K-Prototype Clustering on Blood Transfusion Dataset.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Problem Statement**<br><br>\n",
    "To demonstrate the RFMTC marketing model (a modified version of RFM), this study adopted the donor database of Blood Transfusion Service Center in Hsin-Chu City in Taiwan. The center passes their blood transfusion service bus to one university in Hsin-Chu City to gather blood donated about every three months. To build a FRMTC model, we selected 748 donors at random from the donor database. These 748 donor data, each one included R (Recency - months since last donation), F (Frequency - total number of donation), M (Monetary - total blood donated in c.c.), T (Time - months since first donation), and a binary variable representing whether he/she donated blood in March 2007 (1 stand for donating blood; 0 stands for not donating blood)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Attribute Information:**\n",
    "\n",
    "- R (Recency - months since last donation), \n",
    "- F (Frequency - total number of donation), \n",
    "- M (Monetary - total blood donated in c.c.), \n",
    "- T (Time - months since first donation), and a binary variable representing whether he/she donated blood in March 2007 (1 stand for donating blood; 0 stands for not donating blood). \n",
    "\n",
    "- Variable\tData Type\tMeasurement\tDescription\tmin\tmax\tmean\tstd \n",
    "- Recency quantitative\tMonths\tInput\t0.03\t74.4\t9.74\t8.07 \n",
    "- Frequency quantitative\tTimes\tInput\t1\t50\t5.51\t5.84 \n",
    "- Monetary\tquantitative\tc.c. blood\tInput\t250\t12500\t1378.68\t1459.83 \n",
    "- Time quantitative\tMonths\tInput\t2.27\t98.3\t34.42\t24.32 \n",
    "- Whether he/she donated blood in March 2007\tbinary\t1=yes 0=no\tOutput\t0\t1\t1 (24%) 0 (76%) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing Libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from kmodes.kprototypes import KPrototypes\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#help(KPrototypes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reading Dataset\n",
    "blood = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/blood-transfusion/transfusion.data', sep=\",\",engine = 'python')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Recency (months)</th>\n",
       "      <th>Frequency (times)</th>\n",
       "      <th>Monetary (c.c. blood)</th>\n",
       "      <th>Time (months)</th>\n",
       "      <th>whether he/she donated blood in March 2007</th>\n",
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       "      <th>4</th>\n",
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      "text/plain": [
       "   Recency (months)  Frequency (times)  Monetary (c.c. blood)  Time (months)  \\\n",
       "0                 2                 50                  12500             98   \n",
       "1                 0                 13                   3250             28   \n",
       "2                 1                 16                   4000             35   \n",
       "3                 2                 20                   5000             45   \n",
       "4                 1                 24                   6000             77   \n",
       "\n",
       "   whether he/she donated blood in March 2007  \n",
       "0                                           1  \n",
       "1                                           1  \n",
       "2                                           1  \n",
       "3                                           1  \n",
       "4                                           0  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Sanity Check\n",
    "blood.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# standardizing data\n",
    "columns_to_normalize = ['Recency (months)','Frequency (times)','Monetary (c.c. blood)','Time (months)']\n",
    "blood[columns_to_normalize] = blood[columns_to_normalize].apply(lambda x: (x - x.mean()) / np.std(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>Recency (months)</th>\n",
       "      <th>Frequency (times)</th>\n",
       "      <th>Monetary (c.c. blood)</th>\n",
       "      <th>Time (months)</th>\n",
       "      <th>whether he/she donated blood in March 2007</th>\n",
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       "      <td>2.482313</td>\n",
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       "      <td>1</td>\n",
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       "      <th>4</th>\n",
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       "      <td>0</td>\n",
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      "text/plain": [
       "   Recency (months)  Frequency (times)  Monetary (c.c. blood)  Time (months)  \\\n",
       "0         -0.927899           7.623346               7.623346       2.615633   \n",
       "1         -1.175118           1.282738               1.282738      -0.257881   \n",
       "2         -1.051508           1.796842               1.796842       0.029471   \n",
       "3         -0.927899           2.482313               2.482313       0.439973   \n",
       "4         -1.051508           3.167784               3.167784       1.753579   \n",
       "\n",
       "   whether he/she donated blood in March 2007  \n",
       "0                                           1  \n",
       "1                                           1  \n",
       "2                                           1  \n",
       "3                                           1  \n",
       "4                                           0  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Re-check after standardizing data\n",
    "blood.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Converting the dataset into matrix\n",
    "blood_matrix = blood.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.92789873,  7.62334626,  7.62334626,  2.61563344,  1.        ],\n",
       "       [-1.17511806,  1.28273826,  1.28273826, -0.2578809 ,  1.        ],\n",
       "       [-1.0515084 ,  1.79684161,  1.79684161,  0.02947053,  1.        ],\n",
       "       ...,\n",
       "       [ 1.66790417, -0.43093957, -0.43093957,  1.13782607,  0.        ],\n",
       "       [ 3.64565877, -0.77367514, -0.77367514,  0.19367135,  0.        ],\n",
       "       [ 7.72477762, -0.77367514, -0.77367514,  1.54832812,  0.        ]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Martix for analysis\n",
    "blood_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Running K-Prototype clustering\n",
    "kproto = KPrototypes(n_clusters=5, init='Cao')\n",
    "clusters = kproto.fit_predict(blood_matrix, categorical=[4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.64668675, -0.52090766, -0.52090766, -0.90254016,  0.        ],\n",
       "       [-0.29352462,  0.23674811,  0.23674811,  0.56815766,  0.        ],\n",
       "       [ 1.15986255, -0.4965349 , -0.4965349 , -0.17872668,  0.        ],\n",
       "       [-0.26291005,  1.64282753,  1.64282753,  1.44232506,  0.        ],\n",
       "       [-0.52616733,  6.10245718,  6.10245718,  2.44630135,  1.        ]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kproto.cluster_centroids_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "909.3681461274581"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checking the cost of the clusters created.\n",
    "kproto.cost_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Adding the predicted clusters to the main dataset\n",
    "blood['cluster_id'] = clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "      <th>Recency (months)</th>\n",
       "      <th>Frequency (times)</th>\n",
       "      <th>Monetary (c.c. blood)</th>\n",
       "      <th>Time (months)</th>\n",
       "      <th>whether he/she donated blood in March 2007</th>\n",
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      "text/plain": [
       "   Recency (months)  Frequency (times)  Monetary (c.c. blood)  Time (months)  \\\n",
       "0         -0.927899           7.623346               7.623346       2.615633   \n",
       "1         -1.175118           1.282738               1.282738      -0.257881   \n",
       "2         -1.051508           1.796842               1.796842       0.029471   \n",
       "3         -0.927899           2.482313               2.482313       0.439973   \n",
       "4         -1.051508           3.167784               3.167784       1.753579   \n",
       "\n",
       "   whether he/she donated blood in March 2007  cluster_id  \n",
       "0                                           1           4  \n",
       "1                                           1           1  \n",
       "2                                           1           3  \n",
       "3                                           1           3  \n",
       "4                                           0           3  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Re-check\n",
    "blood.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
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       "   cluster_id\n",
       "0         240\n",
       "1         212\n",
       "2         209\n",
       "3          79\n",
       "4           8"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# Checking the clusters created\n",
    "blooddf = pd.DataFrame(blood['cluster_id'].value_counts())\n",
    "blooddf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='cluster_id'>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WHk/yIeDsvkPMAbuBq6rq+cAZwOXz+P/F48CZVfVCYAVwdpIz+o3UuyuBzX2HmIrFcHi8hceQqrob+GHfOfpWVTuq6qvd9GMMfgnMyyv4a+DH3ewx3WPeHthMsgj4TeCDfWeZisVweLyFh6aUZClwOvDlnqP0ptt1ci+wE1hfVfP2swDeA/wR8JOec0zJYjg8mWRs3v41pFaSY4HbgDdX1aN95+lLVe2pqhUM7mSwMskv9BypF0leBeysqo19ZzkYi+HwTOsWHpp/khzDoBQ+VlUf7zvPXFBVPwL+jfl7HGoV8OokWxnsdj4zyUf7jTQ5i+HweAsPPUmSADcAm6vq+r7z9CnJgiTP6qZ/Gvh14Ju9hupJVV1TVYuqaimD3xX/WlWv7TnWpCyGw1BVu4G9t/DYDKybz7fwSHIL8EXgeUm2Jbms70w9WQVczOAvwnu7xyv7DtWThcBdSb7O4A+p9VU1Z0/T1IBXPkuSGm4xSJIaFoMkqWExSJIaFoMkqWExSJIaFoMkqWExSJIaFoMkqfF/2YUOTqt7ynkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.barplot(x=blooddf.index, y=blooddf['cluster_id'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Clustering algorithm could not initialize. Consider assigning the initial clusters manually.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/sp/kkm21gnx469f0284w2ckt8lm0000gn/T/ipykernel_35564/1910637033.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mnum_clusters\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m14\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0mkproto\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mKPrototypes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn_clusters\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnum_clusters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minit\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Cao'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m     \u001b[0mkproto\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit_predict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mblood_matrix\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcategorical\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m     \u001b[0mcost\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkproto\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcost_\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/kmodes/kmodes.py\u001b[0m in \u001b[0;36mfit_predict\u001b[0;34m(self, X, y, **kwargs)\u001b[0m\n\u001b[1;32m    152\u001b[0m         \u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    153\u001b[0m         \"\"\"\n\u001b[0;32m--> 154\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    155\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    156\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/kmodes/kprototypes.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, X, y, categorical, sample_weight)\u001b[0m\n\u001b[1;32m    159\u001b[0m         \u001b[0;31m# the data. The function below returns its value.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    160\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_enc_cluster_centroids\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_enc_map\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlabels_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcost_\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 161\u001b[0;31m         self.n_iter_, self.epoch_costs_, self.gamma = k_prototypes(\n\u001b[0m\u001b[1;32m    162\u001b[0m             \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    163\u001b[0m             \u001b[0mcategorical\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/kmodes/kprototypes.py\u001b[0m in \u001b[0;36mk_prototypes\u001b[0;34m(X, categorical, n_clusters, max_iter, num_dissim, cat_dissim, gamma, init, n_init, verbose, random_state, n_jobs, sample_weight)\u001b[0m\n\u001b[1;32m    297\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mn_jobs\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    298\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0minit_no\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn_init\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 299\u001b[0;31m             results.append(_k_prototypes_single(Xnum, Xcat, nnumattrs, ncatattrs,\n\u001b[0m\u001b[1;32m    300\u001b[0m                                                 \u001b[0mn_clusters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_points\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmax_iter\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    301\u001b[0m                                                 \u001b[0mnum_dissim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcat_dissim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgamma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/kmodes/kprototypes.py\u001b[0m in \u001b[0;36m_k_prototypes_single\u001b[0;34m(Xnum, Xcat, nnumattrs, ncatattrs, n_clusters, n_points, max_iter, num_dissim, cat_dissim, gamma, init, init_no, verbose, random_state, sample_weight)\u001b[0m\n\u001b[1;32m    408\u001b[0m             \u001b[0minit\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'random'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    409\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0minit_tries\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mRAISE_INIT_TRIES\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 410\u001b[0;31m             raise ValueError(\n\u001b[0m\u001b[1;32m    411\u001b[0m                 \u001b[0;34m\"Clustering algorithm could not initialize. \"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    412\u001b[0m                 \u001b[0;34m\"Consider assigning the initial clusters manually.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Clustering algorithm could not initialize. Consider assigning the initial clusters manually."
     ]
    }
   ],
   "source": [
    "#Choosing optimal K\n",
    "cost = []\n",
    "for num_clusters in list(range(1,14)):\n",
    "    kproto = KPrototypes(n_clusters=num_clusters, init='Cao')\n",
    "    kproto.fit_predict(blood_matrix, categorical=[4])\n",
    "    cost.append(kproto.cost_)\n",
    "    \n",
    "plt.plot(cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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