tutorial/probability_distribution_contact_duration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probability Distribution for different kinds of contact duration\n",
    "\n",
    "**Authors**: Andreas Kruff, Johann Schaible, Marcos Oliveira\n",
    "\n",
    "**Version**: 20.04.2020\n",
    "\n",
    "**Description**: In terms of the probability distribution measurements the face2face toolbox offers you three functions to calculate the probability for contact duration between two people, between a triangle and the duration of inter-contact intervals. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data sets that are used in this tutorial are part of the following paper:\n",
    "\n",
    "**Génois, Mathieu & Zens, Maria & Lechner, Clemens & Rammstedt, Beatrice & Strohmaier, Markus. (2019). Building connections: How scientists meet each other during a conference.**\n",
    "\n",
    "The data sets are available here: \n",
    "\n",
    "https://zenodo.org/record/2531537#.X0OObcgzaUl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For more information about the methods that are explained in this tutorial you can check out the online documentation of this toolbox here:\n",
    "\n",
    "https://gesiscss.github.io/face2face/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table of Contents\n",
    "#### [Contact Duration (Calculating and Plotting)](#contact_duration)\n",
    "#### [Triangle Duration (Calculating and Plotting)](#triangle_duration)\n",
    "#### [Inter-Contact Duration (Calculating and Plotting)](#inter-contact-duration)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At first we have to import a tij data set. For the import we use the Data Class Object that was introduced in the import_data_set tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import face2face as f2f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For now we use the predefined data set, called \"ICCSS17\", but you can import your own data sets as well like i showed you in the already mentioned import_data_set tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_iccss17 = f2f.Data(\"ICCSS17\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time</th>\n",
       "      <th>i</th>\n",
       "      <th>j</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Index</th>\n",
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       "      <th>0</th>\n",
       "      <td>1499752840</td>\n",
       "      <td>85</td>\n",
       "      <td>194</td>\n",
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       "      <td>85</td>\n",
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       "      <td>1499753040</td>\n",
       "      <td>85</td>\n",
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      "text/plain": [
       "             Time   i    j\n",
       "Index                     \n",
       "0      1499752840  85  194\n",
       "1      1499752880  85  194\n",
       "2      1499752940  85  194\n",
       "3      1499753040  85  194\n",
       "4      1499753060  85  194"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_iccss17.interaction.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Dataframe describes that at timestamp x two persons i and j talked for atleast 20 secs with each other. If the pair i and j occur multiple times in consecutive timestamps, they kept talking, if the difference between the timestamps is longer than 20 seconds, there was a break in the conversation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating and Plotting the Distribution of the contact duration <a name = \"contact_duration\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To calculate the probability, that two persons talked for a specific amount of time $\\Delta t$, you can use the function \"calculate_contact_duration\" from the \"distribution\" method.\n",
    "To use this function the function needs a dataframe as a parameter. The function has two lists as output.\n",
    "One list containts the probabilities in one list and the belonging $\\Delta ts$ in an additional list. The other list contains every $\\Delta t$ that is part of the data set. The second list is important for the powerlaw tutorials \"Statistical_characterization\" and \"How_to_use_statistical_characterization\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([0.0, 0.0, 0.0, 0.0, 0.0],\n",
       " [20.000000000000004,\n",
       "  22.339478214363815,\n",
       "  24.95261434450177,\n",
       "  27.871419227020965,\n",
       "  31.131648131271774])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "contact_duration_x_y_iccss17, delta_t_list = f2f.calculate_contact_duration(df_iccss17)\n",
    "contact_duration_x_y_iccss17[0][:5], contact_duration_x_y_iccss17[1][:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To plot the probability distribution you can use the \"plot_probability_distribution\"-method.\n",
    "For the parameters you need:\n",
    "1. The first list of the \"calculate_contact_duration\"-function\n",
    "2. A list of colors for the color of the marker\n",
    "3. A marker list, where you define the shape of the markers\n",
    "4. A list of the names for the labels to create a legend for the plot\n",
    "\n",
    "The function is defined, so that you can plot multiple datasets with their distributions so you can compare them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_ws16 = f2f.Data(\"WS16\")\n",
    "contact_duration_x_y_ws16, delta_t_list = f2f.calculate_contact_duration(df_ws16)\n",
    "color_list = [\"red\",\"blue\"]\n",
    "marker_list = [\"o\",\"v\"]\n",
    "label_list = [\"ICCSS17\",\"WS16\"]\n",
    "f2f.plot_contact_duration([contact_duration_x_y_iccss17,contact_duration_x_y_ws16], color_list, marker_list,label_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plots in this tutorial are based on the visualization of the paper that is cited below: \n",
    "\n",
    "**Cattuto C, Van den Broeck W, Barrat A, Colizza V, Pinton JF, et al. (2010) Dynamics of Person-to-Person Interactions from Distributed RFID Sensor Networks. PLOS ONE 5(7): e11596. https://doi.org/10.1371/journal.pone.0011596**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The y-axis shows the probability for every possible contact duration of the dataset you used. The x-axis shows the related time intervals that occur in this data sets as possible contact durations. The plot shows that short contact durations are highly likely, while the probability decreases the longer the contact duration is. As you can see the probability decreases pretty much linear for contact durations between one minute and 30 minutes. The probability for contact durations which are longer than 30 minutes are pretty similar and pretty much unlikely."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating and Plotting the Distribution of the triangle duration <a name= \"triangle_duration\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a next step we can analyze the duration of contacts between triangles.\n",
    "The function's in- and output works pretty much the same like the one before"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "triangle_x_y_iccss17, delta_t_list = f2f.calculate_triangle_duration(df_iccss17)\n",
    "triangle_x_y_ws16, delta_t_list = f2f.calculate_triangle_duration(df_ws16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting works the same way like before, you just have to import the \"plot_triangle_duration\"-function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "f2f.plot_triangle_duration([triangle_x_y_iccss17,triangle_x_y_ws16], color_list, marker_list,label_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plots in this tutorial are based on the visualization of the paper that is cited below: \n",
    "\n",
    "**Cattuto C, Van den Broeck W, Barrat A, Colizza V, Pinton JF, et al. (2010) Dynamics of Person-to-Person Interactions from Distributed RFID Sensor Networks. PLOS ONE 5(7): e11596. https://doi.org/10.1371/journal.pone.0011596**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this plot the y-axis shows the probability for the contact duration of triangles, so in this case we focus on three people talking to each other at the same time. The x-axis shows the different occuring contact durations for the triangles in this datasets. The range of variation is a lot smaller than in the previous plot. Although you can see almost a linear distribution for both datasets. It seems like that for the WS16 and the ICCSS17 data set almost every triangle lasts for 20 seconds, because the probability is close to 1. Between the duration of 200 to 500 seconds you can see a lot of noise in the data and not a clear distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating and Plotting the Distribution of the inter-contact duration<a name=\"inter-contact-duration\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At last we can analyze the interval between the contact of person A and B and the contact between A and C.\n",
    "This function works the same way as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "intervall_x_y_iccss17, delta_t_list = f2f.calculate_inter_contact_duration(df_iccss17)\n",
    "intervall_x_y_ws16, delta_t_list = f2f.calculate_inter_contact_duration(df_ws16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the plotting you need \"plot_inter_contact_duration\"-function this time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "f2f.plot_inter_contact_duration([intervall_x_y_iccss17,intervall_x_y_ws16], color_list, marker_list,label_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plots in this tutorial are based on the visualization of the paper that is cited below: \n",
    "\n",
    "**Cattuto C, Van den Broeck W, Barrat A, Colizza V, Pinton JF, et al. (2010) Dynamics of Person-to-Person Interactions from Distributed RFID Sensor Networks. PLOS ONE 5(7): e11596. https://doi.org/10.1371/journal.pone.0011596**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The y-axis of this plot shows the probability for the inter-contact duration and the x-axis the related occuring durations. From the start until the mark of 30 minutes the decreasing probability by an increasing inter-contact duration is pretty linear. After the 30 minutes mark the plot/the probabilty decreases more before high fluctuations occur. The reason for this fluctuations could be that the WS16 conference took two days so if a person A talked to person B at day one and then talked to person C at day 2 long inter-contact durations results of this. And this inter-contact durations are highly likely, because every person who was there on two or more days and talked to different persons day 1 and the next time on day 2 would be part of this fluctuation. The same applies for the ICCSS17 conference data set, which took three days."
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}