Modeling Customer Relationships as Markov Chains.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from collections import Counter\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "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>cust_id</th>\n",
       "      <th>purchase_amt</th>\n",
       "      <th>date</th>\n",
       "      <th>year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>760</td>\n",
       "      <td>25.0</td>\n",
       "      <td>2009-11-06</td>\n",
       "      <td>2009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>860</td>\n",
       "      <td>50.0</td>\n",
       "      <td>2012-09-28</td>\n",
       "      <td>2012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1200</td>\n",
       "      <td>100.0</td>\n",
       "      <td>2005-10-25</td>\n",
       "      <td>2005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1420</td>\n",
       "      <td>50.0</td>\n",
       "      <td>2009-07-09</td>\n",
       "      <td>2009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1940</td>\n",
       "      <td>70.0</td>\n",
       "      <td>2013-01-25</td>\n",
       "      <td>2013</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   cust_id  purchase_amt        date  year\n",
       "0      760          25.0  2009-11-06  2009\n",
       "1      860          50.0  2012-09-28  2012\n",
       "2     1200         100.0  2005-10-25  2005\n",
       "3     1420          50.0  2009-07-09  2009\n",
       "4     1940          70.0  2013-01-25  2013"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transactions = pd.read_csv(\"purchases.txt\", delimiter=\"\\t\", header=None)\n",
    "\n",
    "transactions.columns = ['cust_id', 'purchase_amt', 'date']\n",
    "transactions['year'] = transactions['date'].apply(lambda x: x[:4])\n",
    "transactions['purchase_amt'] = transactions['purchase_amt'].apply(lambda x: float(x))\n",
    "\n",
    "transactions.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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3tOmzk7wvyWLg0CSbJ/mPJJe0z9PaavOSfDDJZUm+3F4XRZKDknyjLfuJid6s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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ee07fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n",
    "\n",
    "axs.hist(transactions['purchase_amt'], bins=50);\n",
    "axs.set_title('Histogram of Purchase Amounts');\n",
    "\n",
    "axs.set_xlabel(\"Purchase Amount (Dollars)\");\n",
    "axs.set_ylabel(\"Count\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "71.03911622114485"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transactions = transactions.groupby(['cust_id', 'year'])['purchase_amt'].sum().reset_index()\n",
    "purchase_amts = transactions['purchase_amt']\n",
    "purchase_amts.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "boolean_matrix = pd.crosstab(transactions.cust_id, [transactions.year], rownames=['cust_id'], colnames=['year'])\n",
    "boolean_matrix = boolean_matrix.applymap(lambda x: 1 if x > 0 else 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "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>year</th>\n",
       "      <th>2005</th>\n",
       "      <th>2006</th>\n",
       "      <th>2007</th>\n",
       "      <th>2008</th>\n",
       "      <th>2009</th>\n",
       "      <th>2010</th>\n",
       "      <th>2011</th>\n",
       "      <th>2012</th>\n",
       "      <th>2013</th>\n",
       "      <th>2014</th>\n",
       "      <th>2015</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cust_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</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>80</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>130</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</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>190</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</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",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "year     2005  2006  2007  2008  2009  2010  2011  2012  2013  2014  2015\n",
       "cust_id                                                                  \n",
       "10          1     0     0     0     0     0     0     0     0     0     0\n",
       "80          1     0     1     0     1     0     1     0     1     1     1\n",
       "90          1     1     1     1     1     1     1     1     1     0     0\n",
       "130         1     0     1     0     0     0     0     0     0     0     0\n",
       "190         1     1     1     1     1     0     0     0     0     0     0"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boolean_matrix_restricted = boolean_matrix[boolean_matrix['2005'] == 1]\n",
    "boolean_matrix_restricted.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# some useful functions\n",
    "\n",
    "def build_recency_and_RFM_matrix(boolean_matrix, transactions):\n",
    "    \"\"\"\n",
    "    INPUT: boolean matrix with users as rows, years as columns.\n",
    "    cell value 1 if user made a purchase in that year.\n",
    "    cell value 0 if user made no purchase in that year.\n",
    "    OUTPUT:\n",
    "    recency matrix: matrix showing user's recency score for a given year.\n",
    "    RFM matrix: matrix showing user's RFM tuple for a given year\n",
    "    \"\"\"\n",
    "    recency_matrix = []\n",
    "    RFM_matrix = []\n",
    "\n",
    "    for row_num, boolean_row in enumerate(boolean_matrix.values):\n",
    "        cust_id = int(boolean_matrix.index[row_num])\n",
    "\n",
    "        frequency = 0\n",
    "        recency = 0\n",
    "\n",
    "        recency_row = []\n",
    "        RFM_row = []\n",
    "\n",
    "        for col_num, cell_value in enumerate(boolean_row):\n",
    "            year = boolean_matrix.columns[col_num]\n",
    "\n",
    "            if cell_value == 1:\n",
    "                transactions_by_cust = transactions[transactions['cust_id'] == cust_id]\n",
    "                transactions_by_cust_by_year = transactions_by_cust[transactions_by_cust['year'] == year]\n",
    "\n",
    "                monetary = float(transactions_by_cust_by_year['purchase_amt'])\n",
    "\n",
    "                frequency += 1\n",
    "                recency = 0\n",
    "            else:\n",
    "                recency += 1\n",
    "\n",
    "            recency_row.append(recency)\n",
    "            RFM_row.append((recency, frequency, monetary))\n",
    "\n",
    "        recency_matrix.append(recency_row)\n",
    "        RFM_matrix.append(RFM_row)\n",
    "\n",
    "    return recency_matrix, RFM_matrix\n",
    "\n",
    "\n",
    "def convert_to_discrete_tuple(continuous_tuple):\n",
    "    \"\"\"\n",
    "    INPUT: continuous RFM tuple corresponding to a user\n",
    "    OUTPUT: discrete tuple according to the segementation we defined\n",
    "    \"\"\"\n",
    "\n",
    "    if continuous_tuple[0] <= 0:\n",
    "        R = 1\n",
    "    elif continuous_tuple[0] < 6:\n",
    "        R = 2\n",
    "    else:\n",
    "        R = 3\n",
    "    if continuous_tuple[1] > 5:\n",
    "        F = 1\n",
    "    else:\n",
    "        F = 2\n",
    "    if continuous_tuple[2] > 50:\n",
    "        M = 1\n",
    "    elif continuous_tuple[2] > 30 or continuous_tuple[2] == 50:\n",
    "        M = 2\n",
    "    else:\n",
    "        M = 3\n",
    "    return R, F, M\n",
    "\n",
    "\n",
    "def convert_to_state_matrix(continuous_tuple_matrix, RFM_states):\n",
    "    \"\"\"\n",
    "    INPUT:\n",
    "    matrix of RFM tuples for each user/year\n",
    "    dictionary mapping RFM tuples to state numbers\n",
    "\n",
    "    OUTPUT:\n",
    "    matrix of states for each user/year\n",
    "    \"\"\"\n",
    "\n",
    "    new_matrix = []\n",
    "    \n",
    "    for row in continuous_tuple_matrix:\n",
    "        new_row = []\n",
    "\n",
    "        for continuous_tuple in row:\n",
    "            discrete_tuple = convert_to_discrete_tuple(continuous_tuple)\n",
    "\n",
    "            state = RFM_states[discrete_tuple]\n",
    "\n",
    "            new_row.append(state)\n",
    "\n",
    "        new_matrix.append(new_row)\n",
    "\n",
    "    return new_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# dictionary mapping RFM tuples to numbered states\n",
    "RFM_states = {(1, 1, 1): 1,\n",
    "              (1, 1, 2): 2,\n",
    "              (1, 1, 3): 3,\n",
    "              (1, 2, 1): 4,\n",
    "              (1, 2, 2): 5,\n",
    "              (1, 2, 3): 6,\n",
    "              (2, 1, 1): 7,\n",
    "              (2, 1, 2): 8,\n",
    "              (2, 1, 3): 9,\n",
    "              (2, 2, 1): 10,\n",
    "              (2, 2, 2): 11,\n",
    "              (2, 2, 3): 12,\n",
    "              (3, 1, 1): 13,\n",
    "              (3, 1, 2): 14,\n",
    "              (3, 1, 3): 15,\n",
    "              (3, 2, 1): 16,\n",
    "              (3, 2, 2): 17,\n",
    "              (3, 2, 3): 18}\n",
    "\n",
    "recency_matrix, RFM_matrix = build_recency_and_RFM_matrix(boolean_matrix_restricted, transactions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "state_matrix = convert_to_state_matrix(RFM_matrix, RFM_states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "frequencies = []\n",
    "\n",
    "for row in RFM_matrix:\n",
    "    for cell_value in row:\n",
    "        frequencies.append(cell_value[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>year</th>\n",
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       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "year     2005  2006  2007  2008  2009  2010  2011  2012  2013  2014  2015\n",
       "cust_id                                                                  \n",
       "10          0     1     2     3     4     5     6     7     8     9    10\n",
       "80          0     1     0     1     0     1     0     1     0     0     0\n",
       "90          0     0     0     0     0     0     0     0     0     1     2\n",
       "130         0     1     0     1     2     3     4     5     6     7     8\n",
       "190         0     0     0     0     0     1     2     3     4     5     6"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recency_df = pd.DataFrame(np.array(recency_matrix))\n",
    "\n",
    "recency_df.index = boolean_matrix_restricted.index\n",
    "recency_df.columns = boolean_matrix_restricted.columns\n",
    "\n",
    "recency_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "year     2005  2006  2007  2008  2009  2010  2011  2012  2013  2014  2015\n",
       "cust_id                                                                  \n",
       "10          6    12    12    12    12    12    18    18    18    18    18\n",
       "80          5    11     4    10     4    10     4    10     4     1     1\n",
       "90          4     4     4     4     4     1     1     1     1     7     7\n",
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       "190         5     4     6     4     4    10    10    10    10    10    16"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_at_recency_dict = {}\n",
    "total_transition_recencies_dict = {}\n",
    "\n",
    "state_df = pd.DataFrame(np.array(state_matrix))\n",
    "\n",
    "state_df.columns = boolean_matrix_restricted.columns\n",
    "state_df.index = boolean_matrix_restricted.index\n",
    "\n",
    "state_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# build transition matrix for recency\n",
    "for recency_score in range(11):\n",
    "    total_at_recency = 0\n",
    "\n",
    "    total_transition_states_observed = Counter()\n",
    "\n",
    "    for year in state_df.columns:\n",
    "        # no data for 2016 so leave 2015 out\n",
    "        if year == '2015':\n",
    "            break\n",
    "\n",
    "        # reduce dataframe to people who were in this state this year\n",
    "        this_recency_this_year = recency_df[recency_df[year] == recency_score]\n",
    "\n",
    "        # total number of people observed in this state this year\n",
    "        total_this_recency_this_year = this_recency_this_year.shape[0]\n",
    "        total_at_recency += total_this_recency_this_year\n",
    "\n",
    "        # get count of states observed the next year\n",
    "        next_year = str(int(year) + 1)\n",
    "\n",
    "        observed_recencies_next_year = Counter(list(this_recency_this_year[next_year]))\n",
    "\n",
    "        total_transition_states_observed += observed_recencies_next_year\n",
    "\n",
    "    total_at_recency_dict[recency_score] = total_at_recency\n",
    "    total_transition_recencies_dict[recency_score] = total_transition_states_observed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "# build recency transition matrix\n",
    "recency_transition_matrix = np.zeros((11, 11))\n",
    "\n",
    "for i in range(10):\n",
    "    for j in range(11):\n",
    "        transition_prob = total_transition_recencies_dict[i][j] / total_at_recency_dict[i]\n",
    "\n",
    "        recency_transition_matrix[i, j] = transition_prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.000000</td>\n",
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       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
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       "      <td>0.000000</td>\n",
       "      <td>0.990415</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.020492</td>\n",
       "      <td>0.00000</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>0.979508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.00000</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",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0        1         2         3         4         5         6   \\\n",
       "0   0.716090  0.28391  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
       "1   0.329261  0.00000  0.670739  0.000000  0.000000  0.000000  0.000000   \n",
       "2   0.137864  0.00000  0.000000  0.862136  0.000000  0.000000  0.000000   \n",
       "3   0.086849  0.00000  0.000000  0.000000  0.913151  0.000000  0.000000   \n",
       "4   0.074963  0.00000  0.000000  0.000000  0.000000  0.925037  0.000000   \n",
       "5   0.035842  0.00000  0.000000  0.000000  0.000000  0.000000  0.964158   \n",
       "6   0.057732  0.00000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
       "7   0.041162  0.00000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
       "8   0.009585  0.00000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
       "9   0.020492  0.00000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
       "10  0.000000  0.00000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
       "\n",
       "          7         8         9         10  \n",
       "0   0.000000  0.000000  0.000000  0.000000  \n",
       "1   0.000000  0.000000  0.000000  0.000000  \n",
       "2   0.000000  0.000000  0.000000  0.000000  \n",
       "3   0.000000  0.000000  0.000000  0.000000  \n",
       "4   0.000000  0.000000  0.000000  0.000000  \n",
       "5   0.000000  0.000000  0.000000  0.000000  \n",
       "6   0.942268  0.000000  0.000000  0.000000  \n",
       "7   0.000000  0.958838  0.000000  0.000000  \n",
       "8   0.000000  0.000000  0.990415  0.000000  \n",
       "9   0.000000  0.000000  0.000000  0.979508  \n",
       "10  0.000000  0.000000  0.000000  0.000000  "
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(recency_transition_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "frequencies = []\n",
    "\n",
    "for row in RFM_matrix:\n",
    "    for cell_value in row:\n",
    "        frequencies.append(cell_value[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "# dictionary that maps states to the total customers observed in that state\n",
    "# key: state number\n",
    "# value: integer giving total number\n",
    "total_in_state_dict = {}\n",
    "\n",
    "# dictionary that maps states to the distribution of states the year following\n",
    "# key: state number\n",
    "# value: counter of states the following year\n",
    "total_transition_states_dict = {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 862,\n",
       " 2: 419,\n",
       " 3: 477,\n",
       " 4: 1708,\n",
       " 5: 813,\n",
       " 6: 1818,\n",
       " 7: 173,\n",
       " 8: 102,\n",
       " 9: 137,\n",
       " 10: 1345,\n",
       " 11: 652,\n",
       " 12: 2289,\n",
       " 13: 0,\n",
       " 14: 0,\n",
       " 15: 0,\n",
       " 16: 393,\n",
       " 17: 218,\n",
       " 18: 844}"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# build transition matrix for RFMs\n",
    "for state in range(1, 19):\n",
    "    total_in_state = 0\n",
    "\n",
    "    total_transition_states_observed = Counter()\n",
    "\n",
    "    for year in state_df.columns:\n",
    "        # no data for 2016 so leave 2015 out\n",
    "        if year == '2015':\n",
    "            break\n",
    "\n",
    "        # reduce dataframe to people who were in this state this year\n",
    "        this_state_this_year = state_df[state_df[year] == state]\n",
    "\n",
    "        # total number of people observed in this state this year\n",
    "        total_this_state_this_year = this_state_this_year.shape[0]\n",
    "        total_in_state += total_this_state_this_year\n",
    "\n",
    "        # get count of states observed the next year\n",
    "        next_year = str(int(year) + 1)\n",
    "\n",
    "        observed_states_next_year = Counter(list(this_state_this_year[next_year]))\n",
    "\n",
    "        total_transition_states_observed += observed_states_next_year\n",
    "\n",
    "    total_in_state_dict[state] = total_in_state\n",
    "    total_transition_states_dict[state] = total_transition_states_observed\n",
    "\n",
    "total_in_state_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: Counter({1: 659, 2: 47, 3: 34, 7: 122}),\n",
       " 2: Counter({1: 67, 2: 256, 3: 30, 8: 66}),\n",
       " 3: Counter({1: 24, 2: 46, 3: 302, 9: 105}),\n",
       " 4: Counter({1: 177, 2: 23, 3: 9, 4: 817, 5: 111, 6: 100, 10: 471}),\n",
       " 5: Counter({1: 18, 2: 68, 3: 13, 4: 149, 5: 235, 6: 97, 11: 233}),\n",
       " 6: Counter({1: 16, 2: 23, 3: 114, 4: 115, 5: 100, 6: 716, 12: 734}),\n",
       " 7: Counter({1: 25, 2: 4, 3: 6, 7: 138}),\n",
       " 8: Counter({1: 8, 2: 9, 3: 4, 8: 81}),\n",
       " 9: Counter({1: 4, 2: 2, 3: 19, 9: 112}),\n",
       " 10: Counter({1: 25, 2: 4, 3: 1, 4: 160, 5: 31, 6: 37, 10: 920, 16: 167}),\n",
       " 11: Counter({1: 6, 2: 5, 3: 5, 4: 48, 5: 28, 6: 27, 11: 457, 17: 76}),\n",
       " 12: Counter({1: 1, 2: 7, 3: 22, 4: 59, 5: 44, 6: 230, 12: 1631, 18: 295}),\n",
       " 13: Counter(),\n",
       " 14: Counter(),\n",
       " 15: Counter(),\n",
       " 16: Counter({4: 13, 6: 4, 16: 376}),\n",
       " 17: Counter({4: 3, 5: 4, 6: 1, 17: 210}),\n",
       " 18: Counter({4: 5, 5: 1, 6: 22, 18: 816})}"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_transition_states_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# build transition matrix\n",
    "RFM_transition_matrix = np.zeros((18, 18))\n",
    "\n",
    "for i in range(1, 18):\n",
    "    for j in range(1, 18):\n",
    "        # absorbtion states\n",
    "        if i >= 13 and i == j:\n",
    "            transition_prob = 1\n",
    "        elif i >= 13 and i != j:\n",
    "            transition_prob = 0\n",
    "        else:\n",
    "            transition_prob = total_transition_states_dict[i][j] / total_in_state_dict[i]\n",
    "\n",
    "        RFM_transition_matrix[i - 1, j - 1] = transition_prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.764501</td>\n",
       "      <td>0.054524</td>\n",
       "      <td>0.039443</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.141531</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>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.159905</td>\n",
       "      <td>0.610979</td>\n",
       "      <td>0.071599</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.157518</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.050314</td>\n",
       "      <td>0.096436</td>\n",
       "      <td>0.633124</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>0.220126</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.103630</td>\n",
       "      <td>0.013466</td>\n",
       "      <td>0.005269</td>\n",
       "      <td>0.478337</td>\n",
       "      <td>0.064988</td>\n",
       "      <td>0.058548</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.275761</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.022140</td>\n",
       "      <td>0.083641</td>\n",
       "      <td>0.015990</td>\n",
       "      <td>0.183272</td>\n",
       "      <td>0.289053</td>\n",
       "      <td>0.119311</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.286593</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.008801</td>\n",
       "      <td>0.012651</td>\n",
       "      <td>0.062706</td>\n",
       "      <td>0.063256</td>\n",
       "      <td>0.055006</td>\n",
       "      <td>0.393839</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>0.403740</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.144509</td>\n",
       "      <td>0.023121</td>\n",
       "      <td>0.034682</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.797688</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>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.078431</td>\n",
       "      <td>0.088235</td>\n",
       "      <td>0.039216</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.794118</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.029197</td>\n",
       "      <td>0.014599</td>\n",
       "      <td>0.138686</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>0.817518</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.018587</td>\n",
       "      <td>0.002974</td>\n",
       "      <td>0.000743</td>\n",
       "      <td>0.118959</td>\n",
       "      <td>0.023048</td>\n",
       "      <td>0.027509</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.684015</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.124164</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.009202</td>\n",
       "      <td>0.007669</td>\n",
       "      <td>0.007669</td>\n",
       "      <td>0.073620</td>\n",
       "      <td>0.042945</td>\n",
       "      <td>0.041411</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.700920</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.116564</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.000437</td>\n",
       "      <td>0.003058</td>\n",
       "      <td>0.009611</td>\n",
       "      <td>0.025775</td>\n",
       "      <td>0.019222</td>\n",
       "      <td>0.100481</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>0.712538</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</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>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</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>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</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>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</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>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</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>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</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>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5         6   \\\n",
       "0   0.764501  0.054524  0.039443  0.000000  0.000000  0.000000  0.141531   \n",
       "1   0.159905  0.610979  0.071599  0.000000  0.000000  0.000000  0.000000   \n",
       "2   0.050314  0.096436  0.633124  0.000000  0.000000  0.000000  0.000000   \n",
       "3   0.103630  0.013466  0.005269  0.478337  0.064988  0.058548  0.000000   \n",
       "4   0.022140  0.083641  0.015990  0.183272  0.289053  0.119311  0.000000   \n",
       "5   0.008801  0.012651  0.062706  0.063256  0.055006  0.393839  0.000000   \n",
       "6   0.144509  0.023121  0.034682  0.000000  0.000000  0.000000  0.797688   \n",
       "7   0.078431  0.088235  0.039216  0.000000  0.000000  0.000000  0.000000   \n",
       "8   0.029197  0.014599  0.138686  0.000000  0.000000  0.000000  0.000000   \n",
       "9   0.018587  0.002974  0.000743  0.118959  0.023048  0.027509  0.000000   \n",
       "10  0.009202  0.007669  0.007669  0.073620  0.042945  0.041411  0.000000   \n",
       "11  0.000437  0.003058  0.009611  0.025775  0.019222  0.100481  0.000000   \n",
       "12  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
       "13  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
       "14  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
       "15  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
       "16  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
       "17  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
       "\n",
       "          7         8         9         10        11   12   13   14        15  \\\n",
       "0   0.000000  0.000000  0.000000  0.000000  0.000000  0.0  0.0  0.0  0.000000   \n",
       "1   0.157518  0.000000  0.000000  0.000000  0.000000  0.0  0.0  0.0  0.000000   \n",
       "2   0.000000  0.220126  0.000000  0.000000  0.000000  0.0  0.0  0.0  0.000000   \n",
       "3   0.000000  0.000000  0.275761  0.000000  0.000000  0.0  0.0  0.0  0.000000   \n",
       "4   0.000000  0.000000  0.000000  0.286593  0.000000  0.0  0.0  0.0  0.000000   \n",
       "5   0.000000  0.000000  0.000000  0.000000  0.403740  0.0  0.0  0.0  0.000000   \n",
       "6   0.000000  0.000000  0.000000  0.000000  0.000000  0.0  0.0  0.0  0.000000   \n",
       "7   0.794118  0.000000  0.000000  0.000000  0.000000  0.0  0.0  0.0  0.000000   \n",
       "8   0.000000  0.817518  0.000000  0.000000  0.000000  0.0  0.0  0.0  0.000000   \n",
       "9   0.000000  0.000000  0.684015  0.000000  0.000000  0.0  0.0  0.0  0.124164   \n",
       "10  0.000000  0.000000  0.000000  0.700920  0.000000  0.0  0.0  0.0  0.000000   \n",
       "11  0.000000  0.000000  0.000000  0.000000  0.712538  0.0  0.0  0.0  0.000000   \n",
       "12  0.000000  0.000000  0.000000  0.000000  0.000000  1.0  0.0  0.0  0.000000   \n",
       "13  0.000000  0.000000  0.000000  0.000000  0.000000  0.0  1.0  0.0  0.000000   \n",
       "14  0.000000  0.000000  0.000000  0.000000  0.000000  0.0  0.0  1.0  0.000000   \n",
       "15  0.000000  0.000000  0.000000  0.000000  0.000000  0.0  0.0  0.0  1.000000   \n",
       "16  0.000000  0.000000  0.000000  0.000000  0.000000  0.0  0.0  0.0  0.000000   \n",
       "17  0.000000  0.000000  0.000000  0.000000  0.000000  0.0  0.0  0.0  0.000000   \n",
       "\n",
       "          16   17  \n",
       "0   0.000000  0.0  \n",
       "1   0.000000  0.0  \n",
       "2   0.000000  0.0  \n",
       "3   0.000000  0.0  \n",
       "4   0.000000  0.0  \n",
       "5   0.000000  0.0  \n",
       "6   0.000000  0.0  \n",
       "7   0.000000  0.0  \n",
       "8   0.000000  0.0  \n",
       "9   0.000000  0.0  \n",
       "10  0.116564  0.0  \n",
       "11  0.000000  0.0  \n",
       "12  0.000000  0.0  \n",
       "13  0.000000  0.0  \n",
       "14  0.000000  0.0  \n",
       "15  0.000000  0.0  \n",
       "16  1.000000  0.0  \n",
       "17  0.000000  0.0  "
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(RFM_transition_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/justw/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:12: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n"
     ]
    }
   ],
   "source": [
    "# build state matrices for all customers that started after 2005\n",
    "\n",
    "years = ['2005', '2006', '2007', '2008', '2009', '2010', '2011', '2012', '2013', '2014']\n",
    "\n",
    "boolean_matrix_test = boolean_matrix.copy()\n",
    "\n",
    "state_dataframes = []\n",
    "\n",
    "for year in years:\n",
    "    no_purchase_first_year = boolean_matrix_test[boolean_matrix_test[year] == 0]\n",
    "    first_purchase_next_year = no_purchase_first_year[no_purchase_first_year[str(int(year) + 1)] == 1]\n",
    "    first_purchase_next_year.drop(year, axis=1, inplace=True)\n",
    "\n",
    "    recency_matrix_here, RFM_matrix_here = build_recency_and_RFM_matrix(first_purchase_next_year, transactions)\n",
    "    state_matrix_here = convert_to_state_matrix(RFM_matrix_here, RFM_states)\n",
    "\n",
    "    state_df_here = pd.DataFrame(state_matrix_here)\n",
    "    state_df_here.columns = first_purchase_next_year.columns\n",
    "    state_df_here.index = first_purchase_next_year.index\n",
    "\n",
    "    state_dataframes.append(state_df_here)\n",
    "\n",
    "    boolean_matrix_test.drop(year, axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_counter = Counter(state_df['2015'])\n",
    "\n",
    "for individual_state_df in state_dataframes:\n",
    "    individual_counter = Counter(individual_state_df['2015'])\n",
    "\n",
    "    initial_counter += individual_counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "# build starting state vector\n",
    "\n",
    "starting_state = []\n",
    "\n",
    "for i in range(1, 19):\n",
    "    if i in initial_counter:\n",
    "#         starting_state.append(starting_state_counts[i])\n",
    "        starting_state.append(initial_counter[i])\n",
    "    else:\n",
    "        starting_state.append(0)\n",
    "\n",
    "starting_state = np.array(starting_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 833,  402,  437, 2129, 1336, 2581,  213,  136,  219, 2473, 2281,\n",
       "       5763,    0,    0,    0,  806,  961, 3039])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "starting_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    0.,     0.,     0.,   511.,   460.,  1173.,     0.,     0.,\n",
       "           0.,     0.,     0.,     0.,     0.,     0.,     0.,     0.,\n",
       "           0.,     0.])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_customer_state_counts = Counter(state_df['2005'])\n",
    "\n",
    "total_new_customers = [state_df['2005'].count()]\n",
    "\n",
    "for individual_state_df in state_dataframes:\n",
    "    new_customer_state_counts += Counter(individual_state_df[individual_state_df.columns[0]])\n",
    "\n",
    "    total_new_customers.append(individual_state_df.shape[0])\n",
    "\n",
    "average_new_customers = np.mean(total_new_customers) // 1\n",
    "\n",
    "new_customer_state_dist = {}\n",
    "\n",
    "for state, state_count in new_customer_state_counts.items():\n",
    "    new_customer_state_dist[state] = state_count / np.sum(total_new_customers)\n",
    "\n",
    "new_customer_state_dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    0.,     0.,     0.,   511.,   460.,  1173.,     0.,     0.,\n",
       "           0.,     0.,     0.,     0.,     0.,     0.,     0.,     0.,\n",
       "           0.,     0.])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_state_vector_each_year = np.zeros(18)\n",
    "new_state_vector_each_year[3] = average_new_customers * new_customer_state_dist[4] // 1\n",
    "new_state_vector_each_year[4] = average_new_customers * new_customer_state_dist[5] // 1\n",
    "new_state_vector_each_year[5] = average_new_customers * new_customer_state_dist[6] // 1\n",
    "\n",
    "new_state_vector_each_year"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "# build the reward vector\n",
    "\n",
    "avg_purchase_amt = purchase_amts.mean()\n",
    "\n",
    "reward_vector = np.zeros(18)\n",
    "\n",
    "for i in range(6):\n",
    "    reward_vector[i] = avg_purchase_amt - 25\n",
    "\n",
    "for i in range(6, 12):\n",
    "    reward_vector[i] = - 25\n",
    "\n",
    "for i in range(12, 18):\n",
    "    reward_vector[i] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 159.14211651],\n",
       "       [ 154.022231  ],\n",
       "       [ 133.06375833],\n",
       "       [ 113.8820981 ],\n",
       "       [ 108.77766952],\n",
       "       [  84.30834718],\n",
       "       [   2.91701705],\n",
       "       [   3.1785518 ],\n",
       "       [ -12.15984091],\n",
       "       [ -15.7199454 ],\n",
       "       [ -19.61056092],\n",
       "       [ -30.12109561],\n",
       "       [   0.        ],\n",
       "       [   0.        ],\n",
       "       [   0.        ],\n",
       "       [   0.        ],\n",
       "       [   0.        ],\n",
       "       [   0.        ]])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I_18 = np.identity(18)\n",
    "d = .2  # discount rate\n",
    "CLV = (np.linalg.inv(I_18 - (1 + d) ** (-1) * RFM_transition_matrix)).dot(reward_vector)\n",
    "\n",
    "CLV.reshape(len(CLV), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[148713.2146689537,\n",
       " 245277.07984708826,\n",
       " 274705.03597826493,\n",
       " 266706.73232970835,\n",
       " 251447.07983963928,\n",
       " 237185.76537106108,\n",
       " 225628.47407888254,\n",
       " 216672.59572615713,\n",
       " 209825.78460564278,\n",
       " 204600.18899193767]"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# without policy\n",
    "\n",
    "revenue_no_policy = []\n",
    "\n",
    "total_reward = reward_vector * (((1 + d) ** -1) * RFM_transition_matrix).dot(\n",
    "    starting_state) + new_state_vector_each_year\n",
    "new_state = starting_state.copy()\n",
    "\n",
    "revenue_no_policy.append(np.sum(total_reward))\n",
    "\n",
    "for i in range(9):\n",
    "    new_state = (((1 + d) ** -1) * RFM_transition_matrix).dot(new_state) + new_state_vector_each_year\n",
    "    reward_this_year = reward_vector * new_state\n",
    "\n",
    "    revenue_no_policy.append(np.sum(reward_this_year))\n",
    "\n",
    "    total_reward += reward_this_year\n",
    "\n",
    "revenue_no_policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2280761.9514373359"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(revenue_no_policy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2016\t148713.214669\n",
      "2017\t245277.079847\n",
      "2018\t274705.035978\n",
      "2019\t266706.73233\n",
      "2020\t251447.07984\n",
      "2021\t237185.765371\n",
      "2022\t225628.474079\n",
      "2023\t216672.595726\n",
      "2024\t209825.784606\n",
      "2025\t204600.188992\n"
     ]
    }
   ],
   "source": [
    "for year, rev in enumerate(revenue_no_policy, 2016):\n",
    "    print(str(year) + \"\\t\" + str(rev))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2016\t334786.057137\n",
      "2017\t431349.922316\n",
      "2018\t418106.563984\n",
      "2019\t383602.358018\n",
      "2020\t349896.26675\n",
      "2021\t322041.043505\n",
      "2022\t300205.533857\n",
      "2023\t283390.943334\n",
      "2024\t270503.207027\n",
      "2025\t260618.696498\n"
     ]
    }
   ],
   "source": [
    "# with policy\n",
    "\n",
    "revenue_with_policy = []\n",
    "\n",
    "reward_vector_with_policy = reward_vector.copy()\n",
    "\n",
    "# set all the negative CLVs to zero\n",
    "reward_vector_with_policy[8:] = 0\n",
    "\n",
    "total_reward = reward_vector_with_policy * (((1 + d) ** -1) * RFM_transition_matrix).dot(\n",
    "    starting_state) + new_state_vector_each_year\n",
    "new_state = starting_state.copy()\n",
    "\n",
    "revenue_with_policy.append(np.sum(total_reward))\n",
    "\n",
    "for i in range(9):\n",
    "    new_state = (((1 + d) ** -1) * RFM_transition_matrix).dot(new_state) + new_state_vector_each_year\n",
    "    reward_this_year = reward_vector_with_policy * new_state\n",
    "\n",
    "    revenue_with_policy.append(np.sum(reward_this_year))\n",
    "\n",
    "    total_reward += reward_this_year\n",
    "\n",
    "money = []\n",
    "\n",
    "for year, rev in enumerate(revenue_with_policy, 2016):\n",
    "    print(str(year) + \"\\t\" + str(rev))\n",
    "    money.append(str(year) + \"\\t\" + str(rev))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10ee210f0>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4cD5rkyRJ6sXYnoOW5CRgb2CbJDcCfwbsnWQ3oIDrgNcBVNXlSU4BrgBWAm+sqnvGVZsk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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e318f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n",
    "\n",
    "total_purchases = boolean_matrix_restricted.apply(lambda x: sum(x), axis=1)\n",
    "\n",
    "axs.hist(total_purchases, bins=11)\n",
    "\n",
    "axs.set_title(\"Histogram of Total Purchases\")\n",
    "axs.set_xlabel(\"Total Purchases Made\")\n",
    "axs.set_ylabel(\"Count\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3354500.5924256132"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(revenue_with_policy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 46.03911622],\n",
       "       [ 46.03911622],\n",
       "       [ 46.03911622],\n",
       "       [ 46.03911622],\n",
       "       [ 46.03911622],\n",
       "       [ 46.03911622],\n",
       "       [-25.        ],\n",
       "       [-25.        ],\n",
       "       [-25.        ],\n",
       "       [-25.        ],\n",
       "       [-25.        ],\n",
       "       [-25.        ],\n",
       "       [  0.        ],\n",
       "       [  0.        ],\n",
       "       [  0.        ],\n",
       "       [  0.        ],\n",
       "       [  0.        ],\n",
       "       [  0.        ]])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reward_vector.reshape(18, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 159.14211651],\n",
       "       [ 154.022231  ],\n",
       "       [ 133.06375833],\n",
       "       [ 113.8820981 ],\n",
       "       [ 108.77766952],\n",
       "       [  84.30834718],\n",
       "       [   2.91701705],\n",
       "       [   3.1785518 ],\n",
       "       [ -12.15984091],\n",
       "       [ -15.7199454 ],\n",
       "       [ -19.61056092],\n",
       "       [ -30.12109561],\n",
       "       [   0.        ],\n",
       "       [   0.        ],\n",
       "       [   0.        ],\n",
       "       [   0.        ],\n",
       "       [   0.        ],\n",
       "       [   0.        ]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CLV.reshape(18, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2144.0"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(new_state_vector_each_year)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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