M2_SETI/D3/TP/TP1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TP1 KMEANS\n",
    "\n",
    "On nous propose de coder l'algorithme des kmeans afin de faire du clustering sur 2 classes puis plus de 2 classes.\n",
    "Plus tard, on utilisera notre algorithme pour segmenter une image sur l'information de couleur."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.spatial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# mean = [1,2,3,4]\n",
    "# sd = [0.25, 0.25, 0.1, 0.2]\n",
    "# clusters = 4\n",
    "mean = [1,2]\n",
    "sd = [0.25, 0.25]\n",
    "dim = 2\n",
    "nb = 10\n",
    "clusters = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fonctions à utiliser pour le clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_points(mean=1,sd=0.5, nb=100, dim=2, clusters=2):\n",
    "    size = []\n",
    "    # for i in range(0,dim):\n",
    "    size.append(nb)\n",
    "    size.append(dim)\n",
    "    points = np.random.normal(mean[0],sd[0],size=size)\n",
    "    for i in range(1,clusters):\n",
    "        points = np.concatenate((points,np.random.normal(mean[i],sd[i],size=size)),axis=0)\n",
    "    \n",
    "    return points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def distance(points,Pc):   \n",
    "    return scipy.spatial.distance.cdist(points[:,:], points[:,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kmeans(points = [0,0], K = 1, nb=1, dim=2):\n",
    "    # Initialisation K prototypes\n",
    "    Pc_index = []\n",
    "    for i in range(0,K):\n",
    "        Pc_index.append(np.random.randint(0,nb*dim))\n",
    "    Pc = points[Pc_index,:]\n",
    "\n",
    "    return Pc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def visualisation(points, Pc=[0,0], dim=2):\n",
    "    if(dim==2):\n",
    "        plt.plot(points[:,0], points[:,1], 'o')\n",
    "        plt.plot(Pc[:,0],Pc[:,1],'r+')\n",
    "        plt.grid(True)\n",
    "        plt.axis([min(mean)-1,max(mean)+1,min(mean)-1,max(mean)+1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20, 2)\n"
     ]
    }
   ],
   "source": [
    "points = gen_points(mean,sd,nb,dim,clusters)\n",
    "print(points.shape)\n",
    "# print(points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.         0.39108103 0.34583518 0.70546644 0.3203134  0.3516725\n",
      "  0.67971143 0.12125982 0.61902803 0.25895127 1.56135251 1.16925868\n",
      "  0.89449237 1.43352053 1.0743239  0.93510189 1.41988547 1.58011875\n",
      "  1.08411331 1.18671248]\n",
      " [0.39108103 0.         0.41265824 0.31753789 0.20134828 0.1520557\n",
      "  0.29442779 0.48416069 0.32820193 0.29379395 1.92061143 1.55795192\n",
      "  1.2792717  1.80777689 1.45979562 1.32616725 1.80571725 1.97050583\n",
      "  1.47031622 1.56670796]\n",
      " [0.34583518 0.41265824 0.         0.62859739 0.21220435 0.49592519\n",
      "  0.67380419 0.31854927 0.73773146 0.51626889 1.8336252  1.37308473\n",
      "  1.01281801 1.49334278 1.29787751 1.11001289 1.52748312 1.75952011\n",
      "  1.30415796 1.42577374]\n",
      " [0.70546644 0.31753789 0.62859739 0.         0.44061757 0.42670666\n",
      "  0.13916838 0.7887133  0.38129538 0.58971012 2.2340252  1.87432417\n",
      "  1.58220205 2.09814273 1.77707512 1.63872881 2.10818677 2.28550213\n",
      "  1.78747095 1.88420608]\n",
      " [0.3203134  0.20134828 0.21220435 0.44061757 0.         0.30494113\n",
      "  0.46740546 0.36865442 0.52868835 0.37372177 1.88068426 1.46844245\n",
      "  1.14902285 1.65807412 1.3803439  1.21975293 1.67330997 1.8710176\n",
      "  1.38894595 1.49825024]\n",
      " [0.3516725  0.1520557  0.49592519 0.42670666 0.30494113 0.\n",
      "  0.35637593 0.46606861 0.27034798 0.16380212 1.81240225 1.48388867\n",
      "  1.24193007 1.78456017 1.37947088 1.26763783 1.76514842 1.90097935\n",
      "  1.39123292 1.47795072]\n",
      " [0.67971143 0.29442779 0.67380419 0.13916838 0.46740546 0.35637593\n",
      "  0.         0.77794127 0.24735327 0.51809049 2.16596566 1.83655551\n",
      "  1.57217378 2.1022043  1.7339787  1.61275974 2.09839429 2.25219229\n",
      "  1.74541605 1.83405921]\n",
      " [0.12125982 0.48416069 0.31854927 0.7887133  0.36865442 0.46606861\n",
      "  0.77794127 0.         0.73558536 0.38006228 1.52663824 1.09978826\n",
      "  0.79543522 1.32585453 1.01264344 0.85309758 1.32192905 1.50347121\n",
      "  1.02093103 1.13291852]\n",
      " [0.61902803 0.32820193 0.73773146 0.38129538 0.52868835 0.27034798\n",
      "  0.24735327 0.73558536 0.         0.38834    1.99112336 1.71317083\n",
      "  1.50027904 2.04749497 1.6029451  1.51251266 2.01963574 2.13226014\n",
      "  1.61597543 1.69022564]\n",
      " [0.25895127 0.29379395 0.51626889 0.58971012 0.37372177 0.16380212\n",
      "  0.51809049 0.38006228 0.38834    0.         1.64887732 1.33143897\n",
      "  1.11366524 1.66342238 1.22437768 1.12471467 1.63153555 1.74982768\n",
      "  1.23666771 1.31925162]\n",
      " [1.56135251 1.92061143 1.8336252  2.2340252  1.88068426 1.81240225\n",
      "  2.16596566 1.52663824 1.99112336 1.64887732 0.         0.58770443\n",
      "  1.02271415 1.15136496 0.58808445 0.83705754 0.94499234 0.6037414\n",
      "  0.59102406 0.44614399]\n",
      " [1.16925868 1.55795192 1.37308473 1.87432417 1.46844245 1.48388867\n",
      "  1.83655551 1.09978826 1.71317083 1.33143897 0.58770443 0.\n",
      "  0.44427897 0.64604338 0.12332713 0.27518253 0.47328172 0.41918021\n",
      "  0.10638777 0.1741561 ]\n",
      " [0.89449237 1.2792717  1.01281801 1.58220205 1.14902285 1.24193007\n",
      "  1.57217378 0.79543522 1.50027904 1.11366524 1.02271415 0.44427897\n",
      "  0.         0.55487036 0.44065169 0.19125029 0.52649414 0.76267241\n",
      "  0.43456127 0.57921824]\n",
      " [1.43352053 1.80777689 1.49334278 2.09814273 1.65807412 1.78456017\n",
      "  2.1022043  1.32585453 2.04749497 1.66342238 1.15136496 0.64604338\n",
      "  0.55487036 0.         0.7423045  0.62079242 0.20929273 0.61317826\n",
      "  0.7258323  0.81728057]\n",
      " [1.0743239  1.45979562 1.29787751 1.77707512 1.3803439  1.37947088\n",
      "  1.7339787  1.01264344 1.6029451  1.22437768 0.58808445 0.12332713\n",
      "  0.44065169 0.7423045  0.         0.25088095 0.58359133 0.5339439\n",
      "  0.01763323 0.14206747]\n",
      " [0.93510189 1.32616725 1.11001289 1.63872881 1.21975293 1.26763783\n",
      "  1.61275974 0.85309758 1.51251266 1.12471467 0.83705754 0.27518253\n",
      "  0.19125029 0.62079242 0.25088095 0.         0.52473292 0.65180514\n",
      "  0.24624553 0.3914113 ]\n",
      " [1.41988547 1.80571725 1.52748312 2.10818677 1.67330997 1.76514842\n",
      "  2.09839429 1.32192905 2.01963574 1.63153555 0.94499234 0.47328172\n",
      "  0.52649414 0.20929273 0.58359133 0.52473292 0.         0.40874924\n",
      "  0.56617043 0.63624877]\n",
      " [1.58011875 1.97050583 1.75952011 2.28550213 1.8710176  1.90097935\n",
      "  2.25219229 1.50347121 2.13226014 1.74982768 0.6037414  0.41918021\n",
      "  0.76267241 0.61317826 0.5339439  0.65180514 0.40874924 0.\n",
      "  0.51939313 0.48569502]\n",
      " [1.08411331 1.47031622 1.30415796 1.78747095 1.38894595 1.39123292\n",
      "  1.74541605 1.02093103 1.61597543 1.23666771 0.59102406 0.10638777\n",
      "  0.43456127 0.7258323  0.01763323 0.24624553 0.56617043 0.51939313\n",
      "  0.         0.14516702]\n",
      " [1.18671248 1.56670796 1.42577374 1.88420608 1.49825024 1.47795072\n",
      "  1.83405921 1.13291852 1.69022564 1.31925162 0.44614399 0.1741561\n",
      "  0.57921824 0.81728057 0.14206747 0.3914113  0.63624877 0.48569502\n",
      "  0.14516702 0.        ]]\n"
     ]
    }
   ],
   "source": [
    "dist = distance(points,Pc=[0,0])\n",
    "print(dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.2631266  0.8529462 ]\n",
      " [1.1325475  1.17318217]]\n"
     ]
    }
   ],
   "source": [
    "Pc = kmeans(points,K=2,nb=nb,dim=dim)\n",
    "print(Pc)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualisation(points, Pc, dim=dim)"
   ]
  }
 ],
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