11-Analyse_en_composantes_principales-checkpoint.ipynb 450 KB
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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "# Analyse en composante principale\n",
    "\n",
    "C'est une bonne technique pour visualiser des données multi-dimensionnelles. \n",
    "Travaillons tout de suite avec des données de dimension 3. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Créons et observons des données gaussiennes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 2,
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   "metadata": {
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    "scrolled": true
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X.shape (400, 3)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "def create_gaussianData():    \n",
    "    nbData=400\n",
    "    \n",
    "    cov01=5\n",
    "    cov02=-1\n",
    "    \n",
    "    sigma2=np.array([\n",
    "        [20,    cov01,  cov02],\n",
    "        [cov01, 2,      0],\n",
    "        [cov02, 0,      0.1]\n",
    "    ])\n",
    "    \n",
    "    \"\"\"peut-on choisir n'importe quelles valeurs pour cov01 et cov02 ?\"\"\"\n",
    "    \n",
    "    U,S2,U_T = np.linalg.svd(sigma2)\n",
    "    \n",
    "    S_diag=np.diag(np.sqrt(S2))\n",
    "    \n",
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    "    sigma=U @ S_diag @ U_T\n",
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    "    \n",
    "    return np.random.normal(size=[nbData,3])@sigma+np.array([5,10,-3])\n",
    "\n",
    "\n",
    "X=create_gaussianData()\n",
    "\"\"\" A la la shape habituelle d'une dataFrame : les individus sont les lignes, les variables les colonnes. \"\"\"\n",
    "print(\"X.shape\",X.shape)"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
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   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
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       "<Figure size 576x576 with 1 Axes>"
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
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    "\"\"\"Observons les données dans leur ensemble, avec un tracé 3D \"\"\"\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from mpl_toolkits.mplot3d import proj3d\n",
    "\n",
    "fig = plt.figure(figsize=(8, 8))\n",
    "ax = fig.add_subplot(1,1,1, projection='3d')\n",
    "ax.plot(X[:,0],X[:,1],X[:,2],'o');\n"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 12,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": "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\n",
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      "text/plain": [
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       "<Figure size 432x288 with 1 Axes>"
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
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    "\"\"\"observons les 3 loi marginales\"\"\"\n",
    "plt.hist(X,bins=20)\n",
    "plt.show()"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "observons les va 2 à 2"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 13,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X[:,0],X[:,1],'.')\n",
    "plt.gca().set_aspect('equal')\n",
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    "plt.title(\"$0 → 1$\");"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 14,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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M7hAaz5/M/3WedGIAksi6CQnUnltJz0D+AVi/qNvYE8XChiSC4Vb8pqaq0hMgTtXeDbu7+fkbu3n2vQMMjTBBC6zY0O2L6z259UFMrAhxesjb0RkSHFfyxwP86wP5ycZ379+3pqoy77WVCsVYxiC0sGsyYvnieta2dDoPd6ovZqFHGUtm19Dc3kssnmzpDAwlC5+9MJhtCS6oq2bdti7L6g8ZXF4/haGYSTRuetIwJ00I8/CNF/HE2/s8VpWNAEvn1BCJmbQdOUVLRx9hQ/jSwhl0nzrLB64Ywc0L61jbmvkoIRwSaidVcvRUZumcIUNoPH8Ka6ULUNbbV7BGXF9cOIOeU2e56wqrk3THKGyUgtXvtoMajn3YvUBF2OCxry5i5+F+z4Ql/9IPfvyi7o5v2LiXWHDHA8zE8g6FWG3Vb1wETQAbL8Zy9nxBhF1EfgT8PTBdKZU+p0xTcthZNaM9QzHI95rK0vHbj9OqJwQ+OPbqiy+1dNLS0Udl2OC6+dM9wm6X5XH/hKwZuXHTig+suPUSmtt72XGoH1NZrp4/fNjjiQO4A93uEU4QBvCF+dN45OaL2XN0wJNZFDIEZarA3Ps7l86ibzBCLG4m1vYxnYlwtojZFrDtXhs4E2X1u+3ORCc79kEi9mH7zf1ZTza3L67npYDOampVBScHo4DVN3y2fgqNF0xJ+n74/cv3X3MhT2/aj2kqwqHkIGyQuGcTNA3qpN0jzPEKsI7V7Pm8hV1EZgFfAkb+FmtKntH+UqYKLqWydOxRhL2mip15FCQKze29xMzhrJ9p1ROoDInnWHtf97kgeSq+O/XPziQyBL5wkSXS9n7ulSltKkKWe8juLOz97WPsOIM7qP3HPT28tbsbpaCywsord9ejImygIFDE3GV/fPwTzyS1xQ1TOacixKKZk3n2vQMps57s62Jneb3U0unU/+6lszzusKvn1rLiK5ck3Vu/f7l6YgUvPmil3x4+eYY1Ww7m5XsOWv0ylUHgX0tpvC350aAQFvsvsdZkf7UAZWk+xYwUXMokN3+khzMofXR5IoXPf6z/XCPFEdyZRG5Rt/dzL9MgWNZ2qvP64wx2mmbfYIQbFnwmKWbhrkfb4X7ChjiCG+Qm809S297VTyxu8t7HvZ7c9FTCal+X2131b27v9fjyn960ny8uqks6Pkhk7fLstWqy8T2PtPplJDq8AqnfIHh+80H+6nc7nAlxqQK8pU6+L9pYBhxSSm1PrMeu0eRMLsGlTEcRqaz+fOcDpMoksvezl2lwdyiZ1jldepz9t3t9/buunJVyzoS7I3RbyaA8Kanprru//iFDHFE1zeAZ1ktm17DytkXOiCRVZ5lL+uPyxfVJQXO7De662gvkuZOAUgV4S5283nkK/BTLDZOWsX7nqab0GO3g0mi4ktKVmU+bMkmPc+8Tj5tcMHVi2voEWcnpUlJHKs890a2yIrhjSDfJLZt7478uiuSgeVBZyQvkkXLfUifnd56KyKXAhYBtrdcD20TkSqVU0lS2QrzzVFP+jFVwaSzJtU2ZjGByTaErZCfqnuiWqqxC5nBn41bzHxe0QF45IiO8fzq7gkQOAEszyYoRkWNAR0FODNOAcsnE0W0pTsatLVI5cZJRWVVtRgYHVORM8kypDPdxMS5tkcqJkypqzr+YRGJltO/w3gzqOmJ5RuXEOjNy5mg25WR5rcaSTO/LbKXU9HQ7jUseeyYVyxQRaVFKBb8frsTQbSlOdFuKE92W1BRM2JVScwpVlkaj0WhyJ3ixbI1Go9GULOUg7E+OdwUKiG5LcaLbUpzotqSgYMFTjUaj0RQH5WCxazQajcZFSQq7iNwpIm0iYorIUt9nPxGRfSKyR0S+PF51zAUReUxEDonI+4mfr4x3nbJFRG5JXPt9IrJivOuTDyJyQER2JO5Fy3jXJ1tE5BkR6RGRna5t54nIehH5KPG76CcNpGhHST4rIjJLRN4WkV0JDfvzxPaC3peSFHZgJ3A7sNG9UUQWAncDi4BbgH8VkdDYVy8vfqmUujzx88Z4VyYbEtf6CeBWYCFwT+KelDI3Ju5FKabVPYv1HLhZAbyllJoPvJX4v9h5luR2QGk+KzHgR0qphUAT8HDiGSnofSlJYVdK7VZK7Qn4aBnwglJqSCm1H9gHXDm2tftUcyWwTynVrpSKAC9g3RPNOKCU2gic8G1eBvw68fevga+PaaVyIEU7ShKl1BGl1LbE3wPAbuACCnxfSlLYR+ACoNP1f1diWynxAxH5IDH8LPphso9yuP5uFPCmiLQm1joqB2YopY4k/j4KzBjPyuRJKT8riMgc4HPAZgp8X4pW2EVkg4jsDPgpaQswTbv+DZgHXA4cAX4xrpXVXKOUWozlWnpYRK4b7woVEmWlxJVqWlxJPysici6wDnhEKXXK/Vkh7kvRvhov1eJjaTgEzHL9X5/YVjRk2i4ReQp4fZSrU2iK/vpng1LqUOJ3j4i8guVq2jjyUUVPt4jMVEodEZGZQM94VygXlFLOG0NK7VkRkQosUX9OKfVyYnNB70vRWuw58hpwt4hMEJELgfnAlnGuU8YkbqjNN7CCxKXEVmC+iFwoIpVYgezXxrlOOSEik0Sk2v4ba3nqUrsfQbwGfDvx97cp0RfklOqzItZSuL8Cdiul/sH1UUHvS0lOUBKRbwD/DEwHTgLvK6W+nPjsUeC7WNHnR5RSvx+3imaJiPwGa2ipgAPAgy6/W0mQSDt7HAgBzyilfjbOVcoJEZkLvJL4Nww8X2ptEZE1wA1YKwd2A38N/A74LdCAtcLqN5VSRR2YTNGOGyjBZ0VErgHeBXaA80rbn2L52Qt2X0pS2DUajUaTmnJzxWg0Gs2nHi3sGo1GU2ZoYddoNJoyQwu7RqPRlBla2DUajabM0MKu0Wg0ZYYWdo1GoykztLBrNBpNmfH/DgPj9wpR7M4AAAAASUVORK5CYII=\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X[:, 0], X[:, 2],'.')\n",
    "plt.gca().set_aspect('equal')\n",
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    "plt.title(\"0 → 2\");"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 15,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X[:, 1], X[:, 2],'.')\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
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    "plt.title(\"1 → 2\");"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "estimons la matrice de covariance"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 16,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "cov\n",
      " [[21.06700438  5.31262625 -1.09234643]\n",
      " [ 5.31262625  2.09402173 -0.03962299]\n",
      " [-1.09234643 -0.03962299  0.1621997 ]]\n"
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     ]
    }
   ],
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   "source": [
    "mu = np.mean(X,axis=0)\n",
    "X_cen=X-mu\n",
    "cov=np.cov(X.T)\n",
    "print(\"cov\\n\",cov)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Considérons la décomposition en valeur singulière de la matrice de covariance. \n",
    "$$\n",
    "cov= U S U^T\n",
    "$$\n",
    "Le repère $U_0,U_1,U_2$ composé des trois colonnes de $U$ représente les principales direction du nuage des simulations. Ces directions sont ordonnée par odre décroissant d'importance: le grand axe du nuage étant $U_0$.  Pour observer au mieux le nuage en 2D, il faut le projeter sur le plan engendré par $U_0,U_1$, donc le plan orthogonal à $U_2$. Mais attention: \n",
    "\n",
    "* soit on considère le plan affine passant par l'espérance $\\mu$.\n",
    "* soit on centre le nuage, en soustrayant $\\mu$, et on considére le plan vectoriel passant par zéro. \n",
    "\n",
    "On préfèrera cette la seconde option. L'équation du plan est donc $ax+by+cz=0$ avec $[a,b,c]=U_2$. \n"
   ]
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  },
  {
   "cell_type": "code",
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   "execution_count": 23,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "U, S, V = np.linalg.svd(cov)\n",
    "\n",
    "normal=U[:,2]\n",
    "\n",
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    "# on crée la grille correspondant au plan de base z=0. \n",
    "lim=5\n",
    "xx, yy = np.meshgrid(np.linspace(-lim,+lim,10),np.linspace(-lim,+lim,10))\n",
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    "\n",
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    "#  on calcule les altitudes z\n",
    "z = (-normal[0] * xx - normal[1] * yy) * 1. / normal[2]\n",
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    "\n",
    "\n",
    "fig = plt.figure()\n",
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    "ax = fig.add_subplot(1,1,1, projection='3d')\n",
    "# le plan\n",
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    "ax.plot_surface(xx, yy, z, alpha=0.2)\n",
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    "# les points\n",
    "ax.plot(X_cen[:, 0], X_cen[:, 1], X_cen[:, 2], '.');"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 66,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
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    "U01=U[:,:2]\n",
    "X_proj=X_cen @ U01  \n",
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    "\n",
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    "\"\"\" la base canonique, un peu agrandie \"\"\"\n",
    "axis=np.diag([10,10,10])\n",
    "axis_proj= axis @ U01\n",
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    "\n",
    "plt.plot(X_proj[:,0],X_proj[:,1],'.')\n",
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    "plt.gca().set_aspect(\"equal\")\n",
    "lim=15\n",
    "plt.xlim(-lim,lim)\n",
    "plt.ylim(-lim,lim)\n",
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    "\n",
    "colors=np.diag([1,1,1])\n",
    "for i in range(3):\n",
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    "    plt.arrow(0, 0, axis_proj[i,0], axis_proj[i,1], head_width=0.1, head_length=0.2,color=colors[i,:])\n",
    "    plt.text(axis_proj[i,0]* 1.15, axis_proj[i,1] * 1.15, \"ax\"+str(i), color = 'k', ha = 'center', va = 'center')\n"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "## Interpréter des données\n",
    "\n",
    "Nous créons un jeu de donnée. L'input `X` comprend:\n",
    "* Le poids\n",
    "* La taille\n",
    "* Le tour de tête. \n",
    "\n",
    "L'output `Y` indique si l'individu est en surpoids (`Y=1`) ou pas (`Y=0`) \n",
    "\n",
    "Dans un premier temps, ne regardez pas comment ces données sont construites. Prenez-les comme de vraies données fournie par l'observations d'individus. \n"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 67,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X.shape: (200, 3)\n",
      "Y.shape: (200,)\n",
      "X[:4]: \n",
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      " [[46.46791289  1.44663793 40.51574735]\n",
      " [47.39702587  1.48813053 39.24891413]\n",
      " [58.34976165  1.67450926 38.72502885]\n",
      " [44.37618244  1.3495373  43.90415203]]\n",
      "Y[:10]:  [0 0 0 0 0 0 1 0 0 0]\n"
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     ]
    }
   ],
   "source": [
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    "def makeData_surPoids():\n",
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    "    nbData=200\n",
    "\n",
    "    \"\"\" des poids d'adultes, entre 50 et 100 kilos \"\"\"\n",
    "    poids=np.random.beta(2,5,size=nbData)*100 +30\n",
    "\n",
    "    \"\"\" des IMC (indices de masses corporelles), \"\"\"\n",
    "    IMC = np.random.beta(1,5,size=nbData)*25+16\n",
    "\n",
    "    \"\"\" des tailles, que l'on construit à partir des poids et de l'ICM\"\"\"\n",
    "    taille=np.sqrt(poids/IMC)-0.1\n",
    "\n",
    "    \"\"\" mesure du tour de tête \"\"\"\n",
    "    tete=np.random.beta(3,1)*10+2*IMC\n",
    "\n",
    "    X=np.stack([poids,taille,tete],axis=1)\n",
    "\n",
    "    Y=(IMC>25).astype(np.int32)\n",
    "\n",
    "    return X,Y\n",
    "\n",
    "\n",
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    "X,Y=makeData_surPoids()\n",
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    "print(\"X.shape:\",X.shape)\n",
    "print(\"Y.shape:\",Y.shape)\n",
    "print(\"X[:4]: \\n\",X[:4])\n",
    "print(\"Y[:10]: \",Y[:10])\n"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 68,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class0=X[Y==0]\n",
    "class1=X[Y==1]\n",
    "\n",
    "fig = plt.figure(figsize=(8, 8))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "plt.rcParams['legend.fontsize'] = 10\n",
    "ax.plot(class0[:,0], class0[:,1], class0[:,2], 'o', markersize=8, alpha=0.5, color='blue',label='ok')\n",
    "ax.plot(class1[:,0], class1[:,1], class1[:,2], '^', markersize=8, alpha=0.5, color='red' ,label='sur-poids')\n",
    "\n",
    "plt.title('Samples for class 1 and class 2')\n",
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    "ax.legend(loc='upper right');\n",
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    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A vous : projetez les donnée sur le plan de plus grande variance.\n",
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    "Faut-il centrer-réduire les données dans ce cas là ?\n",
    "\n",
    "Que peut-on en déduire de l'influence de la troisième variable (le tour de tête)?"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "## Iris: la star des jeux de données .\n",
    "\n",
    "Nous observons le jeux données `iris` étudié la première fois par Fisher,R.A. Il s'agit sans doute du jeu de données le plus célèbre au monde.  L'input `X` est constitué des 4 variables:\n",
    "* sepal length (cm)\n",
    "* sepal width (cm)\n",
    "* petal length (cm)\n",
    "* petal width (cm)\n",
    "\n",
    "L'output `Y` correspond à 3 espèces d'iris: \n",
    "* setosa\n",
    "* versicolor\n",
    "* virginica\n",
    "\n",
    "![data_set_iris](./img/iris.png)\n"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data.shape: (150, 5)\n",
      "data[:3]\n",
      " [[5.1 3.5 1.4 0.2 0. ]\n",
      " [4.9 3.  1.4 0.2 0. ]\n",
      " [4.7 3.2 1.3 0.2 0. ]]\n",
      "X.shape: (150, 4)\n",
      "Y.shape: (150,)\n",
      "Y\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
      " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2\n",
      " 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
      " 2 2]\n"
     ]
    }
   ],
   "source": [
    "data=np.loadtxt(\"./data/iris.csv\",delimiter=\",\")\n",
    "print(\"data.shape:\",data.shape)\n",
    "print(\"data[:3]\\n\",data[:3,:])\n",
    "X=data[:,:4]\n",
    "print(\"X.shape:\",X.shape)\n",
    "Y=data[:,4].astype(np.int64)\n",
    "print(\"Y.shape:\",Y.shape)\n",
    "print(\"Y\\n\",Y)"
   ]
  },
  {
   "cell_type": "markdown",
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   "metadata": {},
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   "source": [
    "Ce jeu de donnée est aussi inclus dans de nombreuses bibliothèques, comme `sklearn`. On peut donc le charger ainsi:\n",
    "```python\n",
    "    from sklearn import datasets\n",
    "    iris = datasets.load_iris()\n",
    "    X = iris.data\n",
    "    y = iris.target\n",
    "```\n",
    "et avoir des tas d'informations en tapant\n",
    "```python\n",
    "    print(iris.DESCR)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "scrolled": true
   },
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   "outputs": [
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cov\n",
      " [[ 0.68569351 -0.03926846  1.27368233  0.5169038 ]\n",
      " [-0.03926846  0.18800403 -0.32171275 -0.11798121]\n",
      " [ 1.27368233 -0.32171275  3.11317942  1.29638747]\n",
      " [ 0.5169038  -0.11798121  1.29638747  0.58241432]]\n"
     ]
    },
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    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
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    "\n",
    "input_names=[\"sepal_l\",\"sepal_w\",\"petal_l\",\"petal_w\"]\n",
    "output_names=[\"setosa\",\"versicolor\",\"virginica\"]\n",
    "\n",
    "cov=np.cov(X.T)\n",
    "U,S,U_T=np.linalg.svd(cov)\n",
    "print(\"cov\\n\",cov)\n",
    "\n",
    "X_proj = X@U[:,:3]\n",
    "plt.scatter(X_proj[:,0],X_proj[:,1],c=Y)\n",
    "plt.grid()\n"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "***A vous:*** Rajouter les 3 axes projetés. Mettez des légendes. Quelle est l'input le plus discriminante? Quelle est la combinaisons linéaire d'input la plus discriminante?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Application à la compression d'image\n",
    "\n",
    "Nous allons observer des images représentant des chiffres en écriture manuscrite. Chaque image a une résolution de $8\\times 8$ pixels, et peut donc être considéré comme un vecteur de $\\mathbb R^{64}$. Chaque image est donc un input, chaque chiffre représenté est l'output correspondant.  \n"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 59,
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   "metadata": {
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    "scrolled": false
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "digits.data.shape: (1797, 64)\n"
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     ]
    },
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
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       "<Figure size 432x288 with 40 Axes>"
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      ]
     },
     "metadata": {},
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     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "from sklearn.decomposition import PCA\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.datasets import load_digits\n",
    "\n",
    "digits = load_digits()\n",
    "print(\"digits.data.shape:\",digits.data.shape)\n",
    "\n",
    "k=-1\n",
    "for i in range(4):\n",
    "    for j in range(10):\n",
    "        k+=1\n",
    "        plt.subplot(4,10,k+1)\n",
    "        img=digits.data[k].reshape([8,8])\n",
    "        plt.imshow(img)\n",
    "        #on supprime les ticks\n",
    "        plt.xticks([])\n",
    "        plt.yticks([])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observons comment on fait de l'analyse en composante principale (=PCA=Principal Component Analysis) avec `sklearn`. La syntaxe peut vous paraitre obscure, de même que la syntaxe que nous avons utilisé précédemment peut paraitre obscure à un non-matheux. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1797, 64)\n",
      "(1797, 2)\n"
     ]
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    },
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA(2)  # project from 64 to 2 dimensions\n",
    "projected = pca.fit_transform(digits.data)\n",
    "print(digits.data.shape)\n",
    "print(projected.shape)\n",
    "\n",
    "plt.scatter(projected[:, 0], projected[:, 1],\n",
    "            c=digits.target, edgecolor='none', alpha=0.5,\n",
    "            cmap=plt.cm.get_cmap('nipy_spectral', 10))\n",
    "plt.xlabel('component 1')\n",
    "plt.ylabel('component 2')\n",
    "plt.colorbar();"
   ]
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Exo:*** Imaginons qu'on vous impose de compresser chaque des images de `digit` en résolution $n \\times n$ avec $n<8$.  Quelle technique adopter sachant que vous avez le droit d'effectuer une opération de décompression. Effectuer cette opération avec plusieur $n$ différents. Observez. Vous pouvez utiliser `sklearn`, ou bien `np.linalg.svd`.\n",
    "\n"
   ]
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  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}