notebooks/proximities_testing.ipynb

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    "<a href=\"https://colab.research.google.com/github/ZosoV/aco_random_walk/blob/main/notebooks/proximities_testing.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>\n",
    "\n",
    "# Testing Proximity Measures\n",
    "\n",
    "In this notebook, we aimed to study the behavior of different proximity measures. Somethings to check are how they are distributed across the environment, what is the effect of normalization and the differences or not between two types of proximities.\n"
   ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mounted at /content/gdrive\n"
     ]
    }
   ],
   "source": [
    "from google.colab import drive\n",
    "drive.mount('/content/gdrive')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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    "id": "68SGeWRERJas",
    "outputId": "7521b3fb-c12e-4b37-9b23-a8f784a5c4ab"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/content/gdrive/MyDrive/Proyectos/aco_random_walk\n"
     ]
    }
   ],
   "source": [
    "%cd /content/gdrive/MyDrive/Proyectos/aco_random_walk/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "source": [
    "# import necessary libraries\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.pyplot import figure\n",
    "\n",
    "import numpy as np\n",
    "import random\n",
    "import os\n",
    "\n",
    "#own functions\n",
    "import model.graph_env as ge\n",
    "import utils.visualization as vis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NpCu8uTIDofR"
   },
   "source": [
    "### Proximity and Multiplication Step\n",
    "\n",
    "The `proximity` represents the separation of a node to the target node.\n",
    "\n",
    "On one hand, we have the `proximity`, which is the inverse relative distance of a neighbor node to the target node. In this section, we review the distribution of this metric in environments with different sizes. The proximity of current node $i$ respect to the neighbor node $j$ is\n",
    "\n",
    "$$ \\mathrm{proximity1}_{ij} = \\frac{1}{d_{jt}} = \\upsilon_{ij} $$\n",
    "\n",
    "where $d_{jt}$ is the manhattan or euclidean distance of the neighbor node $j$ to the target node $t$.\n",
    "\n",
    "Additionally, we propose a `proximity-2` to reduce the sparse values. This metric results from multiplying the previous proximity-1 to $d_{it}$, the distance of the current node $i$ to the target node $t$. This little change can alter the proximity values, reducing its variabality. In large environments, this variability is more noticed, because it is divided 1 by a large number $d_{jt}$ in some nodes.\n",
    "\n",
    "$$ \\mathrm{proximity2}_{ij} = \\frac{d_{it}}{d_{jt}} = \\upsilon_{ij} $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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   "source": [
    "def get_distance(pos1, pos2, distance):\n",
    "  x1, y1 = pos1\n",
    "  x2, y2 = pos2\n",
    "\n",
    "  if distance == 'euclidean':\n",
    "    result = np.sqrt((x2-x1)**2 + (y2-y1)**2)\n",
    "  elif distance == 'manhattan':\n",
    "    result = np.abs(x2-x1) + np.abs(y2-y1)\n",
    "\n",
    "  return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "executionInfo": {
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     "timestamp": 1622242616020,
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      "displayName": "Oscar Guarnizo",
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   "source": [
    "def get_proximity(graph, current_node, neighbor_node, target_node, \n",
    "                  mode = 'proximity_1', distance = 'euclidean'):\n",
    "  \"\"\"\n",
    "  Proximity. Calculate the proximity of the neighbor node.\n",
    "  :param graph:         graph environment\n",
    "  :param current_node:  index of the current node i\n",
    "  :param neighbor_node: index of the neihbor node j\n",
    "  :param target_node:   index of the neihbor node t\n",
    "  :param mode:          perform the proximity 1 or proximity 2\n",
    "  :param distance:      used distance to calculate the proximity\n",
    "  \"\"\"\n",
    "  pos_neighbor = graph.nodes[neighbor_node]['pos']\n",
    "  pos_target = graph.nodes[target_node]['pos']\n",
    "  pos_current = graph.nodes[current_node]['pos']\n",
    "\n",
    "  # distance: current node to target\n",
    "  dis_curr2target = get_distance(pos_current, pos_target, distance)\n",
    "  \n",
    "  # distance: neighbor to target\n",
    "  dis_neig2target = get_distance(pos_neighbor, pos_target, distance)\n",
    "  \n",
    "  if neighbor_node == target_node:\n",
    "    proximity = 1\n",
    "  else:\n",
    "\n",
    "    if mode == 'proximity_1':\n",
    "      proximity = 1/ dis_neig2target\n",
    "    elif mode == 'proximity_2':\n",
    "      proximity = dis_curr2target / dis_neig2target\n",
    "\n",
    "  return proximity"
   ]
  },
  {
   "cell_type": "markdown",
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    "id": "ygyOWLnPGkO6"
   },
   "source": [
    "We created some auxiliar functions to test our results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "executionInfo": {
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     "status": "ok",
     "timestamp": 1622242618091,
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   "source": [
    "# Calculate the proximities of the total environment\n",
    "def get_env_proximities(graph, \n",
    "                        normalization = None, \n",
    "                        proximity_mode = 'proximity_1', \n",
    "                        distance = 'manhattan', \n",
    "                        mode = None):\n",
    "\n",
    "  target_node = graph.size * graph.size - 1\n",
    "\n",
    "  proximities_env = []\n",
    "\n",
    "  for current_node in range(graph.number_of_nodes()):\n",
    "    if current_node != target_node:\n",
    "      neighbors = graph[current_node]\n",
    "\n",
    "      # print(\"Node: \", current_node)\n",
    "\n",
    "      tmp_proximities = []\n",
    "      for neighbor_node, _ in neighbors.items():\n",
    "          # get the weight per neighbor\n",
    "          proximity = get_proximity(graph, \n",
    "                                      current_node,\n",
    "                                      neighbor_node, \n",
    "                                      target_node,\n",
    "                                      proximity_mode,\n",
    "                                      distance)\n",
    "          # proximities_env.append(proximity)\n",
    "          tmp_proximities.append(proximity)\n",
    "      \n",
    "      if mode == 'local':\n",
    "        tmp_proximities = normalize_array(tmp_proximities, normalization)\n",
    "\n",
    "      proximities_env = np.concatenate((proximities_env,tmp_proximities))\n",
    "\n",
    "  if mode == 'global':\n",
    "    proximities_env = normalize_array(proximities_env, normalization)\n",
    "\n",
    "  return proximities_env"
   ]
  },
  {
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   "outputs": [],
   "source": [
    "graph = ge.PPGraph(size = 10, tau_0 = 0.1)\n",
    "proximities_env = get_env_proximities(graph, \n",
    "                                      proximity_mode = 'proximity_1', \n",
    "                                      distance = 'manhattan')"
   ]
  },
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     "timestamp": 1622242625065,
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   "source": [
    "proximities_options = ['proximity_1', 'proximity_2']\n",
    "distance_options = ['manhattan', 'euclidean']\n",
    "\n",
    "dict2plot = {}\n",
    "\n",
    "for proximity_mode in proximities_options:\n",
    "  for distance in distance_options:\n",
    "    proximities_env = get_env_proximities(graph, \n",
    "                                      proximity_mode = proximity_mode, \n",
    "                                      distance = distance)\n",
    "    title = proximity_mode + \" \" + distance\n",
    "    dict2plot[title] = proximities_env"
   ]
  },
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\n",
      "text/plain": [
       "<Figure size 1152x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vis.plot_histograms(dict2plot, bins=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QNINJFTMM4rV"
   },
   "source": [
    "Then, another behavior that we want to check is the normalization on this metrics\n",
    "\n",
    "### Local and Global Normalization\n",
    "\n",
    "In this section, we wondered if it is necessary to mantain the proximity values within of acceptable range of values. In this regard, we evaluate diverse normalization steps to a global and local level.\n",
    "\n",
    "* `global`: applies a normalization between all the proximities values of the whole environment.\n",
    "* `local`: applies a normalization in each step of the walker, or, in other words, between the proximities values of the neighbor nodes belonging to $N(n^i)$.\n",
    "\n",
    "In order to check different normalization methods, we used:\n",
    "\n",
    "* `standard`\n",
    "$$ X ^ {\\prime} = \\frac{X-\\mu}{\\sigma} $$ \n",
    "\n",
    "* `l2-norm`\n",
    "\n",
    "$$ X ^ {\\prime} = \\frac{X}{\\|\\boldsymbol{x}\\|_2} $$\n",
    "\n",
    "$$ \\|\\boldsymbol{x}\\|_{2}:=\\sqrt{x_{1}^{2}+\\cdots+x_{n}^{2}} $$\n",
    "\n",
    "* `max-min`\n",
    "$$ X^{\\prime}=\\frac{X-X_{\\min }}{X_{\\max }-X_{\\min }} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "executionInfo": {
     "elapsed": 271,
     "status": "ok",
     "timestamp": 1622243633373,
     "user": {
      "displayName": "Oscar Guarnizo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GheAnA882D9R56DoQ_3Y3rbrnPGkT1zqcIi2ysoQg=s64",
      "userId": "12551427865753564350"
     },
     "user_tz": 300
    },
    "id": "h_UgmmHUls8U"
   },
   "outputs": [],
   "source": [
    "def normalize_array(array, mode):\n",
    "  if mode == 'standard':\n",
    "    mean = np.mean(array)\n",
    "    std = np.std(array)\n",
    "\n",
    "    if std != 0.0:\n",
    "      array = (array - mean) / std\n",
    "\n",
    "  elif mode == 'l2-norm':\n",
    "    array = array / np.linalg.norm(array)\n",
    "\n",
    "\n",
    "  elif mode == 'max-min':\n",
    "    max = np.amax(array)\n",
    "    min = np.amin(array)\n",
    "    if (max - min) != 0.0:\n",
    "      array = (array - min) / (max - min)\n",
    "\n",
    "  return array\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "executionInfo": {
     "elapsed": 11,
     "status": "ok",
     "timestamp": 1622243633958,
     "user": {
      "displayName": "Oscar Guarnizo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GheAnA882D9R56DoQ_3Y3rbrnPGkT1zqcIi2ysoQg=s64",
      "userId": "12551427865753564350"
     },
     "user_tz": 300
    },
    "id": "925YX9bGq3Vl"
   },
   "outputs": [],
   "source": [
    "#function to perform global and local experiments\n",
    "def get_group_proximities(graph, mode = 'global'):\n",
    "  distances_options = ['euclidean', 'manhattan']\n",
    "  proximities_options = ['proximity-1', 'proximity-2']\n",
    "  normalization_options = ['none', 'standard', 'l2-norm', 'max-min']\n",
    "\n",
    "  data = {}\n",
    "\n",
    "  for proxi_mode in proximities_options:\n",
    "    for normalization in normalization_options:\n",
    "      for distance_mode in distances_options:\n",
    "        proximities_env = get_env_proximities(graph, \n",
    "                                              normalization = normalization, \n",
    "                                              proximity_mode = proxi_mode.replace('-','_'), \n",
    "                                              distance = distance_mode,\n",
    "                                              mode = mode)\n",
    "        \n",
    "        id = \"{}_{}_{}\".format(proxi_mode, normalization, distance_mode)\n",
    "\n",
    "\n",
    "        data[id] = proximities_env\n",
    "\n",
    "  return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 934
    },
    "executionInfo": {
     "elapsed": 5670,
     "status": "ok",
     "timestamp": 1622243640192,
     "user": {
      "displayName": "Oscar Guarnizo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GheAnA882D9R56DoQ_3Y3rbrnPGkT1zqcIi2ysoQg=s64",
      "userId": "12551427865753564350"
     },
     "user_tz": 300
    },
    "id": "-Tx6xLjkO-tt",
    "outputId": "80e02e69-d2ea-4c45-e85b-b7a2f37908ce"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x1152 with 16 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph = ge.PPGraph(size = 10, tau_0 = 0.1)\n",
    "dict2plot = get_group_proximities(graph, mode='local')\n",
    "vis.plot_histograms(dict2plot, bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 934
    },
    "executionInfo": {
     "elapsed": 5893,
     "status": "ok",
     "timestamp": 1622243662958,
     "user": {
      "displayName": "Oscar Guarnizo",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GheAnA882D9R56DoQ_3Y3rbrnPGkT1zqcIi2ysoQg=s64",
      "userId": "12551427865753564350"
     },
     "user_tz": 300
    },
    "id": "e0pUgfi3PTMM",
    "outputId": "25573eaf-171e-496d-9956-80d0d3c535e4"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x1152 with 16 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph = ge.PPGraph(size = 10, tau_0 = 0.1)\n",
    "dict2plot = get_group_proximities(graph, mode='global')\n",
    "vis.plot_histograms(dict2plot, bins=100)"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "authorship_tag": "ABX9TyON53t8fcRLS0lVGzE8DnGh",
   "collapsed_sections": [],
   "name": "proximities_testing.ipynb",
   "provenance": []
  },
  "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}