review_normaliser.ipynb

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   "source": [
    "**Pre-requisites:**\n",
    "\n",
    "PDF's, CDF's, distribution plots, types of distribution, difference between distribution, histograms and their types, [KL divergence](https://towardsdatascience.com/kl-divergence-python-example-b87069e4b810), [Jensen-Shannon distance](https://scipy.github.io/devdocs/generated/scipy.spatial.distance.jensenshannon.html)\n",
    "\n",
    "\n"
   ],
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  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd \n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.special import kl_div\n",
    "from scipy.special import rel_entr\n",
    "from scipy.spatial.distance import jensenshannon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "review_1 = np.array([3264,1528,3722,8179,16937])\n",
    "\n",
    "pdf_review_1 = np.array([3264,1528,3722,8179,16937])/33630 ##https://www.flipkart.com/boat-airdopes-201-earbuds-bluetooth-headset/p/itm6297d04b07e12\n",
    "\n",
    "review_2 = np.array([11128,4307,10616,22816,49028])\n",
    "\n",
    "pdf_review_2 = np.array([11128,4307,10616,22816,49028])/97895 ##https://www.flipkart.com/mivi-duopods-m20-true-wireless-bluetooth-headset/p/itmb5ec6b4c2b2e2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
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   "source": [
    "def get_pdf(input_array):\n",
    "\n",
    "    counts, bin_edges = np.histogram(input_array, bins=[1,2,3,4,5,6] \n",
    "                                    ,density = True)\n",
    "    pdf = counts/(sum(counts))\n",
    "\n",
    "    plt.plot(bin_edges[1:],pdf)\n",
    "    plt.show();\n",
    "\n",
    "    return pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "pdf_review_1 = get_pdf(review_1)\n",
    "pdf_review_2 = get_pdf(review_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "kl_divergence direct reviews 1.4547162327316459\nkl_diver pdf inf\n"
     ]
    }
   ],
   "source": [
    "print('kl_diver pdf',sum(kl_div(pdf_review_1,pdf_review_2))) #does not work for zero"
   ]
  },
  {
   "source": [
    "As seen, KL divergence can't handle '0', a complete explanation here: https://mathoverflow.net/questions/72668/how-to-compute-kl-divergence-when-pmf-contains-0s \n",
    "\n",
    "Hence we compute jensen-shannon distance, it provides a smoothed and normalized version of KL divergence, with scores between 0 (identical) and 1 (maximally different). Also it can handle zeroes: "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6f111d50a0>]"
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     },
     "metadata": {},
     "execution_count": 60
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "#! ideal review distribution using trunchnorm\n",
    "from scipy.stats import truncnorm\n",
    "myclip_a = 0\n",
    "myclip_b = 5\n",
    "my_mean = 5\n",
    "my_std = 1.5\n",
    "\n",
    "a, b = (myclip_a - my_mean) / my_std, (myclip_b - my_mean) / my_std\n",
    "x_range = np.linspace(0,5,5)\n",
    "ideal_rating=truncnorm.pdf(x_range, a, b, loc = my_mean, scale = my_std)\n",
    "plt.plot(x_range, ideal_rating)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "JS distance pdf 1:  0.1921150702897133\nJS distance pdf 2:  0.2084848773310317\n"
     ]
    }
   ],
   "source": [
    "#JS distance\n",
    "#print('kl_divergence direct reviews',kl_divergence(review_1,review_2))\n",
    "js_1_ideal=jensenshannon(pdf_review_1,ideal_rating)\n",
    "print('JS distance pdf 1: ',js_1_ideal)\n",
    "\n",
    "js_2_ideal=jensenshannon(pdf_review_2,ideal_rating)\n",
    "print('JS distance pdf 2: ',js_2_ideal)\n",
    "#! can see that pdf 2 is closer!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "NameError",
     "evalue": "name 'rating_1' is not defined",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-73-c9224331c1b2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnormalised_rating_1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrating_1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mjs_1_ideal\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mnormalised_rating_2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrating_2\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mjs_2_ideal\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'rating_1' is not defined"
     ]
    }
   ],
   "source": [
    "normalised_rating_1 = rating_1 - js_1_ideal\n",
    "normalised_rating_2 = rating_2 - js_2_ideal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}