Weight Functions.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experiment with weight functions"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graphs\n",
    "Graphs for\n",
    "- 1/x\n",
    "- 1/x^2\n",
    "- 1/sqrt(x)\n",
    "- 1/log(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.arange(0,10,1)\n",
    "\n",
    "y1 = 1/(1+x) \n",
    "y2 = 1/np.exp2(1+x)\n",
    "y3 = 1/np.sqrt(1+x)\n",
    "y4 = np.exp2(-x-1)\n",
    "K = 2.5\n",
    "w = K*np.exp(-x)\n",
    "\n",
    "# plt.plot(x,w, label=\"2*e^-x\")\n",
    "plt.plot(x,y1,label=\"5.5a: 1/(1+x)\")\n",
    "plt.plot(x,y3, label=\"5.5b: 1/sqrt(1+x)\")\n",
    "plt.plot(x,y2,label=\"5.5c: 2^-(1+x)\")\n",
    "# plt.plot(x,y4, label=\"1/(1 + x)\")\n",
    "plt.legend()\n",
    "plt.title(\"Plots of various inverse functions\")\n",
    "plt.savefig(\"results/figures/ranking/inverse_functions.pdf\",format=\"pdf\", bbox_inches=\"tight\")\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before choosing an inverse weighting function for the operations and the newness, requirements need to be set.\n",
    "- The function should not deteriorate too quickly\n",
    "- Since the buzz will be multiplied to the weighted operation count, it should be taken into account that in can decrease the result rather fast. \n",
    "\n",
    "The importance of newness and recent operations, or the lack of importance of older operations, should be defined. For this, an experiment is set up to answer the following question: How active are APTs generally after they are first seen?\n",
    "\n",
    "Based on the graph, I decide to pursue the 1/x for the operations weighing since it prioritizes recent operations more compared to the inverse square root. \n",
    "For the buzz the inverse square root is chosen, since it does not diminish the number of operations too quickly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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>x</th>\n",
       "      <th>1/x</th>\n",
       "      <th>1/(2^x)</th>\n",
       "      <th>1/sqrt(x)</th>\n",
       "      <th>1/log(x)</th>\n",
       "      <th>w</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>2.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>0.707107</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>0.919699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.125000</td>\n",
       "      <td>0.577350</td>\n",
       "      <td>0.125000</td>\n",
       "      <td>0.338338</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>0.062500</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.062500</td>\n",
       "      <td>0.124468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>0.200000</td>\n",
       "      <td>0.031250</td>\n",
       "      <td>0.447214</td>\n",
       "      <td>0.031250</td>\n",
       "      <td>0.045789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>0.166667</td>\n",
       "      <td>0.015625</td>\n",
       "      <td>0.408248</td>\n",
       "      <td>0.015625</td>\n",
       "      <td>0.016845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>0.142857</td>\n",
       "      <td>0.007812</td>\n",
       "      <td>0.377964</td>\n",
       "      <td>0.007812</td>\n",
       "      <td>0.006197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>0.125000</td>\n",
       "      <td>0.003906</td>\n",
       "      <td>0.353553</td>\n",
       "      <td>0.003906</td>\n",
       "      <td>0.002280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>0.111111</td>\n",
       "      <td>0.001953</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.001953</td>\n",
       "      <td>0.000839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.000977</td>\n",
       "      <td>0.316228</td>\n",
       "      <td>0.000977</td>\n",
       "      <td>0.000309</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x       1/x   1/(2^x)  1/sqrt(x)  1/log(x)         w\n",
       "0  0  1.000000  0.500000   1.000000  0.500000  2.500000\n",
       "1  1  0.500000  0.250000   0.707107  0.250000  0.919699\n",
       "2  2  0.333333  0.125000   0.577350  0.125000  0.338338\n",
       "3  3  0.250000  0.062500   0.500000  0.062500  0.124468\n",
       "4  4  0.200000  0.031250   0.447214  0.031250  0.045789\n",
       "5  5  0.166667  0.015625   0.408248  0.015625  0.016845\n",
       "6  6  0.142857  0.007812   0.377964  0.007812  0.006197\n",
       "7  7  0.125000  0.003906   0.353553  0.003906  0.002280\n",
       "8  8  0.111111  0.001953   0.333333  0.001953  0.000839\n",
       "9  9  0.100000  0.000977   0.316228  0.000977  0.000309"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "pd.DataFrame(list(zip(x,y1,y2,y3,y4,w)),columns=['x','1/x','1/(2^x)','1/sqrt(x)','1/log(x)','w'])"
   ]
  }
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