='latin-1')\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a36fa45c",
   "metadata": {},
   "source": [
    "Valores de las columnas:\n",
    "- Status id: Id de lo que se compartió\n",
    "- Status type: Tipo de archivo que se compartió\n",
    "- Status published: Fecha y hora de la publicación\n",
    "- Num reactions: N° de reacciones a la publicación\n",
    "- Num comentarios\n",
    "- Num shares: N° de veces compartida\n",
    "- Num likes\n",
    "- Num de reacción love\n",
    "- Num de reacción wow\n",
    "- Num de reacción risa\n",
    "- Num reacción triste\n",
    "- Num reacción enojado"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "877cfaca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 7050 entries, 0 to 7049\n",
      "Data columns (total 16 columns):\n",
      " #   Column            Non-Null Count  Dtype  \n",
      "---  ------            --------------  -----  \n",
      " 0   ï»¿status_id      7050 non-null   object \n",
      " 1   status_type       7050 non-null   object \n",
      " 2   status_published  7050 non-null   object \n",
      " 3   num_reactions     7050 non-null   int64  \n",
      " 4   num_comments      7050 non-null   int64  \n",
      " 5   num_shares        7050 non-null   int64  \n",
      " 6   num_likes         7050 non-null   int64  \n",
      " 7   num_loves         7050 non-null   int64  \n",
      " 8   num_wows          7050 non-null   int64  \n",
      " 9   num_hahas         7050 non-null   int64  \n",
      " 10  num_sads          7050 non-null   int64  \n",
      " 11  num_angrys        7050 non-null   int64  \n",
      " 12  Column1           0 non-null      float64\n",
      " 13  Column2           0 non-null      float64\n",
      " 14  Column3           0 non-null      float64\n",
      " 15  Column4           0 non-null      float64\n",
      "dtypes: float64(4), int64(9), object(3)\n",
      "memory usage: 881.4+ KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e6d88e4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ï»¿status_id         object\n",
       "status_type          object\n",
       "status_published     object\n",
       "num_reactions         int64\n",
       "num_comments          int64\n",
       "num_shares            int64\n",
       "num_likes             int64\n",
       "num_loves             int64\n",
       "num_wows              int64\n",
       "num_hahas             int64\n",
       "num_sads              int64\n",
       "num_angrys            int64\n",
       "Column1             float64\n",
       "Column2             float64\n",
       "Column3             float64\n",
       "Column4             float64\n",
       "dtype: object"
      ]
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   "source": [
    "df.dtypes"
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   "id": "ba1c386b",
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    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>num_reactions</th>\n",
       "      <th>num_comments</th>\n",
       "      <th>num_shares</th>\n",
       "      <th>num_likes</th>\n",
       "      <th>num_loves</th>\n",
       "      <th>num_wows</th>\n",
       "      <th>num_hahas</th>\n",
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       "      <th>num_angrys</th>\n",
       "      <th>Column1</th>\n",
       "      <th>Column2</th>\n",
       "      <th>Column3</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
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       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>230.117163</td>\n",
       "      <td>224.356028</td>\n",
       "      <td>40.022553</td>\n",
       "      <td>215.043121</td>\n",
       "      <td>12.728652</td>\n",
       "      <td>1.289362</td>\n",
       "      <td>0.696454</td>\n",
       "      <td>0.243688</td>\n",
       "      <td>0.113191</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>462.625309</td>\n",
       "      <td>889.636820</td>\n",
       "      <td>131.599965</td>\n",
       "      <td>449.472357</td>\n",
       "      <td>39.972930</td>\n",
       "      <td>8.719650</td>\n",
       "      <td>3.957183</td>\n",
       "      <td>1.597156</td>\n",
       "      <td>0.726812</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>17.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>59.500000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>58.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>219.000000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>184.750000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>4710.000000</td>\n",
       "      <td>20990.000000</td>\n",
       "      <td>3424.000000</td>\n",
       "      <td>4710.000000</td>\n",
       "      <td>657.000000</td>\n",
       "      <td>278.000000</td>\n",
       "      <td>157.000000</td>\n",
       "      <td>51.000000</td>\n",
       "      <td>31.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       num_reactions  num_comments   num_shares    num_likes    num_loves  \\\n",
       "count    7050.000000   7050.000000  7050.000000  7050.000000  7050.000000   \n",
       "mean      230.117163    224.356028    40.022553   215.043121    12.728652   \n",
       "std       462.625309    889.636820   131.599965   449.472357    39.972930   \n",
       "min         0.000000      0.000000     0.000000     0.000000     0.000000   \n",
       "25%        17.000000      0.000000     0.000000    17.000000     0.000000   \n",
       "50%        59.500000      4.000000     0.000000    58.000000     0.000000   \n",
       "75%       219.000000     23.000000     4.000000   184.750000     3.000000   \n",
       "max      4710.000000  20990.000000  3424.000000  4710.000000   657.000000   \n",
       "\n",
       "          num_wows    num_hahas     num_sads   num_angrys  Column1  Column2  \\\n",
       "count  7050.000000  7050.000000  7050.000000  7050.000000      0.0      0.0   \n",
       "mean      1.289362     0.696454     0.243688     0.113191      NaN      NaN   \n",
       "std       8.719650     3.957183     1.597156     0.726812      NaN      NaN   \n",
       "min       0.000000     0.000000     0.000000     0.000000      NaN      NaN   \n",
       "25%       0.000000     0.000000     0.000000     0.000000      NaN      NaN   \n",
       "50%       0.000000     0.000000     0.000000     0.000000      NaN      NaN   \n",
       "75%       0.000000     0.000000     0.000000     0.000000      NaN      NaN   \n",
       "max     278.000000   157.000000    51.000000    31.000000      NaN      NaN   \n",
       "\n",
       "       Column3  Column4  \n",
       "count      0.0      0.0  \n",
       "mean       NaN      NaN  \n",
       "std        NaN      NaN  \n",
       "min        NaN      NaN  \n",
       "25%        NaN      NaN  \n",
       "50%        NaN      NaN  \n",
       "75%        NaN      NaN  \n",
       "max        NaN      NaN  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "dcc1ea57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Column1             7050\n",
       "Column2             7050\n",
       "Column3             7050\n",
       "Column4             7050\n",
       "ï»¿status_id           0\n",
       "status_type            0\n",
       "status_published       0\n",
       "num_reactions          0\n",
       "num_comments           0\n",
       "num_shares             0\n",
       "num_likes              0\n",
       "num_loves              0\n",
       "num_wows               0\n",
       "num_hahas              0\n",
       "num_sads               0\n",
       "num_angrys             0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isna().sum().sort_values(ascending = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cc77e85d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Column1             7050\n",
       "Column2             7050\n",
       "Column3             7050\n",
       "Column4             7050\n",
       "ï»¿status_id           0\n",
       "status_type            0\n",
       "status_published       0\n",
       "num_reactions          0\n",
       "num_comments           0\n",
       "num_shares             0\n",
       "num_likes              0\n",
       "num_loves              0\n",
       "num_wows               0\n",
       "num_hahas              0\n",
       "num_sads               0\n",
       "num_angrys             0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum().sort_values(ascending = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69cabbfe",
   "metadata": {},
   "source": [
    "Podemos ver, como las column 1, 2, 3 y 4 no presentan valores, por lo que procedemos a borrarlas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c5c74e3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ï»¿status_id</th>\n",
       "      <th>status_type</th>\n",
       "      <th>status_published</th>\n",
       "      <th>num_reactions</th>\n",
       "      <th>num_comments</th>\n",
       "      <th>num_shares</th>\n",
       "      <th>num_likes</th>\n",
       "      <th>num_loves</th>\n",
       "      <th>num_wows</th>\n",
       "      <th>num_hahas</th>\n",
       "      <th>num_sads</th>\n",
       "      <th>num_angrys</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>246675545449582_1649696485147474</td>\n",
       "      <td>video</td>\n",
       "      <td>4/22/2018 6:00</td>\n",
       "      <td>529</td>\n",
       "      <td>512</td>\n",
       "      <td>262</td>\n",
       "      <td>432</td>\n",
       "      <td>92</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>246675545449582_1649426988507757</td>\n",
       "      <td>photo</td>\n",
       "      <td>4/21/2018 22:45</td>\n",
       "      <td>150</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>150</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>246675545449582_1648730588577397</td>\n",
       "      <td>video</td>\n",
       "      <td>4/21/2018 6:17</td>\n",
       "      <td>227</td>\n",
       "      <td>236</td>\n",
       "      <td>57</td>\n",
       "      <td>204</td>\n",
       "      <td>21</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>246675545449582_1648576705259452</td>\n",
       "      <td>photo</td>\n",
       "      <td>4/21/2018 2:29</td>\n",
       "      <td>111</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>111</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>246675545449582_1645700502213739</td>\n",
       "      <td>photo</td>\n",
       "      <td>4/18/2018 3:22</td>\n",
       "      <td>213</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>204</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7045</th>\n",
       "      <td>1050855161656896_1061863470556065</td>\n",
       "      <td>photo</td>\n",
       "      <td>9/24/2016 2:58</td>\n",
       "      <td>89</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>89</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7046</th>\n",
       "      <td>1050855161656896_1061334757275603</td>\n",
       "      <td>photo</td>\n",
       "      <td>9/23/2016 11:19</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7047</th>\n",
       "      <td>1050855161656896_1060126464063099</td>\n",
       "      <td>photo</td>\n",
       "      <td>9/21/2016 23:03</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7048</th>\n",
       "      <td>1050855161656896_1058663487542730</td>\n",
       "      <td>photo</td>\n",
       "      <td>9/20/2016 0:43</td>\n",
       "      <td>351</td>\n",
       "      <td>12</td>\n",
       "      <td>22</td>\n",
       "      <td>349</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7049</th>\n",
       "      <td>1050855161656896_1050858841656528</td>\n",
       "      <td>photo</td>\n",
       "      <td>9/10/2016 10:30</td>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7050 rows × 12 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                           ï»¿status_id status_type status_published  \\\n",
       "0      246675545449582_1649696485147474       video   4/22/2018 6:00   \n",
       "1      246675545449582_1649426988507757       photo  4/21/2018 22:45   \n",
       "2      246675545449582_1648730588577397       video   4/21/2018 6:17   \n",
       "3      246675545449582_1648576705259452       photo   4/21/2018 2:29   \n",
       "4      246675545449582_1645700502213739       photo   4/18/2018 3:22   \n",
       "...                                 ...         ...              ...   \n",
       "7045  1050855161656896_1061863470556065       photo   9/24/2016 2:58   \n",
       "7046  1050855161656896_1061334757275603       photo  9/23/2016 11:19   \n",
       "7047  1050855161656896_1060126464063099       photo  9/21/2016 23:03   \n",
       "7048  1050855161656896_1058663487542730       photo   9/20/2016 0:43   \n",
       "7049  1050855161656896_1050858841656528       photo  9/10/2016 10:30   \n",
       "\n",
       "      num_reactions  num_comments  num_shares  num_likes  num_loves  num_wows  \\\n",
       "0               529           512         262        432         92         3   \n",
       "1               150             0           0        150          0         0   \n",
       "2               227           236          57        204         21         1   \n",
       "3               111             0           0        111          0         0   \n",
       "4               213             0           0        204          9         0   \n",
       "...             ...           ...         ...        ...        ...       ...   \n",
       "7045             89             0           0         89          0         0   \n",
       "7046             16             0           0         14          1         0   \n",
       "7047              2             0           0          1          1         0   \n",
       "7048            351            12          22        349          2         0   \n",
       "7049             17             0           0         17          0         0   \n",
       "\n",
       "      num_hahas  num_sads  num_angrys  \n",
       "0             1         1           0  \n",
       "1             0         0           0  \n",
       "2             1         0           0  \n",
       "3             0         0           0  \n",
       "4             0         0           0  \n",
       "...         ...       ...         ...  \n",
       "7045          0         0           0  \n",
       "7046          1         0           0  \n",
       "7047          0         0           0  \n",
       "7048          0         0           0  \n",
       "7049          0         0           0  \n",
       "\n",
       "[7050 rows x 12 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2=df.drop(columns=['Column1', 'Column2', 'Column3', 'Column4'], axis=1)\n",
    "df2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c581fc3",
   "metadata": {},
   "source": [
    "Otra modificación que haremos será con la variable status_type, la transformaremos a dummy para poder interpretarlas por separado y facilitar su visualización y evaluación:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7f648e2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "dummies = pd.get_dummies(df['status_type'])\n",
    "df_def = pd.concat([df2, dummies], axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7639708f",
   "metadata": {},
   "source": [
    "Eliminamos las columnas: 'status id' ya que en este caso no nos sirve diferenciar por id, la variable 'status_type' porque ya la hemos pasado a dummy y la 'status_published' que tiene los datos de fecha y hora de publicación, que son interesantes, pero en este caso que queremos hacer clustering y necesitamos únciamente variables númericas no nos hacen falta."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "13d1dbda",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_def=df_def.drop(columns=['ï»¿status_id', 'status_type', 'status_published'], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5b3bddcb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['num_reactions', 'num_comments', 'num_shares', 'num_likes', 'num_loves',\n",
       "       'num_wows', 'num_hahas', 'num_sads', 'num_angrys', 'link', 'photo',\n",
       "       'status', 'video'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_def.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f47778f6",
   "metadata": {},
   "source": [
    "Verificamos que variables presentan outliers, a partir de sus gráficas de box-plot.\n",
    "Esto lo haremos apra saber como proceder con su preprocesamiento."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "eb7d2021",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cols = ['num_reactions', 'num_comments', 'num_shares', 'num_likes', 'num_loves', 'num_wows', 'num_hahas', 'num_sads', 'num_angrys']\n",
    "\n",
    "for column in cols:\n",
    "    plt.figure()\n",
    "    df[column].plot.box()\n",
    "    plt.title(column)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fdd3d1d",
   "metadata": {},
   "source": [
    "Podemos ver como todas las variables presentan outliers.\n",
    "\n",
    "Aplico **robust scaler** para las variables: 'num_reactions', 'num_comments', 'num_shares', 'num_likes', 'num_loves', 'num_wows', 'num_hahas', 'num_sads', 'num_angrys', ya que presentan gran cantidad de outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6b644bf1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>num_reactions</th>\n",
       "      <th>num_comments</th>\n",
       "      <th>num_shares</th>\n",
       "      <th>num_likes</th>\n",
       "      <th>num_loves</th>\n",
       "      <th>num_wows</th>\n",
       "      <th>num_hahas</th>\n",
       "      <th>num_sads</th>\n",
       "      <th>num_angrys</th>\n",
       "      <th>link</th>\n",
       "      <th>photo</th>\n",
       "      <th>status</th>\n",
       "      <th>video</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.324257</td>\n",
       "      <td>22.086957</td>\n",
       "      <td>65.50</td>\n",
       "      <td>2.229508</td>\n",
       "      <td>30.666667</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.448020</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.548435</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.829208</td>\n",
       "      <td>10.086957</td>\n",
       "      <td>14.25</td>\n",
       "      <td>0.870343</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.254950</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.315946</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.759901</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.870343</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7045</th>\n",
       "      <td>0.146040</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.184799</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7046</th>\n",
       "      <td>-0.215347</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.262295</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7047</th>\n",
       "      <td>-0.284653</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.339791</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7048</th>\n",
       "      <td>1.443069</td>\n",
       "      <td>0.347826</td>\n",
       "      <td>5.50</td>\n",
       "      <td>1.734724</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7049</th>\n",
       "      <td>-0.210396</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.244411</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7050 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      num_reactions  num_comments  num_shares  num_likes  num_loves  num_wows  \\\n",
       "0          2.324257     22.086957       65.50   2.229508  30.666667       3.0   \n",
       "1          0.448020     -0.173913        0.00   0.548435   0.000000       0.0   \n",
       "2          0.829208     10.086957       14.25   0.870343   7.000000       1.0   \n",
       "3          0.254950     -0.173913        0.00   0.315946   0.000000       0.0   \n",
       "4          0.759901     -0.173913        0.00   0.870343   3.000000       0.0   \n",
       "...             ...           ...         ...        ...        ...       ...   \n",
       "7045       0.146040     -0.173913        0.00   0.184799   0.000000       0.0   \n",
       "7046      -0.215347     -0.173913        0.00  -0.262295   0.333333       0.0   \n",
       "7047      -0.284653     -0.173913        0.00  -0.339791   0.333333       0.0   \n",
       "7048       1.443069      0.347826        5.50   1.734724   0.666667       0.0   \n",
       "7049      -0.210396     -0.173913        0.00  -0.244411   0.000000       0.0   \n",
       "\n",
       "      num_hahas  num_sads  num_angrys  link  photo  status  video  \n",
       "0           1.0       1.0         0.0     0      0       0      1  \n",
       "1           0.0       0.0         0.0     0      1       0      0  \n",
       "2           1.0       0.0         0.0     0      0       0      1  \n",
       "3           0.0       0.0         0.0     0      1       0      0  \n",
       "4           0.0       0.0         0.0     0      1       0      0  \n",
       "...         ...       ...         ...   ...    ...     ...    ...  \n",
       "7045        0.0       0.0         0.0     0      1       0      0  \n",
       "7046        1.0       0.0         0.0     0      1       0      0  \n",
       "7047        0.0       0.0         0.0     0      1       0      0  \n",
       "7048        0.0       0.0         0.0     0      1       0      0  \n",
       "7049        0.0       0.0         0.0     0      1       0      0  \n",
       "\n",
       "[7050 rows x 13 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import RobustScaler\n",
    "scaler=RobustScaler()\n",
    "df_def [['num_reactions', 'num_comments', 'num_shares', 'num_likes', 'num_loves', 'num_wows', 'num_hahas', 'num_sads', 'num_angrys']] = scaler.fit_transform(df_def[['num_reactions', 'num_comments', 'num_shares', 'num_likes', 'num_loves', 'num_wows', 'num_hahas', 'num_sads', 'num_angrys']])\n",
    "\n",
    "df_def"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "6578732f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>num_reactions</th>\n",
       "      <th>num_comments</th>\n",
       "      <th>num_shares</th>\n",
       "      <th>num_likes</th>\n",
       "      <th>num_loves</th>\n",
       "      <th>num_wows</th>\n",
       "      <th>num_hahas</th>\n",
       "      <th>num_sads</th>\n",
       "      <th>num_angrys</th>\n",
       "      <th>link</th>\n",
       "      <th>photo</th>\n",
       "      <th>status</th>\n",
       "      <th>video</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "      <td>7050.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.844639</td>\n",
       "      <td>9.580697</td>\n",
       "      <td>10.005638</td>\n",
       "      <td>0.936174</td>\n",
       "      <td>4.242884</td>\n",
       "      <td>1.289362</td>\n",
       "      <td>0.696454</td>\n",
       "      <td>0.243688</td>\n",
       "      <td>0.113191</td>\n",
       "      <td>0.008936</td>\n",
       "      <td>0.608227</td>\n",
       "      <td>0.051773</td>\n",
       "      <td>0.331064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.290224</td>\n",
       "      <td>38.679862</td>\n",
       "      <td>32.899991</td>\n",
       "      <td>2.679418</td>\n",
       "      <td>13.324310</td>\n",
       "      <td>8.719650</td>\n",
       "      <td>3.957183</td>\n",
       "      <td>1.597156</td>\n",
       "      <td>0.726812</td>\n",
       "      <td>0.094115</td>\n",
       "      <td>0.488181</td>\n",
       "      <td>0.221584</td>\n",
       "      <td>0.470629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-0.294554</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.345753</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.210396</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.244411</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.789604</td>\n",
       "      <td>0.826087</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.755589</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>23.022277</td>\n",
       "      <td>912.434783</td>\n",
       "      <td>856.000000</td>\n",
       "      <td>27.731744</td>\n",
       "      <td>219.000000</td>\n",
       "      <td>278.000000</td>\n",
       "      <td>157.000000</td>\n",
       "      <td>51.000000</td>\n",
       "      <td>31.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       num_reactions  num_comments   num_shares    num_likes    num_loves  \\\n",
       "count    7050.000000   7050.000000  7050.000000  7050.000000  7050.000000   \n",
       "mean        0.844639      9.580697    10.005638     0.936174     4.242884   \n",
       "std         2.290224     38.679862    32.899991     2.679418    13.324310   \n",
       "min        -0.294554     -0.173913     0.000000    -0.345753     0.000000   \n",
       "25%        -0.210396     -0.173913     0.000000    -0.244411     0.000000   \n",
       "50%         0.000000      0.000000     0.000000     0.000000     0.000000   \n",
       "75%         0.789604      0.826087     1.000000     0.755589     1.000000   \n",
       "max        23.022277    912.434783   856.000000    27.731744   219.000000   \n",
       "\n",
       "          num_wows    num_hahas     num_sads   num_angrys         link  \\\n",
       "count  7050.000000  7050.000000  7050.000000  7050.000000  7050.000000   \n",
       "mean      1.289362     0.696454     0.243688     0.113191     0.008936   \n",
       "std       8.719650     3.957183     1.597156     0.726812     0.094115   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "25%       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "50%       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "75%       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "max     278.000000   157.000000    51.000000    31.000000     1.000000   \n",
       "\n",
       "             photo       status        video  \n",
       "count  7050.000000  7050.000000  7050.000000  \n",
       "mean      0.608227     0.051773     0.331064  \n",
       "std       0.488181     0.221584     0.470629  \n",
       "min       0.000000     0.000000     0.000000  \n",
       "25%       0.000000     0.000000     0.000000  \n",
       "50%       1.000000     0.000000     0.000000  \n",
       "75%       1.000000     0.000000     1.000000  \n",
       "max       1.000000     1.000000     1.000000  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_def.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b63f027e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "num_reactions    float64\n",
       "num_comments     float64\n",
       "num_shares       float64\n",
       "num_likes        float64\n",
       "num_loves        float64\n",
       "num_wows         float64\n",
       "num_hahas        float64\n",
       "num_sads         float64\n",
       "num_angrys       float64\n",
       "link               uint8\n",
       "photo              uint8\n",
       "status             uint8\n",
       "video              uint8\n",
       "dtype: object"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_def.dtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04639539",
   "metadata": {},
   "source": [
    "### Exercici 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa89c86c",
   "metadata": {},
   "source": [
    "#### Clasifica los diferentes registros utilizando el algoritmo de K-means"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84cff414",
   "metadata": {},
   "source": [
    "Para saber cuantos clusters son correctos para poder realizar la K-means realizamos el método de **\"Elbow Method\"**. Este método se basa en la observación de la variación de la suma de las distancias al cuadrado de los puntos a su centroide más cercano en función del número de clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36db13c0",
   "metadata": {},
   "source": [
    "Antes de hacer el Elbow Method, hacemos **PCA** (Principal Component Analysis, Análisis de Componentes Principales) es una técnica de análisis multivariante que se utiliza para identificar patrones en datos de alta dimensionalidad. Sirve para encontrar las dimensiones principales de los datos, lo que puede ser útil para reducir la dimensionalidad de los datos y visualizarlos en un espacio de menor dimensión. El PCA también puede ayudar a identificar patrones y relaciones entre las variables en los datos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ceb5814d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "from scipy.spatial.distance import cdist\n",
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ea7a8c6f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: kneed in c:\\users\\flore\\appdata\\local\\programs\\python\\python310\\lib\\site-packages (0.8.2)\n",
      "Requirement already satisfied: scipy>=1.0.0 in c:\\users\\flore\\appdata\\local\\programs\\python\\python310\\lib\\site-packages (from kneed) (1.9.3)\n",
      "Requirement already satisfied: numpy>=1.14.2 in c:\\users\\flore\\appdata\\local\\programs\\python\\python310\\lib\\site-packages (from kneed) (1.23.0)\n",
      "\n",
      "[notice] A new release of pip available: 22.1.2 -> 23.0\n",
      "[notice] To update, run: python.exe -m pip install --upgrade pip\n"
     ]
    }
   ],
   "source": [
    "!pip install kneed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "67fd704f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Varianza acumulada explicada')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kneed import KneeLocator\n",
    "\n",
    "pca = PCA().fit(df_def)\n",
    "plt.plot(np.cumsum(pca.explained_variance_ratio_), marker = \"*\")\n",
    "plt.axhline(0.95, linestyle = '--')\n",
    "plt.xlim([-1,10])\n",
    "plt.xlabel('Numero componentes')\n",
    "plt.ylabel('Varianza acumulada explicada')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2fe54b13",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "pca = PCA(.95).fit(df_def)\n",
    "print(pca.n_components_)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa1ea9e2",
   "metadata": {},
   "source": [
    "Ahora que ya tenemos la cantidad óptima de clusters, los realizamos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "489b18d0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\flore\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\sklearn\\cluster\\_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 ... 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "# Crear el objeto KMeans con 2 clusters\n",
    "kmeans = KMeans(n_clusters=2)\n",
    "\n",
    "# Entrenar el modelo con el DataFrame df_def\n",
    "kmeans.fit(df_def)\n",
    "\n",
    "# Obtener las etiquetas de los clusters para cada fila del DataFrame\n",
    "labels = kmeans.predict(df_def)\n",
    "\n",
    "# Imprimir las etiquetas\n",
    "print(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "ed8526b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>num_reactions</th>\n",
       "      <th>num_comments</th>\n",
       "      <th>num_shares</th>\n",
       "      <th>num_likes</th>\n",
       "      <th>num_loves</th>\n",
       "      <th>num_wows</th>\n",
       "      <th>num_hahas</th>\n",
       "      <th>num_sads</th>\n",
       "      <th>num_angrys</th>\n",
       "      <th>link</th>\n",
       "      <th>photo</th>\n",
       "      <th>status</th>\n",
       "      <th>video</th>\n",
       "      <th>Cluster K-means</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.324257</td>\n",
       "      <td>22.086957</td>\n",
       "      <td>65.50</td>\n",
       "      <td>2.229508</td>\n",
       "      <td>30.666667</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.448020</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.548435</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.829208</td>\n",
       "      <td>10.086957</td>\n",
       "      <td>14.25</td>\n",
       "      <td>0.870343</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.254950</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.315946</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.759901</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.870343</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   num_reactions  num_comments  num_shares  num_likes  num_loves  num_wows  \\\n",
       "0       2.324257     22.086957       65.50   2.229508  30.666667       3.0   \n",
       "1       0.448020     -0.173913        0.00   0.548435   0.000000       0.0   \n",
       "2       0.829208     10.086957       14.25   0.870343   7.000000       1.0   \n",
       "3       0.254950     -0.173913        0.00   0.315946   0.000000       0.0   \n",
       "4       0.759901     -0.173913        0.00   0.870343   3.000000       0.0   \n",
       "\n",
       "   num_hahas  num_sads  num_angrys  link  photo  status  video  \\\n",
       "0        1.0       1.0         0.0     0      0       0      1   \n",
       "1        0.0       0.0         0.0     0      1       0      0   \n",
       "2        1.0       0.0         0.0     0      0       0      1   \n",
       "3        0.0       0.0         0.0     0      1       0      0   \n",
       "4        0.0       0.0         0.0     0      1       0      0   \n",
       "\n",
       "   Cluster K-means  \n",
       "0                0  \n",
       "1                0  \n",
       "2                0  \n",
       "3                0  \n",
       "4                0  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_cluster = df_def.copy()\n",
    "\n",
    "df_cluster['Cluster K-means'] = labels\n",
    "df_cluster.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "c2799fa3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    6741\n",
       "1     309\n",
       "Name: Cluster K-means, dtype: int64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_cluster['Cluster K-means'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "e1685d8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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xEbNvBwq5wJctW3bF15966qmwhYEzxcf3Vm7up/L7fXK53FyHAyIoOrqlpk17yeoYMEHIBf5/PwNeVVWlL7/8Ug899JApoeAsXu8Qbd588VJLIBBgJgAAYRBygc+bN6/W+OTJkxFfBx32ZRjG/9yFbnUSAHCGG34aWatWrVRcXBzOLHCo7OwsGf/T3IZhsJgEAITBDV0DDwQC2r17t1q3bm1KKDjLxcUkfJIkn8/HTWwAEAY3dA3cMAy1bdtW06ZNMyUUnIXFJAAg/EI+hZ6SkqKioiLt2bNHu3fvVm5ursaOHXvN71myZImSk5OVnJys1157TZKUn58vr9erfv36KT09/ebSwxZYTAIAwi/kGfjLL7+sYcOGqXPnzsHrmdeSn5+vvLw8ZWVdvP45duxYrVu3TgsXLtR7772n22+/XRMmTFBubq6SkpJu6odA/cZiEgAQfiEXeKNGjer0me+YmBhNmzZNjRs3liTdddddKiwsVIcOHdSuXTtJktfrVU5ODgXeALCYBACEV8gFfs899+irr75Sp06dQt7+ksLCQq1fv15PPPGEYmJigq/HxsaqpKSkDnGl1q2b1Wl71A8xMbfpjTdetzoGADhGyAV++PBhDRs2TG3atFGTJk2Cr19aI/1q9u3bpwkTJui3v/2tPB6PDhw4UOvroZyO/7/KyiqCz7eFfWzblq933lmiSZOm6sEHe1odBwDqPZfLuOakNeQCT0tLq/Obf/nll5o6daqmT5+u5ORkbd++XSdOnAh+vbS0VLGxsXXeL+znP/7jbUlSRsZSChwAwiDkAu/Ro0eddnz06FFNmTJF6enpio+PlyTdd999OnDggA4ePKg77rhD69at07Bhw+qWGLazbVu+fL4aSZLPV6PPP/+MEgeAm2QELj2oOcxeeeUVffzxx2rfvn3wtREjRujOO+/UvHnzdOHCBSUlJemFF16o02l0TqHbz7hxqcEClyS326M//OFdCxMBQP13vVPophW4WShw+xkzZtRlr/3pTystSAIA9nG9Ar/htdCBULndnmuOAQB1R4HDdGPHTqw1Hj9+skVJAMA5KHCY7qGHegVn3W63hxvYACAMKHBExKVZOLNvAAgPbmIDAKAe4iY21Avl5ac0f/4cnT5dbnUUoEHh2HMuChwRkZ2dpX37vtLatZlWRwEaFI4956LAYbry8lPKy8tVIBBQXt4WZgJAhHDsORsFDtNlZ2cF71vw+/3MBIAI4dhzNgocpiso2FprLfSCgq0WJwIaBo49Z6PAYbr4+N61PgceH9/b4kRAw8Cx52wUOEzn9Q6Ry3XxgTUul0uDBw+1OBHQMHDsORsFDtNFR7dUQkKSDMNQQkKiWrSItjoS0CBw7DkbT5VARHi9Q1RcXMQMAIgwjj3nYiU2AADqIVZiAwDAgShwAABsiAIHAMCGKHAAAGyIAkdE8EQkAAgvChwRwRORACC8KHCYjiciAUD4UeAwHU9EAoDwo8BhOp6IBADhR4HDdBefiOSWJLndbp6IBABhQIHDdF7vEPl8PkmSz+djTWYACAMKHKb77rvT1xwDAOqOAofpMjJ+X2v8zjtLLEoCAM5BgcN0R44UX3MMAKg7Chyma9Om7TXHAIC6o8BhuvHjp9QaT5jwtEVJAMA5KHAAAGyIAofpuIkNAMKPAofpuIkNAMKPAofpuIkNAMKPAofpuIkNAMKPAofpmjdvcc0xAKDuKHCYLjs7S4Zx8Y+aYbh4nCgAhAEFDtMVFGxVIOCXJAUCfh4nCkTQoUOFmjLllzp8+KDVURBmphd4RUWFBg0apKKiIklSfn6+vF6v+vXrp/T0dLPfHvXA9x8fyuNEgcjJyPi9Kisr+fimA5la4Dt37tTIkSNVWFgoSTp//rymT5+upUuXav369dqzZ49yc3PNjIB6oG3bdrXG7dt3sCgJ0LAcOlQY/NjmkSPFzMIdxtQC//DDDzVr1izFxsZKknbt2qUOHTqoXbt28ng88nq9ysnJMTMC6oG//OW9WuMVK5ZblARoWFhEydk8Zu587ty5tcalpaWKiYkJjmNjY1VSUlKnfbZu3Sws2RA5Pl/NZeOYmNssSgM0HFdaRIljzzlMLfDvCwQCl71mGEad9lFWViG///L9oP5yuz21Stzt9uj48TMWJgIahjZt2tYq8TZt2nLs2YjLZVxz0hrRu9Dj4uJ04sSJ4Li0tDR4eh3ONXbsxFrj8eMnW5QEaFhYRMnZIlrg9913nw4cOKCDBw/K5/Np3bp1SkxMjGQEWOChh3rJ7b54ssft9ujBB3tanAhoGFhEydkiWuBNmjTR/Pnz9cwzz2jgwIHq2LGjBgwYEMkIsMilWTizbyBysrOz5Ha7JUlut5tFlBzGCFzpwnQ9xjVwAAjN5Mm/1PnzlcHxLbdEaenSP1qYCHVRr66Bo+H66KO/asyYUcrK+tDqKECDER/fWy7Xxb/mXS4Xiyg5DAWOiPjP/1wrScrOXm1tEKAB8XqHyO+/uIyx3+/X4MFDLU6EcKLAYbqPPvprrTGzcCAy/uu/vqg1/u///tKiJDADBQ7TXZp9X8IsHIiMFSv+XGu8fPmfrAkCU1DgAOBY37/hlxuAnYQCBwDH+v5Kl3Vb+RL1GwUO0/3sZ4Nrjb3eFGuCAA3Mv//7k7XGo0ePsSYITEGBw3SdO3euNe7UqfNVtgQQTo880lf/O+s2lJT0qJVxEGYs5ALTPf30OJ07dzY4btr0Vi1Z8gcLEwE3ZuvWLcrLy7U6Rp0UFxepouKMYmPj1LJlK6vjhCwhIUm9ezfspbZZyAWW+7/lfaUxAPP4fD5FRTW1VXkjNBF9nCgapqZNb71sBg7YUe/eibabFS5Y8LIk6be/nWlxEoQbM3CYbtKkZ2qNJ09+1qIkAOAcFDhMV1BQUGu8fXvBVbYEAISKAofp8vNr3/SzZcunFiUBAOegwAEAsCEKHAAAG6LAYbpevZJqjRMTH7YoCQA4BwUO0zVp0uSaYwBA3VHgMN2nn26oNd64MceiJADgHBQ4AAA2RIEDAGBDFDhM9/DD/WqN+/YdYFESAHAOChym27fv62uOAQB1R4HDdEVFhbXGhYX7rQkCAA5CgQMAYEMUOAAANkSBAwBgQx6rAwBouFaufFeHDx+0OoajHTp08fd3wYKXLU7ibO3addCoUakRfU8KHIBlDh8+qMJv9uoHzfiryCxN5ZcknT/2jcVJnOtYRY0l78tRA8BSP2jm0VNdW1kdA7hhy3adtOR9uQYO0zVq1LjWuHFjHmYCADeLAofpqqurao2rqi5YlAQAnIMCBwDAhihwAABsiAIHAMCGKHAAAGyIAgcAwIb4HDgAy5w+Xa5TFTWWfY4WCIdjFTVqebo84u/LDBwAABtiBg7AMi1aRKtJ5QlWYoOtLdt1Ure0iI74+1oyA8/OztbAgQPVt29fvf/++1ZEAADA1iJe4CUlJUpPT9fKlSu1Zs0affDBB/rmGxbZd7I//WnlNccAgLqL+Cn0/Px89ezZU9HR0ZKk/v37KycnR08//XSko0iStm7dopUr37XkvW9UVdUF+Xw+q2PcsDFjRlkdISRut9t267aPGpWq3r0TrY5RJ8dsdBNbRZVfFVV+q2M0CM0au9SssT1u0zpWUaM7LXjfiBd4aWmpYmJiguPY2Fjt2rUr5O9v3bpZWPM0bx4lwwjrLk1n2C2wTRmGYbs/G82bRykm5jarY4SsU6d71KiR2+oYIas5dUqVp05ZHaNBuKVlS93WsqXVMUJym6SOHTtG/NiLeIEHAoHLXqtLIZWVVcjvv3wfN+rf/u1BLVnyYNj2B1jt+PEzVkcIWUrKCKsjAGET7mPP5TKuOWmN+PmJuLg4nThxIjguLS1VbGxspGMAAGBrES/wXr16qaCgQCdPnlRlZaU2bNigxER7XbMDAMBqET+FHhcXp7S0NKWmpqq6ulrDhw9X165dIx0DAABbMwJXuihdj4X7GjgAAPVRvbsGDgAAbh4FDgCADVHgAADYEAUOAIANUeAAANiQ7R4n6nLZbG1LAABuwPX6znYfIwMAAJxCBwDAlihwAABsiAIHAMCGKHAAAGyIAgcAwIYocAAAbIgCBwDAhihwAABsiAIHAMCGKHAAAGyIAofpsrOzNXDgQPXt21fvv/++1XGABqWiokKDBg1SUVGR1VEQZhQ4TFVSUqL09HStXLlSa9as0QcffKBvvvnG6lhAg7Bz506NHDlShYWFVkeBCShwmCo/P189e/ZUdHS0mjZtqv79+ysnJ8fqWECD8OGHH2rWrFmKjY21OgpMYLvHicJeSktLFRMTExzHxsZq165dFiYCGo65c+daHQEmYgYOU13pabWGwTPdAeBmUeAwVVxcnE6cOBEcl5aWcjoPAMKAAoepevXqpYKCAp08eVKVlZXasGGDEhMTrY4FALbHNXCYKi4uTmlpaUpNTVV1dbWGDx+url27Wh0LAGzPCFzpIiUAAKjXOIUOAIANUeAAANgQBQ4AgA1R4AAA2BAFDgCADVHggEV8Pp+WLVumoUOH6rHHHtPAgQP1+uuvq6qqSpI0bdo0/fGPf7zh/Y8ZM0YnT568qYzfz3DmzBk9/vjjmjp1qi5cuHBT+wZwcyhwwCKzZ8/Wjh07tHz5cq1Zs0arVq3SgQMH9OKLL4Zl/1u3bg3Lfi4pKytTamqqOnXqpDfffFNNmjQJ6/4B1A0LuQAWOHz4sLKzs5WXl6dmzZpJkpo2barf/e532rFjx2Xbd+rUSQUFBWrVqlWtcZMmTfTCCy/o4MGDcrlc6tKli+bMmRP8R8Do0aOVkZEhl8ulOXPm6OjRo6qurlZycrImTpyooqIiPf7447rrrrtUXFys995774pL3R45ckRjxoxRSkqKJk6ceNWf64knnlCXLl302WefBQu/rKxM27dvV2Vlpd5880116tRJZ86c0dy5c/X111+rurpa8fHxev755+XxeLRq1Sp98MEHqq6u1unTpzVu3DiNGjVKmZmZ2rhxo1wulw4ePKhGjRppwYIF+uEPf6gNGzborbfekmEYcrvdev755/Xggw+G438VUG8xAwcs8M9//lN33313sLwviYmJUb9+/ULez8aNG3X27NngDF66+I+DefPmSZKWL1+u22+/Xc8995yGDRumzMxMrVq1Svn5+Vq/fr0k6dixY5o8ebI++eSTK5b3gQMHNGrUKFVVVWn06NHXzVRcXKzVq1dryZIlWrhwoXr06KHMzEz16dNHK1askCS9+uqr6tKlizIzM7V69WqdOnVKy5Yt09mzZ/XRRx8pIyNDq1evVnp6ul5//fXgvj///HPNnDlT69at0wMPPBA8vf/aa69p1qxZyszM1LPPPqtt27aF/HsI2BUzcMACLpdLfr//pvfTvXt3paen64knnlCvXr00evRodejQodY2586d0+eff67Tp09r0aJFwdf27t2rrl27yuPxqFu3bld9j+zsbKWnp+v999/XjBkz9MYbb1wzU9++fSVJ7dq1kyT16dNHktS+fXtt375dkrR582bt3r07+I+O8+fPS5JuvfVWvf3228rNzVVhYaH27t2rc+fOBffdpUsX/eAHP5Akde7cWRs3bpQkJScn6+mnn1ZSUpJ69+6tcePGXf83D7A5ChywQNeuXbV//35VVFTUmoWXlJRo5syZWrx48VW/99JNbtLFkty4caO2bdumzz77TE899ZRmzJihAQMGBLfx+/0KBAL661//qqioKEnSyZMn1aRJE506dUqNGzeWx3P1vwomTpyoRx55RN26dVNKSoqWLVump556SiUlJRo/fnxwu4yMDElS48aNa31/o0aNLtun3+/XokWLdNddd0mSvvvuOxmGoWPHjukXv/iFfv7zn6t79+4aMGCAPv300+D33XLLLcH/Ngwj+LjatLQ0DR8+XHl5ecrMzFRGRoYyMzPlcnGSEc7Fn27AAnFxcfJ6vZo+fboqKiokSRUVFZo9e7aio6NrFZUktWrVSrt375ak4KxTklauXKkXXnhBCQkJeu6555SQkKB9+/ZJktxut2pqatSsWTN169ZNy5Ytk3SxLEeOHKlNmzaFlPVSIbdq1Urp6elKT0/Xtm3bFBcXpzVr1gR/xcXFhfzzJyQk6M9//rMCgYCqqqo0adIkrVixQnv27FGrVq00efJk9enTJ1jePp/vqvuqqanRI488onPnzmnkyJGaNWuWvv32W9XU1IScB7AjZuCARWbNmqWlS5dqxIgRcrvdqqqq0k9/+lM988wzl207Y8YMzZkzR82bN1evXr0UExMjSUpJSdH27ds1cOBARUVFqU2bNkpNTZV08VT2qFGjtHTpUi1cuFAvv/yyvF6vqqqqNGjQIA0ePFhFRUV1yty9e3dNnTpVaWlpyszMDJ7OrqsXX3xRc+fOldfrVXV1tXr16qWxY8eqpqZGq1at0oABAxQVFaWuXbuqVatWOnjw4FX35fF4NH36dP3mN7+Rx+ORYRh69dVXLzsTADgNTyMDAMCGOIUOAIANUeAAANgQBQ4AgA1R4AAA2BAFDgCADVHgAADYEAUOAIAN/X+ACrscPaARwwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/rgGvqanR3r171bdvX9NCIfBUVlbo9df/jx5/fJratQuzOg4A2J5XBf7SSy81GJ8+fdqS66DDvrKzN+jIkUP66KMsjRv3qNVxAMD2rupuZOHh4Tpx4oSvsyBAVVZWKC8vVx6PR3l5n6qqqtLqSABge40+B+7xeHTgwAF16NDBtFAILNnZG+q/eOh2u5mFA4APNPocuGEYuummmzRjxgzTQiGwFBTskMtVJ0lyuepUULCDAgeAJvLqEHpCQoJKSkpUWFioAwcOKDc3VxMmTDA7GwJE//4DFBR04WfFoKBg9e8/wOJEAGB/Xs3AX3jhBT344IO67bbbZBiG2ZkQYJzOUcrLy5XLJTkcDo0c+YDVkQDA9rwq8FatWrHmG1ctLKy9Bg6M1fbtH2vgwBiWkQGAD3h1CL179+46dOiQ2VkQwJzOUerevQezbwDwEa8upZqUlKQDBw6oY8eOatOmTf3j2dnZpoa7GC6lCgBoCXxyKdXU1FSfBQIAAE3HzUwAAGiGrjQDv6orsQEAAGtR4AAA2BAFDgCADVHgAADYEAUOv6isrNCCBXO5ExkA+IipBV5dXa0RI0aopKREkpSfny+n06m4uDhlZGSYuWs0M/96P3AAQNOZVuD79u1TUlKSioqKJEk//PCD0tLStHz5cm3evFmFhYXKzc01a/doRrgfOAD4nmkFvm7dOqWnpysyMlKStH//fnXp0kWdOnVScHCwnE6ntmzZYtbu0Yxc7H7gAICm8epKbFdj3rx5DcZlZWWKiIioH0dGRurkyZON3u7lFrWjedq5s+H9wHfu3KHf//4pi1MBgL2ZVuD/7mIXfLuaW5NyJTb76ddvgD79dLtcrjoFBQWrX78B+vbbM1bHAoBmrdlciS0qKkqnTp2qH5eVldUfXkdgczpHyeG48MMa9wMHAN/wW4HfcccdOnbsmIqLi+VyubRp0ybFxMT4a/ew0I/3AzcMg/uBA4CP+K3A27RpowULFmjq1KkaPny4unbtqmHDhvlr97BYbOxgXXPNNbrnnv+0OgoABATuRga/WLXqbW3f/rHuuec/NW7co1bHAYBmr9mcA0fLxTpwAPA9ChymYx04APgeBQ7TFRQ0XAdeULDD4kQAYH8UOEzXv/8ABQVduORAUFCw+vcfYHEiALA/ChymYx04APgeBQ7TsQ4cAHyPAodf9OnzvyVJd911t8VJgJalsrJCCxbMZfVHAKLA4Rf//d+r5PF4tGbNu1ZHAVqU7OwNOnLkEKs/AhAFDtMdP16k0tITkqTS0hP66qtiixMBLQPXYAhsFDhMl5m5rMH4jTeWWpQEaFm4BkNgo8Bhuh9n35caAzAH12AIbBQ4TNex402XHQMwB9dgCGwUOEw3adKUBuOUlCctSgK0LFyDIbBR4DBd584318+6O3a8SZ06dbE4EdAycA2GwEaBwy+czlGSpPvvf9DiJEDL4nSOUvfuPZh9ByAKHH6Rnb1BkvThhx9YnARoWcLC2mvGjP9i9h2AKHCYjnXgAOB7FDhMxzpwAPA9ChymYx04APgeBQ7TsQ4cAHyPAofpWAcOAL5HgcN0rAMHAN+jwOEXrAMHrHH8eJGmTHmM1R8BiAKHX7AOHLBGZuYynTt3jtUfAYgCh+lYBw5Yg89eYKPAYTrWgQPW4LMX2ChwmI514IA1+OwFNgocpmMdOGANPnuBjQKH6VgHDliDz15go8BhOtaBA9bgsxfYKHD4RVLSOBmGoTFjHrY6CtCiTJo0RSEhIcy+A1CwFTtNTk5WeXm5goMv7H7u3Lm64447rIgCP/mf/9kjSdq7d7duu+1/WZwGaDk6d75Zy5a9ZXUMmMDvBe7xeHT06FFt3769vsAR2CorK5SXlyuPx6O8vE81cuQDatcuzOpYAGBrfm/Qo0ePyjAMTZw4UeXl5XrooYf0u9/9zt8x4EfZ2RvkdnskSW63Wx99lKVx4x61OBXQeDt2fKq8vFyrYzRKVVWlJNnqh+aBA2M1YECM1TGaPb8X+Hfffaf+/ftrzpw5+uGHH5ScnKxf/OIXGjBggFfv79Ah1OSE8LWdO3fI5aqTJLlcddq5c4d+//unLE4FNN7114eoVasgq2M0ynffVUmSfvazDhYn8d7114coIuI6q2M0e4bH4/FYGeCdd95RaWmp0tLSvHp9eXl1/WwO9rBq1dv69NPtcrnqFBQUrJiYe5iBA36ycOELkqTnnpttcRI0lsNhXHbS6vdvoe/Zs0cFBQX1Y4/Hw7nwAOd0jpLDYUiSHA6HRo58wOJEAGB/fi/wM2fO6OWXX9b58+dVXV2tDRs2aMiQIf6OAT8KC2uvgQNjZRiGBg6MsdW5OABorvw+9b333nu1b98+JSQkyO12a8yYMbrzzjv9HQN+duZMtTwej86dO2t1FAAICJYcu3766af19NNPW7FrWGTPnp2SpJ078zVpEheUAICm4kpsMN2bb77RYPzOO//XoiQAEDgocJguP7/hutlPP/3EoiQAEDgocAAAbIgCBwDAhihwmC46OrbBOCbmXouSAEDgoMBhugkTUhqMH3lkokVJACBwUODwi+uuaydJateuvcVJACAwUODwizNnLtxQoaqqwuIkABAYKHCY7pVXXmowzshYaFESAAgcFDhM949/HGgwPnBgn0VJACBwUOAAANgQBQ4AgA1R4DDdf/zH7Q3Gt99+h0VJACBwUOAw3bPPzmwwTk19zqIkABA4KHAAAGyIAgcAwIYocJjuscd+12A8YcI4i5IAQOAItjoAAp/H424wdrtdFiVBc7JmzUp99VWx1TEC3vHjF/6MFy58weIkga1Tpy4aMybZr/ukwAFY4quvilX0z4O6IZR/hszUVhd+gP7hm39anCRwfVNdZ8l++eQAsMwNocEa3yvc6hhAk6zYf9qS/XIOHKYzjIZ/zRyOIIuSAEDgoMBhurfeWt1g/OabqyxKAgCBgwIHAMCGKHAAAGyIAofpHn10zGXHAIDG41voACxRVVWpiuo6y77BC/jKN9V1al9V6ff9MgMHAMCGmIEDsES7dmFqc+4U68Bheyv2n9Y17cL8vl9m4AAA2BAFDtO9/faay44BAI1HgQMAYEOWnAPPzs7Wa6+9ptraWj3yyCMaO3asFTHgR8y6AcC3/F7gJ0+eVEZGhrKystS6dWslJiaqb9++uuWWW/wdBQAA2/J7gefn56tfv34KCwuTJA0dOlRbtmzRk08+6e8okqQdOz7VmjUrLdn31aqpOS+Xi3tqmy0oKEitW7exOkajjBmTrAEDYqyO4bVvbLYOvLrGreoa95VfiCYJbe1QaGv7nOH9prpON1uwX78XeFlZmSIiIurHkZGR2r9/v9fv79Ah1Kd5rr8+RIbh002azrBbYJsyDMN2fzeuvz5EERHXWR3DKz16dFerVva6M11dRYXOVVRYHSPgXdO+va5r397qGF67TlLXrl39/tnze4F7PJ6fPNaYQiovr5bb/dNtXK3bb/+Vli79lc+2B1jt22/PWB3BKwkJiVZHAHzK1589h8O47KTV78cooqKidOrUqfpxWVmZIiMj/R0DAABb83uBR0dHq6CgQKdPn9a5c+e0bds2xcTY55wdAADNgd8PoUdFRSk1NVXJycmqra3V6NGj1atXL3/HAADA1gzPxU5KN2O+PgcOAEBz1OzOgQMAgKajwAEAsCEKHAAAG6LAAQCwIQocAAAbsuRuZE3hcNjs2pYAAFyFK/Wd7ZaRAQAADqEDAGBLFDgAADZEgQMAYEMUOAAANkSBAwBgQxQ4AAA2RIEDAGBDFDgAADZEgQMAYEMUOAAANkSBw3TZ2dkaPny4hgwZovfee8/qOECLUl1drREjRqikpMTqKPAxChymOnnypDIyMrRmzRp9+OGHWrt2rf75z39aHQtoEfbt26ekpCQVFRVZHQUmoMBhqvz8fPXr109hYWFq27athg4dqi1btlgdC2gR1q1bp/T0dEVGRlodBSaw3e1EYS9lZWWKiIioH0dGRmr//v0WJgJajnnz5lkdASZiBg5TXexutYbBPd0BoKkocJgqKipKp06dqh+XlZVxOA8AfIACh6mio6NVUFCg06dP69y5c9q2bZtiYmKsjgUAtsc5cJgqKipKqampSk5OVm1trUaPHq1evXpZHQsAbM/wXOwkJQAAaNY4hA4AgA1R4AAA2BAFDgCADVHgAADYEAUOAIANUeCABVwul1asWKEHHnhA999/v4YPH65XXnlFNTU1kqQZM2borbfeuurtP/roozp9+nSTMv57hjNnzmjs2LGaNm2azp8/36RtA2g6ChywwJw5c/T555/r3Xff1Ycffqj169fr2LFjev75532y/R07dvhkOz8qLy9XcnKyevTooVdffVVt2rTx6fYBNB4XcgH87KuvvlJ2drby8vIUGhoqSWrbtq3++Mc/6vPPP//J63v06KGCggKFh4c3GLdp00YzZ85UcXGxHA6Hevbsqblz59b/EPDwww8rMzNTDodDc+fO1ddff63a2lrFx8dr8uTJKikp0dixY9WtWzedOHFCq1atuuhlbktLS/Xoo48qISFBkydPvuTva9y4cerZs6d27txZX/jl5eXavXu3zp07p1dffVU9evTQmTNnNG/ePB0+fFi1tbXq37+/pk+fruDgYK1fv15r165VbW2tqqqqNHHiRI0ZM0ZZWVnKycmRw+FQcXGxWrVqpYULF+rWW2/Vtm3b9Nprr8kwDAUFBWn69On61a9+5Yv/VUCzxgwc8LMvvvhCt9xyS315/ygiIkJxcXFebycnJ0fff/99/QxeuvDDwUsvvSRJevfdd3XjjTfq2Wef1YMPPqisrCytX79e+fn52rx5syTpm2++0RNPPKGtW7detLyPHTumMWPGqKamRg8//PAVM504cUIbN27U0qVLtWjRIt19993KysrSoEGDtHr1aknS/Pnz1bNnT2VlZWnjxo2qqKjQihUr9P333+v9999XZmamNm7cqIyMDL3yyiv12/7ss880e/Zsbdq0SX369Kk/vP/yyy8rPT1dWVlZeuqpp7Rr1y6v/wwBO2MGDviZw+GQ2+1u8nbuuusuZWRkaNy4cYqOjtbDDz+sLl26NHjN2bNn9dlnn6mqqkqLFy+uf+zgwYPq1auXgoOD1bt370vuIzs7WxkZGXrvvfc0a9Ys/elPf7pspiFDhkiSOnXqJEkaNGiQJKlz587avXu3JGn79u06cOBA/Q8dP/zwgyTp2muv1euvv67c3FwVFRXp4MGDOnv2bP22e/bsqRtuuEGSdNtttyknJ0eSFB8fryeffFKxsbEaMGCAJk6ceOU/PCAAUOCAn/Xq1UtHjx5VdXV1g1n4yZMnNXv2bC1ZsuSS7/3xS27ShZLMycnRrl27tHPnTo0fP16zZs3SsGHD6l/jdrvl8Xj05z//WSEhIZKk06dPq02bNqqoqFDr1q0VHHzpfwYmT56swYMHq3fv3kpISNCKFSs0fvx4nTx5UpMmTap/XWZmpiSpdevWDd7fqlWrn2zT7XZr8eLF6tatmyTpu+++k2EY+uabb/Tb3/5WDz30kO666y4NGzZMn3zySf37rrnmmvr/Ngyj/la1qampGj16tPLy8pSVlaXMzExlZWXJ4eAAIwIbf8MBP4uKipLT6VRaWpqqq6slSdXV1ZozZ47CwsIaFJUkhYeH68CBA5JUP+uUpDVr1mjmzJkaOHCgnn32WQ0cOFBHjhyRJAUFBamurk6hoaHq3bu3VqxYIelCWSYlJenjjz/2KuuPhRweHq6MjAxlZGRo165dioqK0ocfflj/Kyoqyuvf/8CBA/XOO+/I4/GopqZGjz/+uFavXq3CwkKFh4friSee0KBBg+rL2+VyXXJbdXV1Gjx4sM6ePaukpCSlp6fryy+/VF1dndd5ALtiBg5YID09XcuXL1diYqKCgoJUU1Oj++67T1OnTv3Ja2fNmqW5c+fq+uuvV3R0tCIiIiRJCQkJ2r17t4YPH66QkBB17NhRycnJki4cyh4zZoyWL1+uRYsW6YUXXpDT6VRNTY1GjBihkSNHqqSkpFGZ77rrLk2bNk2pqanKysqqP5zdWM8//7zmzZsnp9Op2tpaRUdHa8KECaqrq9P69es1bNgwhYSEqFevXgoPD1dxcfEltxUcHKy0tDQ988wzCg4OlmEYmj9//k+OBACBiLuRAQBgQxxCBwDAhihwAABsiAIHAMCGKHAAAGyIAgcAwIYocAAAbIgCBwDAhv4fDzcsni1zbqkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "columns = df_cluster.columns[:-1]\n",
    "\n",
    "for i in columns:\n",
    "    plt.figure()\n",
    "    plt.tight_layout()\n",
    "    sns.set(rc={\"figure.figsize\":(8, 5)})\n",
    "    plt.gca().set(xlabel= i,ylabel='Frequency')\n",
    "    sns.boxplot(x='Cluster K-means', y=i, data=df_cluster)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "340aae03",
   "metadata": {},
   "source": [
    "- **Cluster 0:** Videos y fotos\n",
    "- **Cluster 1:** Con mas comentarios, más likes, mas reacciones en general (hahaha, loves, angrys)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e922b9e",
   "metadata": {},
   "source": [
    "## Exercici 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f4ec767",
   "metadata": {},
   "source": [
    "#### Classifica els diferents registres utilitzant l'algorisme de clustering jeràrquic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "092c6aa7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.cluster.hierarchy as shc\n",
    "from sklearn.cluster import AgglomerativeClustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "f1ac64ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (16, 7))  \n",
    "plt.title(\"Dendrogram\")  \n",
    "shc.dendrogram(shc.linkage(df_cluster, method = \"ward\"))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34d7f91e",
   "metadata": {},
   "source": [
    "El dendrograma nos representa 2 clusters (primera división azu), igual que nos da el K-means, por lo que coinciden"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "97b84949",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\flore\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\sklearn\\cluster\\_agglomerative.py:983: FutureWarning: Attribute `affinity` was deprecated in version 1.2 and will be removed in 1.4. Use `metric` instead\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, ..., 1, 1, 1], dtype=int64)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aglom = AgglomerativeClustering(n_clusters=2, affinity='euclidean', linkage='ward')  \n",
    "aglom.fit(df_cluster)\n",
    "\n",
    "predicts_aglo = aglom.labels_\n",
    "\n",
    "predicts_aglo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "147e322c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>num_reactions</th>\n",
       "      <th>num_comments</th>\n",
       "      <th>num_shares</th>\n",
       "      <th>num_likes</th>\n",
       "      <th>num_loves</th>\n",
       "      <th>num_wows</th>\n",
       "      <th>num_hahas</th>\n",
       "      <th>num_sads</th>\n",
       "      <th>num_angrys</th>\n",
       "      <th>link</th>\n",
       "      <th>photo</th>\n",
       "      <th>status</th>\n",
       "      <th>video</th>\n",
       "      <th>Cluster K-means</th>\n",
       "      <th>Cluster Agglomerative</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.324257</td>\n",
       "      <td>22.086957</td>\n",
       "      <td>65.50</td>\n",
       "      <td>2.229508</td>\n",
       "      <td>30.666667</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.448020</td>\n",
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       "      <td>0.00</td>\n",
       "      <td>0.548435</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.829208</td>\n",
       "      <td>10.086957</td>\n",
       "      <td>14.25</td>\n",
       "      <td>0.870343</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.254950</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.315946</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.759901</td>\n",
       "      <td>-0.173913</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.870343</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   num_reactions  num_comments  num_shares  num_likes  num_loves  num_wows  \\\n",
       "0       2.324257     22.086957       65.50   2.229508  30.666667       3.0   \n",
       "1       0.448020     -0.173913        0.00   0.548435   0.000000       0.0   \n",
       "2       0.829208     10.086957       14.25   0.870343   7.000000       1.0   \n",
       "3       0.254950     -0.173913        0.00   0.315946   0.000000       0.0   \n",
       "4       0.759901     -0.173913        0.00   0.870343   3.000000       0.0   \n",
       "\n",
       "   num_hahas  num_sads  num_angrys  link  photo  status  video  \\\n",
       "0        1.0       1.0         0.0     0      0       0      1   \n",
       "1        0.0       0.0         0.0     0      1       0      0   \n",
       "2        1.0       0.0         0.0     0      0       0      1   \n",
       "3        0.0       0.0         0.0     0      1       0      0   \n",
       "4        0.0       0.0         0.0     0      1       0      0   \n",
       "\n",
       "   Cluster K-means  Cluster Agglomerative  \n",
       "0                0                      1  \n",
       "1                0                      1  \n",
       "2                0                      1  \n",
       "3                0                      1  \n",
       "4                0                      1  "
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_cluster['Cluster Agglomerative'] = predicts_aglo\n",
    "df_cluster.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "2eac3020",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "columns_aglo = df_cluster.columns[:-2]\n",
    "   \n",
    "for i in columns_aglo:\n",
    "    plt.figure()\n",
    "    plt.tight_layout()\n",
    "    sns.set(rc={\"figure.figsize\":(8, 5)})\n",
    "    plt.gca().set(xlabel= i,ylabel='Frequency')\n",
    "    sns.boxplot(x='Cluster Agglomerative', y=i, data=df_cluster)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38709a1c",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "c04c3a6d",
   "metadata": {},
   "source": [
    "## Exercici 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fdda5e8",
   "metadata": {},
   "source": [
    "#### Calcula el rendiment del clustering mitjançant un paràmetre com pot ser silhouette."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "470d21be",
   "metadata": {},
   "source": [
    "El **Silhouette Score** es una métrica utilizada para evaluar la calidad de un clustering. Esta métrica mide cuán similar es un registro con su propio cluster en comparación con los demás clusters.\n",
    "\n",
    "Tiene un rango de valores entre -1 y 1. Un valor de 1 indica que los registros están muy próximos a los registros de su propio cluster y muy alejados de los registros de los demás clusters, lo que indica una buena calidad de clustering. Un valor de 0 indica que los registros están en la frontera entre dos clusters, mientras que un valor negativo indica que los registros están más próximos a los registros de otro cluster que a los de su propio cluster, lo que indica una mala calidad de clustering."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "2a11bfa2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import silhouette_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "c3cc4a71",
   "metadata": {},
   "outputs": [],
   "source": [
    "score_km = silhouette_score(df_cluster, labels, metric='euclidean')\n",
    "\n",
    "score_aglo = silhouette_score(df_cluster, predicts_aglo, metric='euclidean')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "51403d1d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8892568499677126"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score_km"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "09c81b5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8917391806890405"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score_aglo"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9db23b37",
   "metadata": {},
   "source": [
    "Podemos ver como los valores se aproximan a 1 en ambos casos, por lo que nos están dando bien, no hay mucha diferencia entre ellos, pero si tuviesemos que elegir, nos quedaríamos con K-means"
   ]
  }
 ],
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