Summary.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "\n",
    "import re\n",
    "import pyodbc\n",
    "from collections import OrderedDict\n",
    "from itertools import product\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler, MinMaxScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_rfm_query(typ, count=1000):\n",
    "    query = \"\"\"\n",
    "            select {top} c.Id CustId\n",
    "                ,{field}\n",
    "\n",
    "                from directcrm.Customers c\n",
    "                    join directcrm.CustomerActions ca on c.Id = ca.CustomerId\n",
    "                    join directcrm.RetailOrders ro on ca.Id = ro.FirstCustomerActionId\n",
    "                    join directcrm.RetailOrderHistory roh on ro.Id = roh.OrderId\n",
    "                    join directcrm.RetailPurchaseHistory rph on roh.id = rph.OrderHistoryItemId\n",
    "                    join directcrm.RetailPurchaseStatuses rps on rph.StatusId = rps.Id\n",
    "\n",
    "                where rps.CategorySystemName not in ('Returned','Cancelled','InCart') and roh.IsCurrentOtherwiseNull = 1\n",
    "\n",
    "                group by c.Id\n",
    "\n",
    "                order by c.Id\n",
    "            \"\"\"\n",
    "    \n",
    "    fields = {'r': 'DateDiff(hh, Max(ca.DateTimeUtc), GetDate()) Recency_hours',\n",
    "              'f': 'Count(ca.Id) CountActions',\n",
    "              'm': 'Sum(roh.EffectivePayedAmount) Amount'}\n",
    "    \n",
    "    top = ''\n",
    "    if count is not None:\n",
    "        top = \"top({})\".format(count)\n",
    "    \n",
    "    query = query.format(top=top, field=fields[typ])\n",
    "    return query\n",
    "\n",
    "\n",
    "def get_rfm_data(cnxn, typ, count=1000):\n",
    "    cursor = cnxn.cursor()\n",
    "    cursor.execute(get_rfm_query(typ, count))\n",
    "    rows = list(map(lambda t: [t[0], t[1]], cursor.fetchall()))\n",
    "    df = pd.DataFrame(rows, columns=['id', 'rfm_{}'.format(typ)])\n",
    "    return df\n",
    "\n",
    "\n",
    "def get_full_rfm_data(count = 100): \n",
    "    cnxn = pyodbc.connect(driver='{SQL Server}',\n",
    "                          server='aurora',\n",
    "                          database='hoff')\n",
    "    data_r = get_rfm_data(cnxn, 'r', count=count)\n",
    "    data_f = get_rfm_data(cnxn, 'f', count=count)\n",
    "    data_m = get_rfm_data(cnxn, 'm', count=count)\n",
    "    cnxn.close()\n",
    "    \n",
    "    if sum (data_r.id != data_f.id) or sum(data_r.id != data_m.id):\n",
    "        raise RuntimeError(\"Не совпадают индексы\")\n",
    "    else:\n",
    "        data = pd.concat([data_r, data_f.drop('id', axis=1), data_m.drop('id', axis=1)], axis=1)\n",
    "    data['rfm_m'] = data['rfm_m'].astype(float)\n",
    "    return data\n",
    "\n",
    "\n",
    "def reduce_tails(data, min_q=0.025, max_q=0.975):\n",
    "    filtered_data = data[(data['rfm_r'] >= data['rfm_r'].quantile(min_q)) &\n",
    "                         (data['rfm_r'] <= data['rfm_r'].quantile(max_q)) &\n",
    "                         (data['rfm_f'] >= data['rfm_f'].quantile(min_q)) &\n",
    "                         (data['rfm_f'] <= data['rfm_f'].quantile(max_q)) &\n",
    "                         (data['rfm_m'] >= data['rfm_m'].quantile(min_q)) &\n",
    "                         (data['rfm_m'] <= data['rfm_m'].quantile(max_q))]\n",
    "    return filtered_data\n",
    "\n",
    "\n",
    "def draw_3d_plot(data, labels=None):\n",
    "    fig = plt.figure()\n",
    "    ax = Axes3D(fig)\n",
    "    \n",
    "    ax.set_xlabel(\"R\")\n",
    "    ax.set_ylabel(\"F\")\n",
    "    ax.set_zlabel(\"M\")\n",
    "    \n",
    "    if labels is None:\n",
    "        x = list(data['rfm_r'])\n",
    "        y = list(data['rfm_f'])\n",
    "        z = list(data['rfm_m'])\n",
    "        ax.scatter(x, y, z)\n",
    "        \n",
    "    else:\n",
    "        for n in np.unique(labels):\n",
    "            indices = kmeans.labels_ == n\n",
    "            x = list(data.loc[indices, 'rfm_r'])\n",
    "            y = list(data.loc[indices, 'rfm_f'])\n",
    "            z = list(data.loc[indices, 'rfm_m'])\n",
    "\n",
    "            c = [[n * 2 % 256, n * 5 % 256, n * 13 % 256]]\n",
    "            ax.scatter(x, y, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw_data = get_full_rfm_data(10000)\n",
    "reduced_data = reduce_tails(raw_data.copy(), 0.01, 0.99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Алгоритмы"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Выбор подходящих алгоритмов и метрик"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Алгоритмы с заданным числом кластеров\n",
    "\n",
    "**K-means** - классика, без него никуда.\n",
    "Не слишком быстрый, зато простой и понятный.\n",
    "Можно задать число кластеров.\n",
    "\n",
    "**Spectral clustering** - объединенный подход. Хорошо подходит для небольшого числа кластеров. Не очень хорош для большого числа данных.\n",
    "\n",
    "### Алгоритмы без заданного числа кластеров\n",
    "\n",
    "**Affinity Propagation** - ищет похожие объекты.\n",
    "Плохо, что нельзя задать число кластеров.\n",
    "Еще проблема: выбор метрики.\n",
    "**Mean-shift** - То же, но другая мера растояния\n",
    "\n",
    "**Ward hierarchical clustering** \n",
    "\n",
    "**Agglomerative clustering** - самый простой и понятный алгоритм кластеризации без фиксированного числа кластеров.\n",
    "\n",
    "**DBSCAN** - подходит для большого числа данных и среднего числа кластеров\n",
    "\n",
    "**Birch** - вроде неплохо\n",
    "\n",
    "**Gaussian mixtures** - вроде неплохо"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Метрики, не требующие знания истинных меток классов\n",
    "*Пока рассматриваем только их*\n",
    "\n",
    "**Silhouette Coefficient** - силуэт. От -1 до +1.\n",
    "\n",
    "**Calinski-Harabaz Index** - быстро считается"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import silhouette_score, calinski_harabaz_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = reduced_data\n",
    "X = data[['rfm_r', 'rfm_f', 'rfm_m']]\n",
    "X_scaled_std = pd.DataFrame(StandardScaler().fit_transform(X), columns=X.columns)\n",
    "X_scaled_mm = pd.DataFrame(MinMaxScaler().fit_transform(X), columns=X.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tuning(X, params, clr, rs=None):\n",
    "    #import ipdb; ipdb.set_trace()\n",
    "    names = list(params.keys())\n",
    "    values_lists = list(params.values())\n",
    "    combs = list(product(*values_lists))\n",
    "    \n",
    "    m1, m2 = [], []\n",
    "    for comb in combs:\n",
    "        kwargs = {name: comb[i] for i, name in enumerate(names)}\n",
    "        labels = clr(**kwargs).fit(X).labels_\n",
    "        m1.append(silhouette_score(X, labels, random_state=rs))\n",
    "        m2.append(calinski_harabaz_score(X, labels))\n",
    "    return combs, m1, m2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def choose_best(combs, m1, m2):\n",
    "    best_1, best_2 = np.argmax(m1), np.argmax(m2)\n",
    "    best_comb_1, best_comb_2 = combs[best_1], combs[best_2]\n",
    "    best_res_1, best_res_2 = m1[best_1], m2[best_2]\n",
    "    return {'m1': (best_comb_1, best_res_1), 'm2': (best_comb_2, best_res_2)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tune_kmeans1(X, n_cl_min=8, n_cl_max=12, rs=None, plot=False):\n",
    "    m1, m2 = OrderedDict(), OrderedDict()\n",
    "    inertias = OrderedDict()\n",
    "    for n in range(n_cl_min, n_cl_max + 1):\n",
    "        model = KMeans(n_clusters=n, random_state=rs).fit(X)\n",
    "        m1[n] = silhouette_score(X, model.labels_, random_state=rs)\n",
    "        m2[n] = calinski_harabaz_score(X, model.labels_)\n",
    "        inertias[n] = model.inertia_\n",
    "    if plot:\n",
    "        plt.plot(inertias.keys(), inertias.values())\n",
    "    return m1, m2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "rs=17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = {'n_clusters': list(range(9, 10 + 1)),\n",
    "                  'random_state': [17]}\n",
    "\n",
    "combs, m1, m2 = tuning(X, params, KMeans, rs=rs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([(9, 17), (10, 17)],\n",
       " [0.6162151582279174, 0.5852100665225586],\n",
       " [71426.00663039788, 77187.5485512959])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combs, m1, m2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18e1aedb048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m1, m2 = tune_kmeans(X, 6, 15, rs=17, plot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x18e1ae53470>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18e1aebbb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(m1.keys(), m1.values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x18e1e5530f0>]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18e1ae979b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(m2.keys(), m2.values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18e1af155f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m1, m2 = tune_kmeans(X_scaled_mm, 6, 15, rs=17, plot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x18e1e5a7860>]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18e1e5c8a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(m1.keys(), m1.values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x18e1aedb780>]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18e1e57db70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(m2.keys(), m2.values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}