Livrable1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Livrable 1: Réexpression d'une trajectoire GPS\n",
    "\n",
    "L'objectif de cette séance est de:\n",
    "    \n",
    "    - modéliser une trajectoire \n",
    "    - Transformer une trajectoire en chaine de caractères\n",
    "    - Définir les métriques de travail\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Modélisation d'une trajectoire \n",
    "\n",
    "Une trajectoire pour nous dans cette première étape est un numpy array de dimension $ n \\times m $ où $n$ est le nombre des points composant la trajectoire, et $m$ leur dimension. Du coup une trajectoire est de la forme suivante: \n",
    "\n",
    "\\begin{equation}\n",
    "T= \\begin{bmatrix} \n",
    "t_{0} & x_{0} & y_{0} \\\\\n",
    "t_{1} & x_{1} & y_{1}\\\\\n",
    ".. & .. & .. \\\\\n",
    "t_{n} & x_{n} & y_{n}\\\\ \n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "\n",
    "où: $ (t_{i}, x_{i}, y_{i}) $ est le vecteur représentant le point $i$; $t_{i}$ étant la dimension temporelle, et $(x_{i}, y_{i})$ la dimension spatiale.\n",
    "\n",
    "\n",
    "Par exemple: \n",
    "\n",
    "\\begin{equation}\n",
    "T_{0}= \\begin{bmatrix} \n",
    "0 & 1.5 & 1.5 \\\\\n",
    "6 & 1.8 & 2.5\\\\\n",
    "12 & 13 & 2.8 \\\\\n",
    "18 & 5.5 & 4.8\\\\ \n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "\n",
    "Est la trajectoire suivante:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": [
    "T0=np.array([[0,1.5,1.5],[6,1.8,2.5],[12,13,2.8],[18,5.5,4.8]])\n",
    "X=np.array([1.5,1.8,13,5.5])\n",
    "Y=np.array([1.5,2.5,2.8,4.8])\n",
    "plt.plot(X,Y)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Par la suite on prendra une trajectoire triviale sinusoïdale, et on se focalisera sur les propriétés spatiales.\n",
    "\n",
    "Soit la trajectoire suivante: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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": [
    "t = np.arange(0.0, 2.0, 0.01)\n",
    "s = np.sin(2 * np.pi * t)\n",
    "\n",
    "plt.plot(t,s)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Méthode Edit Distance appliquée au cas d'une trajectoire\n",
    "\n",
    "Soit deux trajectoire $T_{1}, T_{2}$.\n",
    "\n",
    "La méthode Edit Distance dans le cas d'une trajectoire s'inspire de Edit Distance dans le cas d'une chaine de caractères:\n",
    "\n",
    "Étant donné deux chaînes de caractères str1 et str2. L'idée est de trouver le nombre minimum d'éditions (opérations) nécessaires pour convertir 'str1' en 'str2'. cela implique les trois opérations suivantes:\n",
    "\n",
    "1- Insérer \n",
    "\n",
    "2- Enlever\n",
    "\n",
    "3- Remplacer\n",
    "\n",
    "Toutes les opérations ci-dessus ont un coût égal.\n",
    "\n",
    "Dans le cas d'une trajectoire, on se donne un milieu de travaille grillé (grid) , et on représente les deux trajectoires en question, puis on convertit en chaîne de caractères.\n",
    "\n",
    "<img src=\"editdis.png\">\n",
    "\n",
    "Le nombre d'opérations minimale sera alors:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "le nombre des opérations minimales sans simplification: 6\n",
      "le nombre des opérations minimales avec simplification: 3\n"
     ]
    }
   ],
   "source": [
    "def edit_distance(s1, s2):\n",
    "    m=len(s1)+1\n",
    "    n=len(s2)+1\n",
    "\n",
    "    tbl = {}\n",
    "    for i in range(m): tbl[i,0]=i\n",
    "    for j in range(n): tbl[0,j]=j\n",
    "    for i in range(1, m):\n",
    "        for j in range(1, n):\n",
    "            cost = 0 if s1[i-1] == s2[j-1] else 1\n",
    "            tbl[i,j] = min(tbl[i, j-1]+1, tbl[i-1, j]+1, tbl[i-1, j-1]+cost)\n",
    "\n",
    "    return tbl[i,j]\n",
    "\n",
    "print(\"le nombre des opérations minimales sans simplification:\", edit_distance(\"EAABBBCCCDD\", \"EAABBBFGGHHH\"))\n",
    "      \n",
    "print(\"le nombre des opérations minimales avec simplification:\", edit_distance(\"EABCD\", \"EABFGH\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Expression d'une trajectoire en fonction d'un ensemble de motifs: \n",
    "\n",
    "L'objectif maintenant c'est de modéliser une trajectoire avec des motifs simple. C'est à la fois un problème de matching et d'optimisation. \n",
    "\n",
    "Etant données notre trajectoire sinusoidale déssinés sur un grid.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": [
    "X = np.arange(0.0, 2.0, 0.2)\n",
    "Y = np.sin(2 * np.pi * X)\n",
    "plt.plot(X,Y)\n",
    "plt.scatter(X,Y)\n",
    "\n",
    "plt.text(0.25,0.5,\"A\")\n",
    "plt.text(0.75,0.5,\"B\")\n",
    "plt.text(1.25,0.5,\"C\")\n",
    "plt.text(1.75,0.5,\"D\")\n",
    "\n",
    "plt.text(0.25,-0.5,\"E\")\n",
    "plt.text(0.75,-0.5,\"F\")\n",
    "plt.text(1.25,-0.5,\"G\")\n",
    "plt.text(1.75,-0.5,\"H\")\n",
    "\n",
    "plt.axhline(y=0., color='grey')\n",
    "plt.axvline(x=0.,color='grey')\n",
    "plt.axvline(x=0.5,color='grey')\n",
    "plt.axvline(x=1.,color='grey')\n",
    "plt.axvline(x=1.5,color='grey')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La conversion de notre trajectoire sinusoidale en chaine de caractères nous donne alors: $'EAAFFGCCHH'$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Définition des motifs pour simplifier une trajectoire\n",
    "\n",
    "Dans cette partie On va définir des motifs et on va les transformer en chaine de caractères aussi pour après faire la transformation de notre trajectoire sinusoidale.\n",
    "\n",
    "Dans un premier temps nos motifs seront des barres horizontales et verticales, qu'on affinera plus tard. Une barre horizontale peut etre "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1afec6eff28>]"
      ]
     },
     "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": [
    "axes = plt.gca()\n",
    "axes.set_xlim(0., 1.8)\n",
    "axes.set_ylim(-1., 1.)\n",
    "\n",
    "plt.text(0.25,0.5,\"A\")\n",
    "plt.text(0.75,0.5,\"B\")\n",
    "plt.text(1.25,0.5,\"C\")\n",
    "plt.text(1.75,0.5,\"D\")\n",
    "\n",
    "plt.text(0.25,-0.5,\"E\")\n",
    "plt.text(0.75,-0.5,\"F\")\n",
    "plt.text(1.25,-0.5,\"G\")\n",
    "plt.text(1.75,-0.5,\"H\")\n",
    "\n",
    "plt.axhline(y=0., color='grey')\n",
    "plt.axvline(x=0.,color='grey')\n",
    "plt.axvline(x=0.5,color='grey')\n",
    "plt.axvline(x=1.,color='grey')\n",
    "plt.axvline(x=1.5,color='grey')\n",
    "\n",
    "plt.plot([0.2,0.2],[-0.75,0.75],'r')\n",
    "plt.plot([0.25,0.8],[0.75,0.75],'g')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avant de faire la réexpression , on définit les métriques avec lesquelles on va traveiller."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distance Euclidienne: \n",
    "\n",
    "C'est la mesure la plus simple possible entre deux objets de série temporelle. Elle compare les valeurs des objets au même instant $t_{i}$. \n",
    "\n",
    "+ Avantages:\n",
    "\n",
    "    + Facile à implémenter, et approche intuitive.\n",
    "\n",
    "    + Approche rapide \n",
    "\n",
    "+ Inconvénients: \n",
    "    + Approche naive: la dilatation du temps n'est pas pris en compte. \n",
    "    + Le bruit est déterminsite\n",
    "    + Tout décalage entre objets a un effet cumulatif\n",
    "    \n",
    "<img src=\"euc.png\">\n",
    "    \n",
    "Ci-dessous, on définit la distance euclidienne et d'autres fonctions géométriques relatives à cette métrique: distance d'un point à un segment, distance d'une point à une trajectoire, et l'intersection d'un cercle de rayon très petit avec un segment (supposé existant ici). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "def eucl_dist(x,y):\n",
    "    \"\"\"\n",
    "    Usage\n",
    "    -----\n",
    "    L2-norm between point x and y\n",
    "    Parameters\n",
    "    \"\"\"\n",
    "    dist = np.linalg.norm(x-y)\n",
    "    return dist\n",
    "\n",
    "def point_to_seg(p,s1,s2):\n",
    "    \"\"\"\n",
    "    Usage\n",
    "    -----\n",
    "    Point to segment distance between point p and segment delimited by s1 and s2\n",
    "    Parameters\n",
    "\n",
    "    dpl: float\n",
    "         Point to segment distance between p and s\n",
    "    \"\"\"\n",
    "    px = p[0]\n",
    "    py = p[1]\n",
    "    p1x = s1[0]\n",
    "    p1y = s1[1]\n",
    "    p2x = s2[0]\n",
    "    p2y = s2[1]\n",
    "    if p1x==p2x and p1y==p2y:\n",
    "        dpl=eucl_dist(p,s1)\n",
    "    else:\n",
    "        segl= eucl_dist(s1,s2)\n",
    "        u1 = (((px - p1x) * (p2x - p1x)) + ((py - p1y) * (p2y - p1y)))\n",
    "        u = u1 / (segl * segl)\n",
    "\n",
    "        if (u < 0.00001) or (u > 1):\n",
    "            #// closest point does not fall within the line segment, take the shorter distance\n",
    "            #// to an endpoint\n",
    "            ix = eucl_dist(p,s1)\n",
    "            iy = eucl_dist(p, s2)\n",
    "            if ix > iy:\n",
    "                dpl = iy\n",
    "            else:\n",
    "                dpl = ix\n",
    "        else:\n",
    "            # Intersecting point is on the line, use the formula\n",
    "            ix = p1x + u * (p2x - p1x)\n",
    "            iy = p1y + u * (p2y - p1y)\n",
    "            dpl = eucl_dist(p, np.array([ix, iy]))\n",
    "\n",
    "    return dpl\n",
    "\n",
    "def point_to_trajectory (p, t):\n",
    "    \"\"\"\n",
    "    Usage\n",
    "    -----\n",
    "    Point-to-trajectory distance between point p and the trajectory t.\n",
    "    The Point to trajectory distance is the minimum of point-to-segment distance between p and all segment s of t\n",
    "    Parameters\n",
    "    ----------\n",
    "    param p: 1x2 numpy_array\n",
    "    param t : len(t)x2 numpy_array\n",
    "    Returns\n",
    "    -------\n",
    "    dpt : float,\n",
    "          Point-to-trajectory distance between p and trajectory t\n",
    "    \"\"\"\n",
    "    dpt=min(map(lambda s1,s2 : point_to_seg(p,s1,s2), t[:-1],t[1:] ))\n",
    "    return dpt\n",
    "\n",
    "\n",
    "def circle_line_intersection(px,py,s1x,s1y,s2x,s2y,eps):\n",
    "    \"\"\"\n",
    "    Usage\n",
    "    -----\n",
    "    Find the intersections between the circle of radius eps and center (px, py) and the line delimited by points\n",
    "    (s1x, s1y) and (s2x, s2y).\n",
    "    It is supposed here that the intersection between them exists. If no, raise error\n",
    "    -------\n",
    "    intersect : 2x2 numpy_array\n",
    "                Coordinate of the two intersections.\n",
    "                If the two intersections are the same, that's means that the line is a tangent of the circle.\n",
    "    \"\"\"\n",
    "    if s2x==s1x :\n",
    "        rac=math.sqrt((eps*eps) - ((s1x-px)*(s1x-px)))\n",
    "        y1 = py+rac\n",
    "        y2 = py-rac\n",
    "        intersect = np.array([[s1x,y1],[s1x,y2]])\n",
    "    else:\n",
    "        m= (s2y-s1y)/(s2x-s1x)\n",
    "        c= s2y-m*s2x\n",
    "        A=m*m+1\n",
    "        B=2*(m*c-m*py-px)\n",
    "        C=py*py-eps*eps+px*px-2*c*py+c*c\n",
    "        delta=B*B-4*A*C\n",
    "        if delta <= 0 :\n",
    "            x = -B/(2*A)\n",
    "            y = m*x+c\n",
    "            intersect = np.array([[x,y],[x,y]])\n",
    "        elif delta > 0 :\n",
    "            sdelta = math.sqrt(delta)\n",
    "            x1= (-B+sdelta)/(2*A)\n",
    "            y1=m*x1+c\n",
    "            x2= (-B-sdelta)/(2*A)\n",
    "            y2=m*x2+c\n",
    "            intersect = np.array([[x1,y1],[x2,y2]])\n",
    "        else :\n",
    "            raise ValueError(\"The intersection between circle and line is supposed to exist\")\n",
    "    return intersect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dynamic Time Wraping; Métrique et mesures de similarités:\n",
    "\n",
    "C'est une approche différente de l'approche euclidienne, qui utilise la programmation dynamique. \n",
    "\n",
    "+ Avantages: \n",
    "    + Au contraire de l'approche euclidienne, Les différences temporelles sont prises en compte.\n",
    "    + Plus performante que la métrique euclidienne.\n",
    "+ Inconvénients: \n",
    "    + Le mappage entre tous les objets dans les deux trajectoires signifie que chaque écart est pris en compte et ajouté à la pénalité. \n",
    "    + C'est une ditance non métrique: ne satisfait pas l'inégalité triangulaire.\n",
    "    \n",
    "<img src=\"dtw.png\">\n",
    "\n",
    "On définit ci-dessous l'algorithme pour calculer le DTW entre deux trajectoires. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'basic_euclidean'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-30-08ba99890a68>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[0mbasic_euclidean\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0meucl_dist\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mbasic_geographical\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mgreat_circle_distance\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;31m#############\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;31m# euclidean #\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'basic_euclidean'"
     ]
    }
   ],
   "source": [
    "from basic_euclidean import eucl_dist\n",
    "from basic_geographical import great_circle_distance\n",
    "\n",
    "#############\n",
    "# euclidean #\n",
    "#############\n",
    "\n",
    "def e_dtw(t0,t1):\n",
    "    \"\"\"\n",
    "    Usage\n",
    "    -----\n",
    "    The Dynamic-Time Warping distance between trajectory t0 and t1.\n",
    "    Parameters\n",
    "    ----------\n",
    "    param t0 : len(t0)x2 numpy_array\n",
    "    param t1 : len(t1)x2 numpy_array\n",
    "    Returns\n",
    "    -------\n",
    "    dtw : float\n",
    "          The Dynamic-Time Warping distance between trajectory t0 and t1\n",
    "    \"\"\"\n",
    "\n",
    "    n0 = len(t0)\n",
    "    n1 = len(t1)\n",
    "    C=np.zeros((n0+1,n1+1))\n",
    "    C[1:,0]=float('inf')\n",
    "    C[0,1:]=float('inf')\n",
    "    for i in np.arange(n0)+1:\n",
    "        for j in np.arange(n1)+1:\n",
    "            C[i,j]=eucl_dist(t0[i-1],t1[j-1]) + min(C[i,j-1],C[i-1,j-1],C[i-1,j])\n",
    "    dtw = C[n0,n1]\n",
    "    return dtw\n",
    "\n",
    "################\n",
    "# geographical #\n",
    "################\n",
    "\n",
    "def g_dtw(t0,t1):\n",
    "    \"\"\"\n",
    "    Usage\n",
    "    -----\n",
    "    The Dynamic-Time Warping distance between trajectory t0 and t1.\n",
    "    Parameters\n",
    "    ----------\n",
    "    param t0 : len(t0)x2 numpy_array\n",
    "    param t1 : len(t1)x2 numpy_array\n",
    "    Returns\n",
    "    -------\n",
    "    dtw : float\n",
    "          The Dynamic-Time Warping distance between trajectory t0 and t1\n",
    "    \"\"\"\n",
    "    n0 = len(t0)\n",
    "    n1 = len(t1)\n",
    "    C=np.zeros((n0+1,n1+1))\n",
    "    C[1:,0]=float('inf')\n",
    "    C[0,1:]=float('inf')\n",
    "    for i in np.arange(n0)+1:\n",
    "        for j in np.arange(n1)+1:\n",
    "            C[i,j]=great_circle_distance(t0[i-1][0],t0[i-1][1],t1[j-1][0],t1[j-1][1]) + min(C[i,j-1],C[i-1,j-1],C[i-1,j])\n",
    "    dtw = C[n0,n1]\n",
    "    return dtw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Longest Common SubSequence: \n",
    "\n",
    "Ici, on inverse le problème: Quelles parties des trajectoires sont similaires ? \n",
    "\n",
    "+ Avantages: \n",
    "    + ignore les parties qui ne matchent pas.\n",
    "    + Bon avec le bruit et les valeurs aberrantes.\n",
    "    + Permet la distorsion temporelle.\n",
    "+ Incovénients: \n",
    "    + Cette distance n'est pas métrique\n",
    "    \n",
    "<img src=\"lcss.png\">\n",
    "\n",
    "Ci-dessous l'algorithme permettant de calculer la distance LCSS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'basic_euclidean'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-31-d6ba8621b94c>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[0mbasic_euclidean\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0meucl_dist\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mbasic_geographical\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mgreat_circle_distance\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;31m#############\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;31m# euclidean #\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'basic_euclidean'"
     ]
    }
   ],
   "source": [
    "from basic_euclidean import eucl_dist\n",
    "from basic_geographical import great_circle_distance\n",
    "\n",
    "#############\n",
    "# euclidean #\n",
    "#############\n",
    "\n",
    "def e_lcss(t0, t1,eps):\n",
    "    \"\"\"\n",
    "    Usage\n",
    "    -----\n",
    "    The Longuest-Common-Subsequence distance between trajectory t0 and t1.\n",
    "    Parameters\n",
    "    ----------\n",
    "    param t0 : len(t0)x2 numpy_array\n",
    "    param t1 : len(t1)x2 numpy_array\n",
    "    eps : float\n",
    "    Returns\n",
    "    -------\n",
    "    lcss : float\n",
    "           The Longuest-Common-Subsequence distance between trajectory t0 and t1\n",
    "    \"\"\"\n",
    "    n0 = len(t0)\n",
    "    n1 = len(t1)\n",
    "    # An (m+1) times (n+1) matrix\n",
    "    C = [[0] * (n1+1) for _ in range(n0+1)]\n",
    "    for i in range(1, n0+1):\n",
    "        for j in range(1, n1+1):\n",
    "            if eucl_dist(t0[i-1],t1[j-1])<eps:\n",
    "                C[i][j] = C[i-1][j-1] + 1\n",
    "            else:\n",
    "                C[i][j] = max(C[i][j-1], C[i-1][j])\n",
    "    lcss = 1-float(C[n0][n1])/min([n0,n1])\n",
    "    return lcss\n",
    "\n",
    "################\n",
    "# geographical #\n",
    "################\n",
    "\n",
    "def g_lcss(t0, t1,eps):\n",
    "    \"\"\"\n",
    "    Usage\n",
    "    -----\n",
    "    The Longuest-Common-Subsequence distance between trajectory t0 and t1.\n",
    "    Parameters\n",
    "    ----------\n",
    "    param t0 : len(t0)x2 numpy_array\n",
    "    param t1 : len(t1)x2 numpy_array\n",
    "    eps : float\n",
    "    Returns\n",
    "    -------\n",
    "    lcss : float\n",
    "           The Longuest-Common-Subsequence distance between trajectory t0 and t1\n",
    "    \"\"\"\n",
    "    n0 = len(t0)\n",
    "    n1 = len(t1)\n",
    "    # An (m+1) times (n+1) matrix\n",
    "    C = [[0] * (n1+1) for _ in range(n0+1)]\n",
    "    for i in range(1, n0+1):\n",
    "        for j in range(1, n1+1):\n",
    "            if great_circle_distance(t0[i-1,0],t0[i-1,1],t1[j-1,0],t1[j-1,1])<eps:\n",
    "                C[i][j] = C[i-1][j-1] + 1\n",
    "            else:\n",
    "                C[i][j] = max(C[i][j-1], C[i-1][j])\n",
    "    lcss = 1-float(C[n0][n1])/min([n0,n1])\n",
    "    return lcss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparaison des méthodes: \n",
    "\n",
    "Dans cette partie, on crée deux trajectoires et on compart entre les 4 distances ci-dessus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1afec9c28d0>]"
      ]
     },
     "execution_count": 32,
     "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": [
    "traj_A = np.array([[-122.39534, 37.77678],[-122.3992 , 37.77631],[-122.40235, 37.77594],[-122.40553, 37.77848],\n",
    "                   [-122.40801, 37.78043],[-122.40837, 37.78066],[-122.41103, 37.78463],[-122.41207, 37.78954],\n",
    "                   [-122.41252, 37.79232],[-122.41316, 37.7951 ],[-122.41392, 37.7989 ],[-122.41435, 37.80129],\n",
    "                   [-122.41434, 37.80129]])\n",
    "traj_B = np.array([[-122.39472, 37.77672],[-122.3946 , 37.77679],[-122.39314, 37.77846],[-122.39566, 37.78113],\n",
    "                   [-122.39978, 37.78438],[-122.40301, 37.78708],[-122.4048 , 37.78666],[-122.40584, 37.78564],\n",
    "                   [-122.40826, 37.78385],[-122.41061, 37.78321],[-122.41252, 37.78299]])\n",
    "traj_C = np.array([[-122.39542, 37.77665],[-122.3988 , 37.77417],[-122.41042, 37.76944],[-122.41459, 37.77016],\n",
    "                   [-122.41462, 37.77013]])\n",
    "traj_list = [traj_A, traj_B, traj_C]\n",
    "\n",
    "LA1=[traj_A[i][0] for i in range(len(traj_A))]\n",
    "LA2=[traj_A[i][1] for i in range(len(traj_A))]\n",
    "\n",
    "LB1=[traj_B[i][0] for i in range(len(traj_B))]\n",
    "LB2=[traj_B[i][1] for i in range(len(traj_B))]\n",
    "\n",
    "\n",
    "plt.plot(LA1,LA2)\n",
    "#Traj_A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1afec8212e8>]"
      ]
     },
     "execution_count": 33,
     "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": [
    "plt.plot(LB1,LB2,'r')\n",
    "#Traj_B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'e_lcss' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-34-ef2ee29da72b>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0ma\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0me_lcss\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtraj_A\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtraj_B\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0.001\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0me_dtw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtraj_A\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtraj_B\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mc\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0me_edr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtraj_A\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtraj_B\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0.001\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mL\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mc\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'e_lcss' is not defined"
     ]
    }
   ],
   "source": [
    "a=e_lcss(traj_A, traj_B,0.001)\n",
    "b=e_dtw(traj_A, traj_B)\n",
    "c=e_edr(traj_A, traj_B,0.001)\n",
    "\n",
    "L=[a,b,c]\n",
    "\n",
    "plt.scatter([0.,1., 2.],L)\n",
    "plt.plot(L)\n",
    "\n",
    "plt.text(0.1,0.9,'LCSS')\n",
    "plt.text(1.,0.3,'DTW')\n",
    "plt.text(1.75,0.9,'EDR')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "D'après ce petit jeu de données qu'on a créee, la distance et la mesure de similarités la plus efficace est Dynamix Time Warping. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Etapes à venir: \n",
    "\n",
    "+ Créer un jeu de données non aléatoires et tester les algorithmes.\n",
    "\n",
    "+ Réexprimer une trajectoire de notre jeu de données avec des motifs simple Via une programmation dynamique (avec Edit Dist), couplé avec un algorithme d’Optimisation (Glouton) \n",
    "\n",
    "+ Tester sur des données GPS réels (cela dit que nous devons faire la correspondance entre notre modélisation simplifiée d’une trajectoire et une modélisation réelle) \n",
    "\n",
    "    + Tester avec des données qu'on connait à priori\n",
    "    \n",
    "    + revoir Edit Distance\n",
    "    \n",
    "    + Recalage/ notion de repère locale et décider la direction au fur et à mesure.\n",
    "    \n",
    "    + Voir l'usage dans d'autres contextes (financier par exemple)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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