notes/rs/rs_Rate-Popularity.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "from tqdm import tqdm\n",
    "from datetime import datetime\n",
    "from heapq import heappush,heappop\n",
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "PATH=\"/home/yui/Documents/data/recommender/ratings_Beauty.csv\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Amazon - Ratings (Beauty Products)\n",
    "2 Million data points related to Beauty products sold on Amazon.com. It contains.\n",
    "- the unique UserId (Customer Identification),\n",
    "- the product ASIN (Amazon's unique product identification code for each product),\n",
    "- Ratings (ranging from 1-5 based on customer satisfaction) and\n",
    "- the Timestamp of the rating (in UNIX time)\n",
    "\n",
    "https://www.kaggle.com/skillsmuggler/amazon-ratings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>UserId</th>\n",
       "      <th>ProductId</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Timestamp</th>\n",
       "      <th>Date</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>A39HTATAQ9V7YF</td>\n",
       "      <td>0205616461</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1369699200</td>\n",
       "      <td>2013-05-28 00:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A3JM6GV9MNOF9X</td>\n",
       "      <td>0558925278</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1355443200</td>\n",
       "      <td>2012-12-14 00:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A1Z513UWSAAO0F</td>\n",
       "      <td>0558925278</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1404691200</td>\n",
       "      <td>2014-07-07 00:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>A1WMRR494NWEWV</td>\n",
       "      <td>0733001998</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1382572800</td>\n",
       "      <td>2013-10-24 00:00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>A3IAAVS479H7M7</td>\n",
       "      <td>0737104473</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1274227200</td>\n",
       "      <td>2010-05-19 00:00:00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           UserId   ProductId  Rating   Timestamp                 Date\n",
       "0  A39HTATAQ9V7YF  0205616461     5.0  1369699200  2013-05-28 00:00:00\n",
       "1  A3JM6GV9MNOF9X  0558925278     3.0  1355443200  2012-12-14 00:00:00\n",
       "2  A1Z513UWSAAO0F  0558925278     5.0  1404691200  2014-07-07 00:00:00\n",
       "3  A1WMRR494NWEWV  0733001998     4.0  1382572800  2013-10-24 00:00:00\n",
       "4  A3IAAVS479H7M7  0737104473     1.0  1274227200  2010-05-19 00:00:00"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "func = lambda x:datetime.utcfromtimestamp(x).\\\n",
    "        strftime('%Y-%m-%d %H:%M:%S')\n",
    "df=pd.read_csv(PATH)\n",
    "df['Date']=df['Timestamp'].apply(func)\n",
    "df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2023070, 5)              Rating     Timestamp\n",
      "count  2.023070e+06  2.023070e+06\n",
      "mean   4.149036e+00  1.360389e+09\n",
      "std    1.311505e+00  4.611860e+07\n",
      "min    1.000000e+00  9.087552e+08\n",
      "25%    4.000000e+00  1.350259e+09\n",
      "50%    5.000000e+00  1.372810e+09\n",
      "75%    5.000000e+00  1.391472e+09\n",
      "max    5.000000e+00  1.406074e+09\n"
     ]
    }
   ],
   "source": [
    "print(df.shape,df.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1210271,)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['UserId'].unique().shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(249274,)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['ProductId'].unique().shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4231,)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Timestamp'].unique().shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Average Ratings\n",
    "$$s = \\frac{1}{N}\\sum^N_{i=1}x_i$$\n",
    "- Very bad estimation\n",
    "- No previous records, then no ratings\n",
    "- Can cause 0/0 error\n",
    "- Rank by most number of ratings and highest average"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 2023070/2023070 [07:31<00:00, 4475.93it/s]\n"
     ]
    }
   ],
   "source": [
    "def returnSumNProductID(df):\n",
    "    d = dict()\n",
    "    for row in tqdm(range(df.shape[0])):\n",
    "        id_ = df.iloc[row]['ProductId']\n",
    "        total,n,elements = d.get(id_,(0,0,[]))\n",
    "        total+=df.iloc[row]['Rating']\n",
    "        n+=1\n",
    "        elements.append(df.iloc[row]['Rating'])\n",
    "        d[id_]=(total,n,elements)\n",
    "    return d\n",
    "d = returnSumNProductID(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 249274/249274 [00:00<00:00, 2098498.95it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5.0, 'B004CNRDBU', 290.0, 58)\n",
      "(5.0, 'B001F0RBRE', 205.0, 41)\n",
      "(5.0, 'B00466VJ04', 190.0, 38)\n",
      "(5.0, 'B004AI5756', 190.0, 38)\n",
      "(5.0, 'B005V247N8', 185.0, 37)\n",
      "(5.0, 'B0006B65PC', 155.0, 31)\n",
      "(5.0, 'B002DMJM52', 150.0, 30)\n",
      "(5.0, 'B00BFWD6GC', 150.0, 30)\n",
      "(5.0, 'B005XRZP32', 145.0, 29)\n",
      "(5.0, 'B00ANJQ8RC', 145.0, 29)\n"
     ]
    }
   ],
   "source": [
    "def avg(d,first=10):\n",
    "    h = []\n",
    "    for key,val in tqdm(d.items()):\n",
    "        h.append((val[0]/val[1],key,val[0],val[1]))\n",
    "    h = sorted(h,key=lambda x: (-x[0],-x[3]))\n",
    "    for i in range(first):\n",
    "        print(h[i])\n",
    "_ = avg(d,first=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Average Ratings with Smoothing\n",
    "$$s = \\frac{1}{N+\\lambda}(\\lambda\\mu_0+\\sum^N_{i=1}x_i)$$\n",
    "If $N=0$, $s=\\mu_0$. We can set $\\mu=3$ for an initial neutral score for each product without ratings. And $\\lambda=1$ to reduce the effect of denominator to the score.\n",
    "\n",
    "- Solve 0/0 problem but cause product with many ratings get lower average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 249274/249274 [00:00<00:00, 1533731.46it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4.966101694915254, 'B004CNRDBU', 290.0, 58)\n",
      "(4.953488372093023, 'B00K7ER6LU', 423.0, 85)\n",
      "(4.9523809523809526, 'B001F0RBRE', 205.0, 41)\n",
      "(4.948717948717949, 'B00466VJ04', 190.0, 38)\n",
      "(4.948717948717949, 'B004AI5756', 190.0, 38)\n",
      "(4.947368421052632, 'B005V247N8', 185.0, 37)\n",
      "(4.9375, 'B00FPROWWU', 392.0, 79)\n",
      "(4.9375, 'B0006B65PC', 155.0, 31)\n",
      "(4.935483870967742, 'B002DMJM52', 150.0, 30)\n",
      "(4.935483870967742, 'B00BFWD6GC', 150.0, 30)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "def smooth(d,first=10):\n",
    "    h,lamb,init = [],1,3\n",
    "    for key,val in tqdm(d.items()):\n",
    "        h.append(((val[0]+lamb*init)/(val[1]+lamb),\n",
    "                key,val[0],val[1]))\n",
    "    h = sorted(h,key=lambda x: (-x[0],-x[3]))\n",
    "    for i in range(first):\n",
    "        print(h[i])\n",
    "    return h\n",
    "_ = smooth(d,first=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 249274/249274 [00:00<00:00, 680096.20it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5.0, 'B003BQ6QXK', 8872.0, 1918)\n",
      "(5.0, 'B00121UVU0', 8341.0, 1838)\n",
      "(5.0, 'B006IBM21K', 5412.0, 1163)\n",
      "(5.0, 'B001AO0WCG', 5121.0, 1136)\n",
      "(5.0, 'B003UH0528', 5184.0, 1108)\n",
      "(5.0, 'B000L596FE', 4535.0, 992)\n",
      "(5.0, 'B00639DLV2', 4475.0, 981)\n",
      "(5.0, 'B007Q0WW0S', 4431.0, 945)\n",
      "(5.0, 'B000HRVC5I', 4018.0, 885)\n",
      "(5.0, 'B000OYJ9AO', 3908.0, 865)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "def roundSmooth(d,first=10):\n",
    "    h,lamb,init = [],1,3\n",
    "    for key,val in tqdm(d.items()):\n",
    "        h.append((\\\n",
    "            round((val[0]+lamb*init)/(val[1]+lamb)),\n",
    "                key,val[0],val[1]))\n",
    "    h = sorted(h,key=lambda x: (-x[0],-x[3]))\n",
    "    for i in range(first):\n",
    "        print(h[i])\n",
    "    return h\n",
    "_ = roundSmooth(d,first=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Wilson Lower bound Score\n",
    "Rather than ranking with number of ratings $N$, another way is confidence interval which can take $N$ into account as well. The less the $N$ is, the less confident the score is, the score should be thus downgraded. The lower bound of confidence interval can reflect this, since the less certain we are, the more the lower bound is towards 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Bernoulli Confidence Interval Approximation**\n",
    "\n",
    "- Possible outcomes: 0/1\n",
    "- Lower Bound:\n",
    "$$\\bar{X}+\\Phi^{-1}(0.025)\\frac{s}{\\sqrt{N}}=\\hat{p}-1.96\\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{N}}$$\n",
    "where $\\hat{p}=\\frac{1}{N}\\sum_i \\mathbb{I}(x_i=1)$ and $s=\\sqrt{\\frac{1}{N}\\sum^N_{i=1}(x_i-\\bar{x})^2}$.\n",
    "- Wilson Lower Bound:\n",
    "$$\\frac{\\hat{p}+\\frac{z^2}{2N}}{1+\\frac{z^2}{N}}-\\frac{z}{1+\\frac{z^2}{N}}\\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{N}+\\frac{z^2}{4N^2}}$$\n",
    "where $z=\\Phi^{-1}(0.25)$ and $\\Phi$ cdf."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**K star scale**\n",
    "\n",
    "- Wilson Lower Bound:\n",
    "$$\n",
    "\\sum^K_{k=1}s_k\\frac{n_k+1}{N+K}-z_{\\alpha/2}\\sqrt{\\frac{1}{N+K+1}\\bigg(\\sum^K_{k=1}s_k^2\\frac{n_k+1}{N+K}-\\big(\\sum^K_{k=1}\\frac{n_k+1}{N+K}\\big)^2\\bigg)}\n",
    "$$\n",
    "where $K$ is the maximum of stars, $N$ the number of ratings, $n_k$ number of k stars, $s_k$ star scale.\n",
    "\n",
    "https://www.evanmiller.org/ranking-items-with-star-ratings.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'p(x)')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "x = np.linspace(0,5,1000)\n",
    "y0 = norm.pdf(x,2.5,0.5)\n",
    "y1 = norm.pdf(x,2.5,0.2)\n",
    "ax = plt.subplot(1,1,1)\n",
    "plt.plot(x,y0,label='less confident')\n",
    "plt.plot(x,y1,label='more confident')\n",
    "ax.axvline(norm.ppf(0.025,2.5,0.5),\n",
    "        label='lower bound for lower confident')\n",
    "ax.axvline(norm.ppf(0.025,2.5,0.2),\n",
    "        label='lower bound for lower confident')\n",
    "plt.legend()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('p(x)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def wilsonScore(val,z,K=5):\n",
    "    c = Counter(val[2])\n",
    "    N = val[0]\n",
    "    p1,p2 = 0,0\n",
    "    for k in range(K):\n",
    "        p1 += (k+1)*(c.get(k+1,0)+1)/(N+K)\n",
    "        p2 += (k+1)*(k+1)*(c.get(k+1,0)+1)/(N+K)\n",
    "    s=p1-z*np.sqrt((p2-p1**2)/(N+K+1))\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lowerBound(d,first=10,conf=0.95,K=5):\n",
    "    h = []\n",
    "    z = norm.ppf(1-(1-conf)/2)\n",
    "    for key,val in tqdm(d.items()):\n",
    "        s = wilsonScore(val,z,K)\n",
    "        h.append(((s,val[0]/val[1],key,val[0],val[1],val[2])))\n",
    "    h = sorted(h,key=lambda x:(x[0]))\n",
    "    for i in range(first):\n",
    "        print(h[i])\n",
    "    return h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 249274/249274 [00:02<00:00, 95128.62it/s] "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.6085119807568129, 5.0, '5357955786', 20.0, 4, [5.0, 5.0, 5.0, 5.0])\n",
      "(0.6085119807568129, 5.0, '9790773749', 20.0, 4, [5.0, 5.0, 5.0, 5.0])\n",
      "(0.6085119807568129, 5.0, '9790786964', 20.0, 4, [5.0, 5.0, 5.0, 5.0])\n",
      "(0.6085119807568129, 5.0, '9790787707', 20.0, 4, [5.0, 5.0, 5.0, 5.0])\n",
      "(0.6085119807568129, 5.0, '9790789270', 20.0, 4, [5.0, 5.0, 5.0, 5.0])\n",
      "(0.6085119807568129, 5.0, '9790789513', 20.0, 4, [5.0, 5.0, 5.0, 5.0])\n",
      "(0.6085119807568129, 5.0, '979079858X', 20.0, 4, [5.0, 5.0, 5.0, 5.0])\n",
      "(0.6085119807568129, 5.0, 'B00000IAI4', 20.0, 4, [5.0, 5.0, 5.0, 5.0])\n",
      "(0.6085119807568129, 5.0, 'B000052YGB', 20.0, 4, [5.0, 5.0, 5.0, 5.0])\n",
      "(0.6085119807568129, 5.0, 'B000052YPM', 20.0, 4, [5.0, 5.0, 5.0, 5.0])\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "h = lowerBound(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Score')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Varying number of ratings\n",
    "res,val,conf = [],(5,1,[5]),0.95\n",
    "z = norm.ppf(1-(1-conf)/2)\n",
    "for i in range(10):\n",
    "    s = wilsonScore(val,z)\n",
    "    res.append(s)\n",
    "    val = (val[0]+5,val[1]+1,val[2]+[5])\n",
    "plt.plot(range(1,11),res)\n",
    "plt.xlabel('Number of ratings')\n",
    "plt.ylabel('Score')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Score')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Effect of average ratings towards score\n",
    "res,val,conf = [],(1,1,[1]),0.95\n",
    "z = norm.ppf(1-(1-conf)/2)\n",
    "for i in range(5):\n",
    "    s = wilsonScore(val,z)\n",
    "    res.append(s)\n",
    "    val = (val[0]+1,val[1]+1,[val[2][0]+1])\n",
    "plt.plot(range(1,6),res)\n",
    "plt.xlabel('Average ratings')\n",
    "plt.ylabel('Score')"
   ]
  },
  {
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}