OSVM_simulations_kernels.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**novelty detection**:\n",
    "The training data is not polluted by outliers, and we are interested in detecting anomalies in new observations.\n",
    "\n",
    "**outlier detection**:\n",
    "The training data contains outliers, and we need to fit the central mode of the training data, ignoring the deviant observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/bin/sh: activate: No such file or directory\r\n"
     ]
    }
   ],
   "source": [
    "!source activate py2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#!/anaconda3/envs/py2/bin/pip install cvxopt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from cvxopt import solvers, lapack, matrix, spmatrix\n",
    "solvers.options['show_progress'] = 0\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "% matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def RBF_Kernel(X, sigma2, Y = None):\n",
    "    \" Compute the RBF kernel matrix of X\"\n",
    "    from sklearn.metrics.pairwise import euclidean_distances\n",
    "    \n",
    "    if type(Y)==type(None):\n",
    "        Y = X\n",
    "    \n",
    "    K = euclidean_distances(X,Y, squared=True)\n",
    "    K *= -1./sigma2\n",
    "    K = np.exp(K)\n",
    "    return K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Poly_Kernel(X, d, c, Y=None):\n",
    "    if type(Y)==type(None):\n",
    "        Y = X.copy()\n",
    "    K = ( np.dot(X,Y.T) +c)**d\n",
    "    #from sklearn.metrics.pairwise import polynomial_kernel\n",
    "    #K = polynomial_kernel(X,Y,degree=d,coef0=c)\n",
    "    return(K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fit(X, nu, kernel):  #kernel is a list [kernel_type,sigma/d,c]\n",
    "    n = X.shape[0]\n",
    "    if kernel[0] == 'RBF':\n",
    "        sigma2 = kernel[1]\n",
    "        K = RBF_Kernel(X, sigma2)\n",
    "    else:\n",
    "        d, c = kernel[1:]\n",
    "        K = Poly_Kernel(X,d,c)\n",
    "\n",
    "    P = matrix(K, tc = 'd')\n",
    "    q = matrix([0]*n, tc = 'd')\n",
    "    G = matrix(np.concatenate([np.eye(n),-np.eye(n)], axis = 0), tc = 'd')\n",
    "    h_value = [1./(n * nu)]*n\n",
    "    h_value.extend([0]*n)\n",
    "    h = matrix(h_value, tc = 'd')\n",
    "    A = matrix(np.reshape([1]*n, (1,n)), tc = 'd')\n",
    "    b = matrix(1, tc = 'd')\n",
    "    \n",
    "    sol = solvers.qp(P,q,G,h,A,b)\n",
    "    alpha = np.array(sol['x'])\n",
    "    ix_in = np.where((alpha > 1e-5) & (alpha < 1./(n*nu)))[0][0]\n",
    "    rho = np.transpose(np.dot(np.reshape(alpha, (1,n)), K[:,ix_in]))\n",
    "\n",
    "    return alpha, rho\n",
    "\n",
    "def predict(X, newData, alpha, rho, kernel):\n",
    "    n = X.shape[0]\n",
    "    if kernel[0] == 'RBF':\n",
    "        sigma2 = kernel[1]\n",
    "        K = RBF_Kernel(X, sigma2, newData)\n",
    "    else:\n",
    "        d, c = kernel[1:]\n",
    "        K = Poly_Kernel(X,d,c,Y=newData)\n",
    "    return np.transpose(np.dot(np.reshape(alpha, (1,n)), K) - rho)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_grid(X, step = 0.05):\n",
    "    x_axis = np.arange(min(X[:,0])-step,max(X[:,0])+2*step,step)\n",
    "    y_axis = np.arange(min(X[:,1])-step,max(X[:,1])+2*step,step)\n",
    "\n",
    "    my_grid = []\n",
    "    for i in x_axis:\n",
    "        for j in y_axis:\n",
    "            my_grid.append([i,j])#,1])\n",
    "    my_grid = np.array(my_grid)\n",
    "    \n",
    "    return x_axis, y_axis, my_grid\n",
    "\n",
    "def plot(X,step):\n",
    "    plt.scatter(X[:,0], X[:,1], edgecolors  = 'black')\n",
    "    plt.xlim((min(X[:,0])-step,max(X[:,0])+step))\n",
    "    plt.ylim((min(X[:,1])-step,max(X[:,1])+step))\n",
    "    pass\n",
    "\n",
    "def Normalize_Pred(pred):    \n",
    "    pred_100 = pred -np.min(pred)\n",
    "    pred_100 = (pred_100 / np.max(pred_100)) * 100\n",
    "    return pred_100\n",
    "\n",
    "def get_delim(pred_100, x_axis, y_axis, eps = 0):\n",
    "    ix_delim = np.where((pred_100  < eps) & (pred_100  > -eps))[0]\n",
    "    x_delim = []\n",
    "    y_delim = []\n",
    "    for i in range(len(ix_delim)):\n",
    "        a, b = np.divmod(ix_delim[i],len(y_axis))\n",
    "        x_delim.append(x_axis[a])\n",
    "        y_delim.append(y_axis[b])\n",
    "    return x_delim, y_delim\n",
    "\n",
    "def plot_pred(X, x_axis, y_axis, pred_100, x_delim, y_delim, step = 0.05):\n",
    "    norm_colors = mpl.colors.Normalize(vmin=0,vmax=100)\n",
    "    X_axis, Y_axis = np.meshgrid(x_axis, y_axis)\n",
    "    C = np.transpose(pred_100.reshape((len(x_axis), len(y_axis))))\n",
    "    plt.pcolor(X_axis, Y_axis, C, norm= norm_colors, cmap = 'YlOrRd')\n",
    "    plt.scatter(x_delim, y_delim, c = 'blue', s = 10)\n",
    "    plot(X,step)\n",
    "    plt.xlim((min(X[:,0])-step,max(X[:,0])+step))\n",
    "    plt.ylim((min(X[:,1])-step,max(X[:,1])+step))\n",
    "    pass\n",
    "\n",
    "def plot_pred_plan(X, alpha, rho, kernel, step = 0.05, eps = 0):\n",
    "    x_axis, y_axis, my_grid = get_grid(X, step)\n",
    "    pred = predict(X, my_grid, alpha, rho, kernel)\n",
    "    x_delim, y_delim = get_delim(pred, x_axis, y_axis, eps)\n",
    "    pred_100 = Normalize_Pred(pred)\n",
    "    #print(\"pred100\",pred_100.shape)\n",
    "    plot_pred(X, x_axis, y_axis, pred_100, x_delim, y_delim, step)\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Artifical data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.random.normal(0,0.1,size=[200,2])\n",
    "X_2class = np.random.normal(1,0.05,size=[20,2])\n",
    "\n",
    "X2 = np.concatenate((X,X_2class),axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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uj7n7Rne/0N3Xu/tfZTtiAEAZEOgV2MSGMZ168sqk7OIx5wtxDiVValvGoIiyZAAAgP5Q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\nAAAAlAyBHgAAAACUzP8P8w2QIIRdUMIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1081a4588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,5))\n",
    "plt.subplot(121)\n",
    "plt.scatter(X[:,0],X[:,1])\n",
    "plt.subplot(122)\n",
    "plt.scatter(X[:,0],X[:,1])\n",
    "plt.scatter(X_2class[:,0],X_2class[:,1],c='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAO+RNILn0n2pX3rlNB3uHo71RJpfotGVH5IkY0X7bA3pcPewIiOO9xQAAAAA\nFAjlaVNIsZopp2qefe+BQf2i36mhLTJhTySMNVEz8qnWJDuXPlsAAAAAgMkjaTRFFLOZcqov9e8M\nvzG6PYueSBgrU5JkqjbJnmyfLQAAAADA5JE0miKK3UyZL/WZTXZ2ULrnkybZAAAAAIBCIWk0Rfhp\nxampVk6VzMvZQX56XQEAAAAAlYVG2FNEpmbKnerTzmC3tuqYdga71am+go1jNGGyplpDm+eodU21\nOmadLug5/SZxdlB1wEZnB3UEeyd9XzTJBgAAAAAUCkmjKSLdilMLwzNyTuLkkmzyMmFSrqKzgwJj\ntkVnB0UmfV+sJAYAAAAAKBTK06aIdM2Uc+2Jk2uJFeVUl2cHxZ9zKWF20CT7P7GSGAAAAACgUEga\nTSGpmik/ET6VUxIn12STlwmTYihE/6Xo7KB4wi0QS7gNaXl4QU73R9NxAAAAAEAhkDSa4nJN4uQ6\nY8jrhEkhFWo5e2YHAQAAAADKAUmjKS7XJE6uyaZiJUy8mCFUyOXsmR0EAAAAAPA7kkZTXK5JnHxm\nDBU6YeLVDCH6LwEAAAAApjKSRsgpiePnEiuvZgiVW/8lAAAAAAC8RNIIOfNriZVXM4S87L9UiIba\nQDkxs/dL+ktJAUk7nXNfSLp9kaRvSJoX2+czzrmnij5QAEBJECcAwJ9IGqHieDVDyKvZVIVqqA2U\nCzMLSHpM0m9LOinpGTM76Jx7IWG3zZK+7Zz7ipndLOkpSTcUfbAAgKIjTgCAf5E0QsXxcoaQF7Op\nCtlQGygT75D0onPuJUkyszZJd0hK/DLgpNEs6lxJPUUdIQCglIgTAOBTJI1QcfzWb4mG2oCulfRy\nwvWTkpYn7fM5Sf9oZo2SZkn6reIMDQDgA8QJAPApkkZFRm+b4vBTvyUaagOyFNtc0vV6Sbudc182\ns9skfdPMljnnLo25I7MHJD0gSXMJYQBQKYgTAOBT00o9gKlktLfNmmoNbZ6j1jXV6ph1Wp3qK/XQ\nUEDRcrkhHe4eVmTE6XD3cKxcbn6phwYUy0lJ1ydcv07jywrWS/q2JDnnjkoKSboy+Y6cc19zzt3i\nnLtlpgIFGi4AoMiIEwDgUySNiiixt011wEZ723QEe0s9NBRQrWq0vH+BGtoiCj1yXg1tES3vL125\nHFACz0i6ycwWm1lQ0hpJB5P2OSHpvZJkZksV/TLwWlFHCQAoFeIEAPgUczaLiN42U5efyuWAYnPO\nDZvZxyU9regyyV93zj1vZlslPeucOyjpk5L+xsw2KlqSsM45l1yaAACoQMQJAPAvkkZFRG8b/6LX\nFFBYzrmnFF0eOXHbwwl/f0G7E406AAAgAElEQVTSO4s9LgCAPxAnAMCfSBoVkZdLwcM7o72mVoe0\nYlEo9rqclvpF4kgk1AAAAABgqiJpVETxpeDXtL2m18IjmhWUgiM06Cu1xF5TkkZ7TTW09V4uKctB\nJSRbSKgBAAAAwNRFI+wSCFY7/VPDTP3y03P0+NrprKBWYtFeU2OTd9FeU5Gc77NSVsqjeTsAAAAA\nTF0kjYqML+H+E+81lWi011SOKuV1LkRCDQAAAABQHkgaFRlfwv0n2mtqSIe7hxUZcTrcPRzrNTU/\n5/uslNe5EAk1AAAAAEB5IGlUZHwJ959a1Wh5/wI1tEUUeuS8GtoiWt6/IK+ePZXyOhcioQYAAAAA\nKA80wi6ycl5BrRIaO6dTq5rLTa/D+d9fOb/OieLN2xvaetUTHoi97pkTavH3ySvhiGqmm/ouOl1b\nwPdLJb8vAQAAAKCUSBoVWS5fwv2AVbQmp1xf51Qmk1CLv08++vYq7es07Vo1IyFp5v37hfclAAAA\nABQOSaMS8HpWSzEUaln6SlaOr3O+4u+TxvYh7Vo1o+DvF96XAAAAAFA4JI2QlWhj59CYbdHGzgMl\nGhHi/FSeFX+fdJ25lKYRuLfvF96XAAAAAFA4njTCNrP3m9nPzOxFM/tMitt/w8z+1cyGzexuL86J\n4qqUxs6VZrQ8a021hjbPUeuaanXMOq1O9ZVkPPH3ydIrp3nyfulUn3YGu7VVx7Qz2D3ucfG+BAAA\nAIDCyTtpZGYBSY9JqpN0s6R6M7s5abcTktZJ2pfv+VAarKLlT4nlWdUBGy3P6gj2lmQ88ffJh95a\npfUHB/N6v2STEON9CQAAAACF40V52jskveice0mSzKxN0h2SXojv4Jz7r9htlzw4H0qgkho7VxK/\nlWfF3yff6OjVK2GnO781mLB62uTeL9n0K+J9CQAAAACF40XS6FpJLydcPylpuQf3C5+Zio2d/W5e\nIKClj11Q91mnpVdO06Z3TdfVsy1anlWi12jM++RibGMOY8k2Icb7EgAAAAAKw4ukkaXY5nK6I7MH\nJD0gSXPp0V0yfmqsnK9sH0s5PuZO9SkUcvqb2y8va7/uyUFdGJJWht/o+bmSnx9JBX3O4v2K4jON\npIR+RSSHAAAAAKDgvMjMnJR0fcL16yT15HJHzrmvSfqaJC20UE6JJ2QvbSJg1mm1rg5pxaKQjpwY\nUcOB01K/fJ9ESTbaE2eCx5Ltfn7TEezVnqTyrd13zNCatouejjvV83P3t36hUJVpTwGfs2i/ovh5\nA7FzDGl5eIEn9w8AAAAAyMyLpNEzkm4ys8WSXpG0RtK9HtwvPJaYJLoyGNCwXdLj98wY86U/HDG1\nTdBHplxk0xMn036r2k6pQ72+nXWUrnzrTHgkzRG5SfX8XDFT+pvbC/s+oV8RAAAAAJRW3qunOeeG\nJX1c0tOSuiR92zn3vJltNbNVkmRmt5rZSUm/J+mrZvZ8vufF5CSvRNW2Zrpmh6RTF9yYVbdeC49o\nxaLAmGOjfWQiJRp57qJJlYkfS7r9BiIq+RL2mRRruflUz0/3WVeU90mtanR/eLEe1hLdH15MwggA\nAAAAiijvpJEkOeeecs4tcc7d6Jxrjm172Dl3MPb3Z5xz1znnZjnn5jvnfsWL8yJ7qZZm333HDDX/\n+OLoPisWBTQrqKIkIooh26RKuv2WXjktqyXsO9WnncFubdUx7Qx2Fy3BVKzl5lM9P4vnWcW8TwAA\nAAAAqXmSNEJx5ZKkSDebpuvMpdHrR06MKDgSKEoiohiyTaqk2m/9wUFtetd0SZln0CTP4CrmzKRa\n1Wh5/wI1tEUUeuS8GtoiWt7vfflWqufn9QHpIxXyPgEAAAAApMYSZWUm16bN6VaiWjzPFBlxo02G\nV44sqJg+Mtn2xHnc/Z32721XY1OLXmh9VW++wtT8npDqa6OzZo6cGNHSm67RlmP7xp1j2ZLb1Xrb\n+N4+jUdNj6fYP19NNrZdWDGWm0/1PK4Mv1G66P37pBxXsQMAAACASkXSqMxk29w5WaqVqD5yYEhD\nQ9MUeuT8uC/9hU5EFEu2SZX6tXWqX1un/XvbtWnjNl09+3IybX27U/P2DSmP6zp+SivumT1m24pF\nAXXtOeXVQ8ioU336cfA1vRYe0aygFBwJaOXIVZ4nWtI9j16+T8p1FTsAAAAAqFQkjcpMuhWzesID\nGY9LNVvktsSZIWWeHPJK/do6SVJjU4u69pzSwgU1GrkU0dqPfFYP3PdZzXvDXD36pU+N7rf0xqt1\n5MS5cTO4lt54dcHH2qk+HZ11Wm0JicB1Tw7q8NAvpIvll2jJNSEKAAAAACgMehqVmXxWzGIlquzU\nr63Tc8cOaU/rVk0LD2rv70oXN8/RwTUzNW2wT3/yx1u1f2+7JGnTlg1a3+7G9kNqd9q0JfXMJC91\nBHu1J0Vz8ytmKmPjbq942QC8U316JcvV7gAAAAAAxUHSqMwUa8WsQijVKmO5am5q0e4PVo1Lysyp\nGlZzU4ukaIKpeftDajw6V6FtF9R4dK6atz80OhMpX/v3tmvZktsVCNyqZUtuH/Oc9YQjOtl3Scta\nLiiwtU/LWi7oZN8ldZ91BU+0eNkAPH5fb76CFdkAAAAAwE8oTysz2TZ39pty7FeTrl9R91knnbvc\nsyjeD8lr8f5Ku+pMK+6ZrSMnzqmhZ2j0OZsXCGjz4YvafceMMeVpV82UqiPVBS059LKULH5fpy44\nrT84qF2rLj+eaEJ0QSEeAgAAAABgAiSNylAxVszyWjn2q0nXr2jxPFPoysL3LGpuatGuOkv7nFUF\npN13zBhz++47ZuhD3xrQigLPPMu1t1am+6oOmCSpsX1IXWcuaWa19Dvhq32bVAQAAACASkfSCEXh\nZZJhIlucN0vdb9qyQes+8Xnt/qDGzOQZulSlzxehZ1G6mU49w4Pa4vZpa+DWlD2AzhehCXa8t1Zy\nQm1hcPwMp071qSPYq55wJDYzbv6Y8SXeV31tteprq6Nll20REkYAAAAAUEIkjVAUk0ky+EW85Oy+\nT39ZP+85q1lBad4b5ur/S1g9rZAmWpkt3e3XFuE5jfbWipcbpi8lS1eW+HL/gHqCg+oJR3SlArr7\nW4N6/B7K0gAAAADAT0gaoSiyTTL4TaH6FWVj05YNWr9xm3bVDY8+Z+vbnZq3b0h7e7Ge02x7a6Uq\nS/zo26u061/Pa9/qGaOJpI8cGNLdey/q7MhI2fTpAgAAAIBKR9IIRVGuDbxLKZ6samxqUdeeU1p6\n49Vq3r5hdHvy7Qurqor6nGbTWytVWeL3fjqsfavH9mLaszqkhraIPjFyo29nngEAAADAVEPSCEVT\nLg289+9tV3NTi7qORxM1m7ZsKNlso4lmOiXe3mT3Fnw8E/UnSpaqLLHrzKWUvZgK0d8KAAAAAJC7\naaUeAOAn8WXud9x2TkMPzdaO285p08Zt2r+3vdRDK7nR/kRrqjW0eY5a11SrY9Zpdaov7THRssQh\nHe4eVmTE6XD3sOYEo72XEo32twIAAAAA+AZJIyBB4jL31YHon7vqTM1NLaUeWskl9ieKPzetq0Pq\nCPamPaZWNVrev0ANbRGFHjmvhraI/tvFmnGJpGgvpvlFfDQAAAAAgIlQnoaytMXtK8j9plvmvmvP\nqYKcz0vpnhOvytZS9SfKpqwsVVliZ38f/a0AAAAAwOeYaQQkiC5jP750Kr7MvV/t39uuZUtuVyBw\nq5Ytub0g5XTx/kSJEsvKOtWnncFubdUx7Qx2Zyxbq1WN7g8v1sNaovvDi0kYAQAAAIAPkTRCxckn\ngbJpywatb3djSqfWtztt2rKhgCPOT7H6MKXqTxQvK8ul3xEAAAAAwN8oT0NFiSdQdtWZVtwzW0dO\nnNP6jdskKasV0CZa5t6PmptadO9bR9TYPqyuM5e09MppuvetVWpuavF03LWqkfqVsqxsZ7B7tN+R\npNF+Rw1tvZdL0wAAAAAAZYWkESpKYiNrSbFG1sNqnEQCZaJl7v3mhRdf1cBrpl2rZmjFooCOnBjR\n+oOD+q9zr2Y8rlN96gj2qicciSWA5k9YJpaqP5GUe78jAAAAAIB/UZ6GitJ1/JRWLAqM2bZiUUBd\nx/3fyDpX82YEtGvVjLErvq2aoXkzAmmP8bqcbKJ+RwAAAACA8kPSCBXFD42si9GUOtG5wZGUibJz\ngyNpjpA6gr2j5WTxRFPr6pA6gr05jSFTvyOMNZmG4QAAAABQSpSnwdfSLSOfzqYtG7R+4zbtqhu+\nXKrV7tS8vTiNrPPtqZSLpW+5RkdOnBstyZNiibK3XCMp9XO4NXCrp+Vkmfod4bLRGV6rQ1qxKKQj\nJ0bUcOC01C+eKwAAAAC+w0wjVJT6tXVq3v6QGo/OVWjbBTUenavm7Q8VrUdRYk+l0VKxOlNzU0vB\nzpnLim/pZmTlU05WqxrdH16sh7VE94cXkwRJwesZXgAAAABQSMw0QsUpZSPrruOntOKe2WO2rVgU\nUNeewvVUymXFt01bNqjhD7fEZrwEYjNehrQ8vKBg4wQNwwEAAACUF2YaAR4qVU+l+rV1eu7YIY2M\nPKPnjh2aMGlWv7ZOy/sXqKEtotAj59XQFtHyfsrJCm0qNww3s/eb2c/M7EUz+0yafT5sZi+Y2fNm\nNrnaVABAWSNOAIA/kTSC7yQ2Ci5GI2kv5VIqViqUkxXfVG0YbmYBSY9JqpN0s6R6M7s5aZ+bJP25\npHc6535F0p8UfaAAgJIgTgCAf1GeBl8Z3yi48I2kvZRLqRimjincMPwdkl50zr0kSWbWJukOSS8k\n7PMxSY85516XJOfc6aKPEgBQKsQJAPApkkYY1ak+dQR71ROOxL7Mzi/6l9nERsGSYo2kh9XY1FI2\niZdS9lSC/9WqRrXh2L+rcGnHUkTXSno54fpJScuT9lkiSWb2E0kBSZ9zzv1DcYYHACgx4gQA+BRJ\nI0jyz1Lg6RoFe9FIev/edjU3tajreHQG0KYtzADyq1QJTEklT2oiZ5Zim0u6XiXpJknvlnSdpB+b\n2TLn3Nkxd2T2gKQHJGkuIQwAKgVxAgB8ip5GkFT6pcC3uH3a4vZp6U3XTKqR9P697Vq25HYFArdm\n7H+0f2+7Nm3cph23ndPQQ7O147Zz2rRxW1n1S/KzxD5UO4Pd6lRfXvfVMeu0WtdUa2jzHLWuqdbh\n6b/Q0aRtHbNO53UeFNVJSdcnXL9OUk+KfZ50zkWcc92Sfqbol4MxnHNfc87d4py7ZaYCBRswAKCo\niBMA4FMkjSApPsNnbGCNLgUeKeo4JtNIejKJoOamFu2qszFJsV11puamlmI8rIqWKsmTT0InVQLz\nipnSnhImNZG3ZyTdZGaLzSwoaY2kg0n7fE/SSkkysysVLUN4qaijBACUCnECAHyKpBEk+Wcp8Pq1\ndWre/pAaj85VaNsFNR6dq+btD6UsI5tMIqjr+KmUSbGu4/mXvU11Xs9SS5XA7D7rfJHURG6cc8OS\nPi7paUldkr7tnHvezLaa2arYbk9L6jWzFyQdlvRnzjmyggAwBRAnAMC/KPSFpPhS4PGeRoFYT6Mh\nLQ8vKPpYsm0k3XX8lFbcM3vMtnT9j5beeLWOnDg32mBbylz2huyl60PVEx7I6f7iCczE12rxPBu3\nbTSpOXWaSZc159xTkp5K2vZwwt+dpD+NXQAAUwxxAgD8iZlGkBRtdr28f4Ea2iIKPXJeDW0RLe/3\n91Lg0URQdv2PEsvevvkfYb3lf5zXe1sH1N8/SF+jPHk9Sy2awBwaU6L4+oD0kaRt0aTmfC8eAgAA\nAAAgBWYaYZTflwJPXv1s5W+/U+u/8/faVTc8OjtqfbtT8/bx/Y/iM5caPvUlRc73af/qGbFjwlq/\ncduYfTA5Xs9Sq1WN1C81tPWqJzyghcFqrQy/Ubo4dtvysL+TmgAAAABQ7kgawVOplkr34ot9vOn1\nrjrTintm68iJc1r/nb/X7/7e76rx+z9R155oIql5+4a0yZ/6tXVqbmrRjvdFRsucon2QhtXY1OLr\npFFywmzTlvSPs9hSJXnyTeikS2D6OakJAAAAAJWGpBE8M7qK1uqQViwKxWacnJb6lXfiKLHptZSQ\n7Pn+T/TcsUNZ389k+iD5RcqEmQezo7a4fSm3N9m9k74vv89SAwAAAABMHj2N4BmvV9FKlO/qZ/v3\ntmvZkts1s8pl3QfJLyazShwAAAAAAF4haQTPpFoq3atl0dM1vZ5Z5bRsye0Zm1nHZ+rsuO2cWj4Q\n0ronB8c0VF7f7rRpy/g+SH6Rb8IMAAAAAIBcUJ4Gz6RaKt2rZdE3bdmg9Ru3jWl6ve7JQbV8IKTr\najKXayWXtlVNM33s0KBeet3p5puuydgHyQ+iCbNz455XP8+OAgAAAACUP2YawTOplkr3aln0+rV1\nat7+kBqPztX0R87rY4cG9YX3hvT7bwtOWK6VPFOnvrZaXQ/Olk0zPXfskK8TRlIsYdbuSjo7qlN9\n2hns1lYd085gtzrVV7RzAwAAAABKg5lG8EwhVtFKVL+2TvVr6xQI3KquB2erOmCjt2VqZl3uM3Xi\nSa3GppasVonzWiEbnAMAAAAA/IukkU8Uaqn6YivGKlqTTQKlKm1b3+7UvN2/fYySxRNmpZDY4FzS\naIPzhrbey681AAAAAKDiUJ7mA6MzOdZUa2jzHLWuqVbHrNOUAKUx2XKtxNK20LYLajw6V83bH/J9\nWZpfFLLBOQAAAADAv0ga+UAhl6qvRNkkgfbvbdeyJbcrELhVy5bcLkl67tghjYw8UxZ9jPwk3uA8\n0WiDcwAAAABAxSJp5APM5Bif5Nm/tz3j/vVr69Imgfbvbdemjdu047ZzGnpotnbcdk6bNm6b8D69\nMtnH4neFbHAOAAAAAPAvehr5QCGXqi8HnerTNzZu064604p7ZuvIiXNav3GbJOU0I6i5qUW76mxM\nD55ddcNqbGop+AyjeMLKq8fiB4VucD5ZldL/CwAAAAD8jplGPjDVZ3J0BHtHkzzx8rxddabmppac\n7q/r+KmUM7e6jqdeXc1LiQkrLx5LoUx2NlStanR/eLEe1hLdH15c2oQR/b8AAAAAoChIGvlArWq0\nvH+BGtoiCj1yXg1tES3vL91MjmJLV56Xa5Inurra+B486VZX81IpE1aJMiWFsinf61Sfdga7tVXH\ntDPY7ZukDP2/AAAAAKB4SBr5hF9mcpRCukbLuSZ5Jru6Wi7SJWVKmbBKHFumpNBEs6H8PJuH/l8A\nAAAAUDz0NEJRbXH7xm1bsrdd6zdu0666Ya1YFNCREyNa3+7UvD23JE+8d1BjU4u69pzS0huvVvP2\nDZ71FMrUt2jTlg2ePpZU537o01/Wz3vOalZQmveGuXr0S58a89gm6unUdfyUVtwzW/s7I2r+8UV1\nnbmkpVdO0wtnBiSNnc0TP751dUgNbb2qDZc2mTnV+38BAAAAQDGRNELJZZvk2b+3Xc1NLeo6Ht1n\n05b0iaD6tXUFazydKSnz3LFDWT2WXOzf267PfOLz2v3BKq1YNEdHToxo3ZN9+pM/3irp8vMYTwol\nWrEooK490RK5pTderaYf9WpfZ0S7Vs0YTW6tfWJI+/e2x2bzhMYd3xMeyPsx5Cva/+u0WleHRscd\n7f+1oNRDAwAAAICKQ3kafKF+bZ2eO3ZIIyPP6Lljh1ImjCbqw+OlTD2BJupbNNFjyXUsD9z3We3+\nYNWYsrLdd8zQnKrhMY22JyqR27Rlgx57JpowSryvvXeG1NzUkrJcsOlHFzVnupW8x9FU7/8FAAAA\nAMVE0ghloZirkk2UoCpm36LEsQxElDJZ1X3WjWm0PVFPp/q1deq76NImvpJX89v8wyHt+reInrhn\nxrgeR6VomD2V+38BAAAAQDGRNEJZKOaqZBMlqIrRaDvu05/6kqYND+m3vjmgudOjM34SHTkxoprp\n0sIFlxMn9Wvr1Lz9ITUenavQtgtqPDpXzdsfGjPjaelbrkmZ+JpZ5dQR7NXC/tmjs3n+6l8i2nfX\njHErlv04+JpvG2YDAAAAAPJH0ghlId3snplVblz5WL6yKT+bKCnjhf172xU536e/uX2GhjbN0YEP\nz9Suf4to8w+HLierDg7qwVuDmhYeHPMcTFQilyrxte7JQbV8IKTWNdXqmXVBy8Pz9bCW6HyaWUmv\nhUdGG2YnJpM6gr2ePg8AAAAAgNKgETbKQqpVyeJJjutqLq9e5kXiJpqgOjduha7E8rNCNtqOa25q\n0f7VM8Y03N531wzd9e0BbftxWDdfNU3N7wmpvrZa7118eXW0bCQ2H3+h9VW9+QrTF94bvS9JY1ZL\nS7di2axg6nI5PzTMBgAAAADkj5lGKAuJs3umP3JeHzs0qC+8N6Tff1twtHzs05/6Utrm1ZNRzPKz\nTNLNeDo3JH3jQyE9t2H2aJInl1K9+Gwkm2bqevDyfcXvrycckaRxPY4Odw+r4cCQgiOBlLO/Fgar\nBQAAAAAof8w0QtmIz+4JBG5V14OzVR2w0dtO9l1S5HyfdrwvohX3zNaRE7nPPkqchdO155SW3ni1\nmrdvKPjMomTpZjzVzJim62rG5nvzacSd7jwLg9VSONp4Wv1SQ1uvesIDWhisHl3ivuHAabWuDo3O\n/mo4MDR6GwAAAACgvJE0QtlJleRo+tHFcaVcu+omV7KVqBjlZxNJVZK3vt3p9//gLq3/zt+P2968\nPbeZUKnO03BgSAvDs7Uz2K2ecCSWKJofTSCFEw5OkUyKr2bWqT51BHvHHw8AAAAAKAskjVB2UiU5\nXno9zRLye7Ir2Wp88Avau/sJnR0Y0byZAa1dd6d2PPaZQgw/a5lmPP36r7/Ns5lQyedZWFWlheHZ\n6pl1ITaLKBRLJJ2W+jUm8VOrGtWGa6IJIvXqCZ2Krr4WnpHV8QAAAAAA/6KnEcpOqtXL3rRwXsr+\nOktvvFr797Zn7HXU+OAX9HjrAR24e7oubp6jA3dP1+OtB9T44BeK+bBSmmgVtEKc5/7wYvUEB7Ne\nGa1TfeqYdVqta6o1tHmOWtdU62fT+1hZDQAAAADKnCdJIzN7v5n9zMxeNLNx0zPMbLqZfSt2e4eZ\n3eDFeTF1JSdTtj36yZTNq1f+9ju1aeM27bjtnIYemq0dt53Tpo3bxiSO9u5+QvvumjEmwbHvrhna\nu/uJEj7C9Pbvbdemjdv0oat7tXS+qevFV7Xh/oc9TXL1hCNpVkaLjNu3I9g7LkF0PpxuZbXxxwMA\nAAAA/CnvpJGZBSQ9JqlO0s2S6s3s5qTd1kt63Tn3FknbJf1FvucFEqWafdS8/SEd/v5PtKvOxiQ0\ndtWZmptaRo89OzCSMsFxdmAk+TS+0NzUonvfOqJ9nRHtqAtpaNMcfffDM3Tgm9/NecW4ZAuD1Vmv\njJYqwbT0ymmsrAYAAAAAZc6LmUbvkPSic+4l51xYUpukO5L2uUPSN2J/f1zSe83MBHgoVSlXumXr\nE5ennzcz9dLx82aOPW4yJiqJy0fX8VP63k+HtWvV2NlRe+8MjUmG5Tq2LW6fHv36w+NmbkVXRps/\n7v5SJZg+9NYq3fvdwayOBwAAAAD4kxeNsK+V9HLC9ZOSlqfbxzk3bGbnJM2XdMaD8xcVK0KVl3TL\nyScuT7923Z26t/WA9t01Y7Sx9r3fHdTadatzOme8fGxXnWnFPbN15MQ5rd+4TZI86Um09Mar1fXi\nqzk1/s52bKmacC/vr0n5Xl8enq+GA6djTa+jz9++zojuXlqljx0a1EuvO12btLIaAAAAAMD/vJhp\nlGrGkMthH5nZA2b2rJk9OyD/lQalavjbMeu0OtVX6qFl1Kk+7Qx2a6uOaWew2/fj9dKmLRtS9jra\ntOXy8vQ7HvuM7m5YrdWPX9T0R85r9eMXdXfD6pxXT2tuapmwJC7fx1Qz3dI2/vZqbMkzt9IlfGpV\no+X9C7SqbUCh5vNqbB9S83tC2vGBGep6cLZM0v3hxSSMAAAAAKDMeJE0Oinp+oTr10nqSbePmVVJ\nmivpl8l35Jz7mnPuFufcLTOVe2lQoaRq+Ov3FaE61aejSYmuo2WQ6MpkMqVf6XodJc/42fHYZ/TL\n/g5dcs/ql/0dOSeMJGVVEpeP+rV1+sh9q7X2iaGMybDJjO2F/3w1r1K6WtVonqr1g9+fqec2zFZ9\nbbR3EX2MAAAAAKB8eZE0ekbSTWa22MyCktZIOpi0z0FJH439/W5JP3TOjZtp5HeTWVHKL34cfE17\nkhJde1aH9OPga6UeWk7i5VWZVkNLVr+2Tpu2bIiWdR0/peamFk97DCWLlsRNfhbQZOx47DP68lea\nJkyGZTu2N19hWT+f6UTL1IboYwQAAAAAFSLvpJFzbljSxyU9LalL0redc8+b2VYzWxXbbZek+Wb2\noqQ/lZT7NI4SmsyKUn7xWjj1ymCvhYtf/tepvrybQ+dS+pVLoikf2ZTEeSFV4+9cxrbuyUF9fmUo\n71K6eJlaQ1tEoUfOq6EtouX99DECAAAAgHLlRSNsOeeekvRU0raHE/4+JOn3vDhXKaVq+BudSbGg\n1ENLa1YwmthKbgQ9KygpXLxxjPaDui2UV3PoruOntOKe2WO2TdQAOjHRJCmWGBlWY1OLJ42pk6Vq\nIt28fUNBzjVZyWObWeXU8oHQaDmZlF1D7XRqVaPacCxJVMT3FwAAAADAe54kjaaKWtVI/VJDW696\nwgOx1dP8PZMiOBLQuicHtfuOyyuDrXtyUMGR4vaMSuwHJeWeuMlmNbRkuSSa8lW/ts4XSaJUEse2\nbMntuq7m3Jjbj5wY0cKqKjXZvaUYHgAAAADAJ7zoaTSl1KpG94cX62EtKYsVoVaOXKULQ9LHDg0q\n1HxeHzs0qAtD0e3FlK4f1GSbQ+dS+lWMHkP5mkxzby+lej7pQwQAAAAAkJhpVPFqVSNdlDpcr+Qi\nuthfpZXh+UVPdsX7QU1mhlAquZR+bdqyQes3btOuuuHR2Vbr252at3vbYyhX8Z5Lu+osr9K9XKR6\nPpf31/g+GeoXnepTR4nS3igAACAASURBVLBXPeFIbOZh8f9tAQAAAEChmF8XMVtoIfeHelOphwGP\njPY0SugHFU3cTLzilxf2721Xc1OLuo5HEyObtoxPNGWzTyEsW3K7dtw2tuTucPewGo/O1XPHDhX8\n/MkoS8tOqvd0w4GhojX//pyO/R/n3C0FP5GPEScAID3iBHECANKZTIxgphEmJdeZFfF+UI1HrSTN\noSfqMVTK2T6l6LmE/KXq09W6OqSGtt7LzcABAAAAoIyRNCozpSyHGTuzIhSbWXFa6lfWiaPHj+0r\nwkgnr9grrCXKpbl3IYzOtNKrlFplIdqnKzRm24pFAfWEB0o0IgAAAADwFo2wy8ho0mZNtYY2z1Hr\nmmp1zDqtTvUV5fyJMyuqAzY6s6Ij2FuU8xdS1/FTnjTqzkUuzb29Fp9pteO2cyV5b5WjeJ+uREdO\njGhhsLpEI/I3M3u/mf3MzF40s89k2O9uM3NmNqVLKgBgqiFOAIA/kTQqI6VO2qRbAa0nHCnK+Qup\nlCus1a+tU/P2h9R4dK5C2y6o8ejcovV6ikucaVVpCcFCWR6er4YDQ6w8lwUzC0h6TFKdpJsl1ZvZ\nzSn2myPpE5I6ijtCAEApEScAwL9IGpWRdEmbV8IR7Qx2F3xWSCXPrCj1bJ/6tXV67tghjYw8o+eO\nHfI8YbR/b7uWLbldgcCtWrbkdu3f2z7m9nQzrSohIVgotarR8v4FamiLKPTIeTW0RYrWBLsMvUPS\ni865l5xzYUltku5Isd/nJT0qaaiYgwMAlBxxAgB8iqRRGUmXtLn5qmlFKSeq5JkVmWb7TJRw8bsx\npWcPzdaO285p08ZtYx5HuplWlZAQLKRa1ej+8GI9rCW6P7yYhFF610p6OeH6ydi2UWb2a5Kud879\nXaY7MrMHzOxZM3t2QCOZdgUAlA/iBAD4FEmjMpIqabP+4KA2vWt6UcqJ/DCzopAJnFSzfRof/II+\n+cdbMiZc/PQYUklVerarztTc1DK6T6qZVpWSEIQvWIptbvRGs2mStkv65ER35Jz7mnPuFufcLTMV\nmGh3AEB5IE4AgE+xeloZiS9b39DWq1fCA7r5qmlqfk9I9bXR2SDFWLmpVjWXlxMPF/RU48RnzOyq\nM624Z7aOnDin9Ru3SVJB+v/s39uuPV8/oO9+eEbeq6rFVyZ74cVXdfXsadp7Z6goj0GKlZ7dM3vM\nthWLAurac7nJd/zcjU0t6mqNr55GqRU8c1LS9QnXr5PUk3B9jqRlkv6nmUnS1ZIOmtkq59yzRRsl\nAKBUiBMA4FPMNCoz8XKYa4PV2lF3OWEkVX45UTYzZrw+X99Fl/eqaonlYTdfGU0YFesxSNk3+Y7P\ntKLUCgXwjKSbzGyxmQUlrZF0MH6jc+6cc+5K59wNzrkbJP2zJL4IAMDUQZwAAJ8iaVQCnerTzmC3\ntupYzg2sK7m/UDpdx0/pZN8lLWu5oMDWPi1ruaCTfZcmlcCZ7PmWXjkt71XVEpNdXWcu5Z2EmqxS\nN/kGnHPDkj4u6WlJXZK+7Zx73sy2mtmq0o4OAFBqxAkA8C/K04qsU33qmHVaratDWrEopCMnRtRw\n4LTUr0nN7EgsVesJD3heTtSpPnUEe9UTjsTue37JZ54sXFCjzYf7tPuOGVqxKKAjJ0a07slBLVyQ\n/7ji5WNdx09p6Y1Xa9OWDVp649X60NW9Wn9wULtWXT7n2ieG9OWv/HlW91G/tm5MeVg8CRUvd5Mm\nn4SarDGlZ3uiY2vevqFg5XBAKs65pyQ9lbTt4TT7vrsYYwIA+AdxAgD8iaRRkXUEe9W6OjSmR07r\n6pAa2nov9wrKUqH6C3mV2Eqlye5NuX2L2zfhsVXTTF+/Y2x/od13zNB9P0jVOzF76Xol/e7v/a72\nfefvdW+t1Ng+pK4zl1Qz3fSR+1aPS7hk6rcULQ87p5WLq7TpXdPHJaHWtzs1by/srJ/6tXUkiQAA\nAAAAk0J5WpH1hCMpy5N6wpESjWi8xMRWvO9OoVdmy8aJU+dSPncnTp3L637T9Uo6/P2fqHn7Q/re\nqfnq6nVa+pZr1LJzq3Y89pms76O5qWVMedjdN1fp3tpq3fXtQYWaz6vx6P/P3r1Hx1We9+L/vhrN\nTZexwbItbOpEOHEQQScJBVQSU2pD2sqJryK2JBvhg0wuJjqrnGQ1FDmoopbLj9Mu91cFdyWxOb5K\nMiBf5AT9cgK4WTilApq0RwQRc1FiwBaWFawZSTOz5/L+/hjNaC57RnO/fj9rZWFptvbeM5H2s/fz\nvu/zzEPn3kcDEjrp7q6W7ZKxnJOIiIiIiIhix6RRmi3RaVVr5GRTAetsTWxFW9A5VsPvjoatM+Qt\nDu1yvYY3zp8JO1tnrn107n0Ura/Mg2HPJE6NLsC+/Y/D5X49ZJ/+RbNtj5ah644JtD28J67EUT4k\nn3yz3hq0sO0qx+EGLQZLLzNxRERERERElAZMGqVZLhSwztbEVqoKOicjGTXXPqJNPiWrQ1wyk0+Z\nlK2z3oiIiIiIiAoBk0ZpVgMTaqcWobnXAcNuC5p7HaidSl4B62TI1sRW8IwdtaVd8UhGMmqufUQ7\n6yfSjKVYJCv5lGnZOuuNiIiIiIioELAQdgakqoB1sqS6M1siUlHQORndxSLtI1KR7OBj+BfN9opn\nCZ5/xzavlcs0GD4aW/IpUcFd+JYoRlzUWaPuyued9Rb8eSzRabPyb4eIiIiIiCifMGlEqrI9sZVs\nyUhGhduH/6wfADOzfpxo7dgXsn1b+060PLwHB+qcCXVXS1byKRHBXfg6fmHHgV9b0L3JGHVXPs+s\nN+8+NDM/Y0Otsiht74OIiIiIiKhQMWmUBMGzKeaaPUGFJZZZP8mY9QQkL/mUCP96RABw6i0nujcZ\nA5Jnh+sNaO4dn01QBsnmWW9ERERERET5jkmjBAXPpohm9gTlr55jA+js2Ifhdz0Jn7b2nTHP+knW\nrCcg8eRTIjz1iAy+r4evuMPUJ5qOuJ9Cm/VGRERERESULVgIO0Hs7kRe4TqWrfryl5Le9S2awtrR\ndmxLleAufNUVRVnZlY+IiIiIiIjUMWmUIHZ3Iq9wHcvO/vyXSe36Fi45Fa4jW6YEd+HbcGMxmk5Y\nA5Jn2/psmHa58TjOY79uBEMwZ/q0iYiIiIiIaAaXpyUo092dWE8plNoSsXTMsolUuyiZXd9iKayd\nSWr1iJYp5WjuteKiMo0KnQZOIfHcVv8i11zaSURERERElC2YNEpQJrs7sZ5SqFja2ydbujqWxVJY\nO9NU6xHN/Hc/RtC7RR9TYWwiIiIiIiJKHy5PS1ANTKidWoTmXgcMuy1o7nWgdio93Z1YTylUuCVi\nnR37Un7stvadSa9dpMaTnAqtDZTs5FSqcWknERERERFRduNMoyTIVHen4O5UQHTdqLJRh2hS/X67\n7I5pP5mchZOujmVt7TvR8vAeHKhz+ma3tQxIdO6NLTkV7jNPhyGYUa4XMHRaUF1RhLY79Wis0aZ1\naScRERERERFFxqRRDst0PaVslK4lYuEks3ZRpGMAqU9OpYp3WeXJeuNs0qvfit+MuXDoV860LO0k\nIiIiIiKiuXF5Wg4L7k51dsQ5U09pQaZPLWPStUQsWj3HBnDzirXQaG7DzSvWJq3DWePWOrxx/gxc\nrtfwxvkzERNGqTqHeKktqzywzogfvJq+pZ1EREREREQ0N840ymFq3alqFT50S60edx++ilIdMP/a\neXhy73czMgsnk0W5ozmHTAm3rNJilwX/u0tERERERJRNONMox9XAhB1KFR7DCuxQqgr6odubIHn6\nHgX2XeXobyiB1pW5dXqZLMqdTecQzLus0p9vWSURERERERFlDSaNKG9kW4Jk+N1R1e5gw+/OFuVO\n9dKxaM4h3biskoiIiIiIKDdweRrljUx2TlMzV1HudCxfi3gObyflEDHjskoiIiIiIqLcwKQRZbVw\nbeHbZXfI9zLdOS1YW/tObP8ff4eDX4WvS9j2nzjxxD97inL7z4wCMDMzyonWjn1JSxq1te9E8zfa\ncbje4DuH5j4baqcym6CpgQk1ysw5FGinPyIiIiIiomzH5WmUN7KtcxoA2BwSD56xwtBpwYNnrLA5\npO+1dCwda9xah9qpRWjudcCw24LmXnYoIyIiIiIiouhwphHlDe/snNaOfRg+Oorq5ZXo3LszI53T\nAM9Mot6NWqyqMvq+d3bEM5MIAOYZimDotKC6oghtd+rRWKNNycwozuohIiIiIiKieDBpRHmlcWtd\nxpJEwcLVWHrzyCW0PbwHfffqfUvGWvqt+M2YC91vadC5N3Mzo4iIiIiIiIi8uDyNKEU8NZZCW8vP\nN2pCu7ytM2Lff7jQuffRmJNeqe7ARkRERERERIWJSSMqCJlIrISrsTRhdanWMpqwueNKGLU9vAdd\nd0zA9mgZuu6YQNvDe5g4IiIiIiIiooQxaURZawhm7NeN4HGcx37dCIZgjms/mUqsNG6tQ+feR9H6\nyjwY9kyi9ZV56Nz7KKo/dZ3qDKR4ahn5d2DzzVqqE+icqZtEREREREREFC/WNKKsNAQzXim9jKP1\nBqxcZsC5Cy5s67sMTHkKO3eIprA/2y67A75OR2v7cMLVWGp5eA8O1DlnaxoNyLhqGYWrmzR8+FLE\nzyicIZgxqBvHRcWBJTotapUF7LRGRERERERUoDjTiLLSy7oxHK03BMygOVpvwMu6sZj3lY7W9rEI\nNwMpngRWuLpJS3TamPc1BDMGSy/jcIMWtl3lONygxWDp5bhneBEREREREVFuY9KIsob/crQxRb3u\nz5jiCvPT4YVLrCS7tX0sGrfW4Y3zZ+ByvYY3zp+Je8aTWt2k5j4bapUFMe9rUDeOw0GJusP1Bgzq\nxuM6NyIiIiIiIsptTBpRVgie5VKqg2qip1QX+77DFaRua8/91vYBs5Z2W9Dc60Dt1KK4lpRdVByq\nibqLiiNZp0tEREREREQ5hDWNKCsM6sZx/y3FaB2wYfiKG8ZiYPtpKw6uN/rq/mw/bYXOpZl7Z0G8\ns3haO/Zh+OgoqpdXonPvzpTXM0oXb92kDtEEKPHvZ4lOi3MXXL7aT4DfUrcE9ptJrNFEREREREQU\nPyaNClgmH6iDj/2h4kD3kMCBdZ4kUccv7HjqVQUPnrFi5KpE1XyBSRuwyrUwruOFK0idLj3HBtDZ\nsQ/D73qSVm3t2Ze0qlUWoLnvMg7XG3yJOs9St0WZPrW4+Gav+RVTb/Yrpk5UqJhMJSKiSBgniMgf\nk0YFKpMP1GrHbuxzoqlG65vlsnu1AQDQ9aoCSMA+VYxVORqweo4NoO3hPThQJ7BySxnOXZhAy8N7\nACCrEkc1MAFTQHPvOC4q0zM3CfEtdUulaG9k/Gs0AfDVaGruHUeNkl3viShdmEwlIqJIGCeIKBiT\nRgUqkw/UasfuqTei+aQVp95yYviKG9UVRfjel3Sw2IF2rIhpeVSsrebbZXdM28eqs2MfDtSJgPd7\noM6J1o59YZNGsb6HZKmBafb//yxckhbLjYynRpMh4HueGk3T6TxloqzCZCoREUXCOEFEwVgIu0Bl\nsuix2rE/MLvhcANddQbY2srRVWfArrN2XKOJvYZROvQcG8DNK9ZCo7kNN69Yi55jA2G3HX53VPWz\nHn53NNWnmXdi6fDmrdHkz1ejiahAseA9ERFFwjhBRMGYNCpQmXygVjt2xy/s6Kk3BiQDDq43ojhC\nzmgIZuzXjeBxnMd+3QiGYE7xmXt4l5ttqBxH9QKB4XcuYeeOx9D60BOq21cvr1T9rKuXV6bjdPNK\nLDcynhpNtoCueZ4aTQvSdbpEWYfJVCIiioRxgoiCMWmUxyIlVTL5QK127Pc+lqrJgCuKS3UfvmVK\nDVrYdpXjcIMWg6WX05I46uzYh6YbXegecvhmRp3YbETfkROqM47a2neiZUAGvN+WAYm29p0pP9d8\nE8uNTA1MqJ1ahOZeBwy7LWjudaB2KvtqNBGlE5OpREQUCeMEEQVjTaM8NVftl0wWPVY79kKdJqZ2\n75lcbz387ihw1dPpzf/4xzYaVOsUeb9u7diH4aOe7mmde7Ove1q80tlhI9YOb9leo4ko3XKl4D0R\nEWUG4wQRBWPSKE9Fk1TJ5AN18LGHYI4pGZDJIsfVyysx/M4l9TpFR9XrFDVurcv6JFE8yZ90d9jg\njQxR4phMJSKiSBgniMgfk0Z5Ktc6R8WaDPAuU4p2ZlIytbXvxM4dj6keP1frFA3BjFdKL+OoX/Jn\nWxTJn0zM+MrHG5l0ztYiIiIiIiKKFmsa5alcLGJXAxN2KFV4DCuwQ6mK+NCcyfXWjVvrsO2Bemw9\nacubOkUv68ZwNKgr2dF6A17WjUX8OXbYSFwm63MRERERERFFwplGeSrW2i+5JpnLlDpEU8w/UwHg\ni1gUdPwFOL/tCDq2HQGQW7NHxhSXavJnLEwhcq9MzvjKF5msz0VERERERBQJk0Z5qhBqvyRjmVIi\niZ1Ix093rZ9Eleqgmvwp1SHiZ5vvycl0yLWlpPESQvwlgP8XgAbAfinlE0Gv/08AOwA4AYwBeEBK\n+fu0n2gOyIaEdDacAxHlF8aJ5MmGa3Q2nAMRJQeTRnksH2u/JFMqEzvhZo9sPP4RTtpHsy546lwa\nbD9txcH1Rl/yZ/tpK3QuTcSfK4TkZKoVwmwtIYQGwFMAvgzgAwCvCSH6pZRv+m32awC3SimnhRDf\nAvAkgC3pP9vslg0J6Ww4ByLKL4wTyZMN1+hsOAciSh7WNKKC5Z/Y8dbxOVxvwKBuPOF9h6v1Y1Fk\nVtatWeVaiEkb8OAZKwydFjx4xopJm+f7c4mlFhWFymR9rjS6HcA7Usr3pJQKgF4A6/03kFKelVJ6\np1f9O4Dr03yOOSGV161cOgciyjuME0mSDdfobDgHIkqehGYaCSGuBXAcwCcB/A7AZinlxyrb/X8A\n/gTAOSnlVxM5JlGypHJZULjZI9UVRQHBM1vq1tTABNiBQTkOSAfsU8VYlUUzofJZgczWWgrgfb+v\nPwBQG2H7FgADai8IIb4O4OsAMC8LJsume/p9NixnzIZzIKK8wziRJNlwjc6GcyCi5En0SvoIgBel\nlE8IIR6Z+fp7Ktv9LwAlAL6R4PEoSbjOOLXLgtRq/bT0W9G5ejaAZlvw5HLGzCmAz16ofE+qbijE\nNgC3ArhL7XUp5Y8A/AgAlgiD6j7SJRPT77NhOWM2nAMR5R3GiSTJhmt0NpwDESVPosvT1gM4NPPv\nQwA2qG0kpXwRgCXBY1GSsMW3R6qXBU3bBNb1TkO/24INvVY01WjRWKP1ve4LnkT57wMAf+T39fUA\nLgZvJIS4B0AbgHVSSnuazi1umZh+nw3LGbPhHIgo7zBOJEk2XKOz4RyIKHkSnWm0WEp5CQCklJeE\nECltmcTZMcnBFt8eqVoW5E3KPec3y2hbnw3/8qoDd1cVs8sYFaLXAHxaCFEF4EMADQCa/DcQQnwB\nwA8B/KWU8nL6TzF2mZh+nw3LGbPhHIgo7zBOJEk2XKOz4RyIKHnmTBoJIV4AUKnyUluyTybSGmRW\n4U8erjOelYplQWpJuaP1BjT02tHc62DwpIJLgEspnUKIbwP4GTytlJ+WUv5GCPE4gNellP3wLGMu\nA/CsEAIALkgp12XspKOQqen32bCcMRvOgYjyB+NEcmXDNTobzoGIkmPOpJGU8p5wrwkhPhJCXDcz\ny+g6AAll/SOtQebsmOThOuPUCpeUu6K48BiWe77Bz7lgFWoCXEr5PIDng773mN+/w8aabKVWu0xt\nBmGhJQmJiOLBOME4QUTZKdHlaf0A7gfwxMx/Tyd8RmFwdkzyRBvAKD5MylEkTIDnj2im3+d7kpAP\nOkRE4TFOME4Q5YNEk0ZPAHhGCNEC4AKArwGAEOJWAN+UUu6Y+fplADcCKBNCfACgRUr5s1gOxAfx\n5OE649RiUo4iYQI8v8w1/T6fk4T5/qBDRJQMjBOME0S5LqGkkZRyHMDdKt9/HcAOv6/vTOQ4AB/E\nk43rjFOHSTmKhAnw/KU2mprPScJ8ftAhIkoFxgnGCaJclOhMo7TJhQdxTr8kLyblKBwmwPNTuNHU\nCocmb5OE+fygQ0SUbIwTHowTRLknZ5JGQHY/iHP6JRFFIxcS4BS7cKOpG45Z0dRnRXe90Zck3NZn\nwx1pSBKmeiDDO2tudFKi82U7hq+4UTVfYL5GA7iSdhgiorzAOME4QZSrcipplM04/ZKIopXNCXCK\nT7jRVItLovUWHVoHbBi+4oZJDzidqT+fdAxk1CoLcO/xj1BmAA6uD3zYGZoyMxFKROSHcYJxgihX\nFWX6BPKFJxBoAr7nmX7pyNAZERFRqgzBjP26ETyO89ivG0GFznMj7O/cBRduuEZg92oD3thZBtdj\nJpzYXILF5QKDuvGUnp//QIZWI3wDGT/TjWK/bgRDMCd8jBqYUCyLcHC9MeA4R+sNKX9/RETZjnGC\ncYIoXzBplCTe6Zf+fOuRKWsEB/BkBEQiKiy+0dkGLQ5uMEBf6sSY4sLG49PY9ZINDpfE2REnGvus\naL9LH/CzK5dpMHJV4kPFkfTrj//17cMwAxnTDuBwgxaDpZeTcvwriosDJkREQRgnZjFOEOU+Jo2S\nxFPc1oazI05fIPAUt12Q6VOjGc9jFL8s/QiHG7Sw7SpPakAkosLhHZ0dnZRo/1c7frzWCPuucpzc\nUoIDv3JAv9uCjcetmLBJXG8KDLPnLrhQNV/ghmtEUq8//g8otl3luOEaoTqQUV1R5BtNTsYoLwdM\niIhCMU7MYpwgyn1MGiVJDUyonVqE5l4HDLstaO51oHaKxW2zxRDM+K3ejO56Y8g0XE6PJaJYeJcj\nd75sx4F1gdeU7nojTHrg5BYjfrTWgOZT1oDBhO2nrbDYJf5ulUH1+hNpNmSk14KXGfzdKgO2nw48\ndku/FW13eka0kzXKywETIqJQmYgTc82mZ5wgonixEHYSsbht9hrUjcOiIMz0WLb9JKLoeUdNh6+4\nVa8pFgW+pgjFRQL3nbTiokWiVAfM1wv8018a0VijhcMlA64/kYqSAoj42lU4cM8RB6oritB2px6N\nNVo43RLreqcxpQA3XCPQudqAxhrPyG6y2jmzGyARUah0x4n3p6ZxsXQybFHrIZgZJ4gobkwaUUG4\nqDhQvbAI5y64fEEaSF5AJKLC4Rk1vYyq+UL1mlJdMTuJt7FGi3tvKoZ+twX9DSURrz+RunACUH3t\n3mNjKDFI9NeX+LrStPRbAQDXm4owH1r8BRZgULmMyjIBh0vOPEzYUJukds4cMCEiCpTuOLHxuAUn\nZ2bT+3+/uXccUDyDDowTRBQvJo2oICzRabHhRoGWfisOrJtt+dnUZ8WXlMWZPj0iyrAhmDGoG8dF\nxTEzCrog7Ciod9T0rG0MjX1W9NQHXlNabgms03DuggsLdRo099lmRoE1qjfk4doxe0eZ1V5TNC48\nV18S8KBwYJ0RD56xwq6I2dFcjvISESUkm+OE2S7DzqZXSzQxThBRLJg0ooJQqyzAoV9dxv23aNE6\nYMPwFTfKdcBn7CYGxDnEcpNElIsiLQuL9EBQ4zJhaMoccJO9TCnHoV9N4u4qZ8BN/53KIkCJfEPu\nXc4QPMpcrhdwSan62lSYZbfvfSyxCYt9++coLxFR/LI/TiDsbPpwiSbGCSKKFpNGVBC8IyiHBsdx\nUXF7ArE9fcmPXE28xHOTRJRrwk33b+gdm72BDkPtJjv4AcH/pj/SDbl3OYP/KHPTCSu+fbsWn1lQ\nhO2nrTi43hjwkHGtTn3Z7VKdds5zD5ar1ykiolSLtHw4G+LE6k9qQmbTe2cpvawbY5wgooQwaUQ5\nIRlBKlMjKLmceEnkJokoV4QbhR1TXBiCOW3XmuDlAeV6gW/frsXu1Z5zKy4SePCMFe99LLFUp8US\npQzv6C0hyaRtfTbcEWMdily+ThERpdqHYeLEh3E2U0lFnOgZcvjNphe4x+4pv+AUbsYJIkoIk0aU\n9XI9SOVy4mWuGitE+SDcdP8brhEYnIrt7zTRBLf/g8Tj9vNov0vve81bLNWw24IdShX260bw3BYj\nRiel70Ghar6AzVYU87Ux3HVq3ZGP8ILuI5jtEia9wGfs5ViDyqS/byKibGbSqxe0NukFYI9tX6mK\nE401Wl/HNcNuC2pgYpwgoqRg0oiyXi4nXYDcTryEe5hmxznKJ7XKAjT2fRRQqLSl34qOP9Nj+ylb\n1PtJdoJ7rr8/77VFqxG+FsnehwXVc4tws652nXr2TQfKSoHuTX4FXE9Y8PwksAaVvn1+qDiwuFSg\nu96Yk4l9IqK5mO0yZPlXS78VZruMaT+ME4wTRLmoaO5NiDLLE6TUOkI4MnRGsfEGdH++gJ7lPGvn\nbTg74oTDJXF2xDmzRn5Bpk+NKGlqYILDVoQHz1hh6LSgdcCGztUGXG8qiunv1D/BrdUIX4J7UDce\n13nN9fcX7bVlCGac1X8EfakTEIC+1Imz+o8wBLNvG7V99bzhQPcmY8D76d5kxG/1ltkHnwYtblpY\nhO56Y9LeNxFRtlmq06KpxtNMxRsnmmq0WBrjvVy2xonnMYoX9KO46HCgemER7q8VGCy9zDhBRAA4\n04hyQK7PdlErWhjcQjVbsQUrFYpVroUYVC7jhftCi4iqGYIZL+vGMKa4UKoD3G7AqiApswr9R3uv\ncRThK8emYXMBpTqgyCV820V7bTmrGUOZAfjx2tn3tv20FWedY6hxmUL29YHZjY5f2DFhU+/MZrbL\ngAef4SvusK2eiYjygbcLbyz3cqmKE8EzgvRTemzotcKiyLjixBDMuFBqwcn6koBZVPffosWhwdlZ\n/bXKAmzru4yjjBNEBYdJI8p6uZx0AXI/8cIWrFQIYvk7HYIZr5ReRq/fNWn7aSuKEL7lcbR/O2pL\nF7aftmL3Kj2uN3k6qJ21fYT37dO4qLPiwyk3Nh73LJFYGuacFY0LB9eXBCzxPbjeiHW904Br9v2/\nPzWNr3abUa4XdjcJzAAAIABJREFU6Kk3ov6Z6bA1PC7aZ5cpVFeod3DLlcQ+EdFcYr2XS1WcUIsR\nTSesaP2CFu136WcHBWKIE4O6cd8sIMATIw6sM6J1wIaLijvg+DanRGPfNADGCaJCwqQRZb1cT7oA\nTLwQ5QLVtsgqNR4GdeM4GlRn7eB6I5pPWsO2PI6WWg23g+s9N+9v7CzDwfVGPHjGit/CjJNbSvxq\nQ9hQO6VeVHRKAT4wu3HzvkkMX3GjuqII3/uSDlNB16KLOiuuKxX48VrPw8PWGi2aTliDalVYUWE3\nAHrPEo3qiiKsitDqmYgoX4S7l0tnnFCLEd2bPDFi92qD7zixxAlvraKeIQc6X7b74sSbY27P8jtl\n9tjPbfEcq6vOwDhBVECYNKKcwKQLEaVbuIKlH0651ZcXTEoc3ei5ofbebHsT3NF2jQlXOH/4itt3\nQ//ex54lCKOTMqA2RHBzAO8xoQDf+qkN8w2eJQs2p8T//JkN5Rrhm2nkPTYcs0sNutYYAVhR/8w0\nrto83YMM9mJMldpwMqho+OcWF2Hj8WmY7Qg744mIKN+kO05EihEA4ooT5XoBQ6cFxmIExAmTHlhi\nN4Yc23+pGeMEUWFgIewsNQQz9utG8DjOY79uJKAQHRERpV64gqXe1sv+zl1wobqiCI01WnTVGbBU\np8UOpWr2QWCmGKhtVzkON2hDCox6hS1aWibQ9pJndNe+qxz9DSVoe8mGniFPQ4CVyzS46HSiXXYD\nQMAxv3mrFloNcGlSorqiCA03a1GiE6rHvq4s8L11rTGib3MJFuo0uMe+GDa9I6SY6YF1Rpz9nRv3\n2CvRjhW+901ElO/SHSfCxYjqiiL0DDnmjhN+TWS8xzy5xYhv/HFonJhnEHhHMxVy7GXzGCeICg2T\nRlkolgcMIiJKjXCdG812iW1B3Wq2n7bie1/SqXYYjKVbjlonnO2nrSguAg6sC70J73zZDmDmoWF5\nZcgxRyclTr3lxInNJbC1laOrzoDuIQfu+29auDUy5NgfW6WnHkbQ8SfdLvxUMwqzXb3oqcUu+QBA\nRAUn3XFCLUY0nbBiw43F6HzZPmec8O+aFk2cUDSukGNbHYwTRIWGy9OykNp6ZbUppURElDrhOjcu\n1WlRO7UADb2BXXHuP2VTnXIfbjmBWteYgBpuTiuWVc6D2eXExKSiehM+fMWNsyNOtAxIdO7dGXLM\nL/xwCsc2qRc4Da5pVAMTTjhHsXuVHq0DNl9di92r9Lj/lA2LSgXKdIkX+yYiyhfpjhNqdT6XKeV4\n+k0nRscjx4ngGkKxxgnvsU9gFIc2ME4QFRImjbJQLA8YRESUGpE6N4ats6ZyQxzuoULtBtq7vMyr\n59gA2h7egwVaobqPEi3Q+so8dO7dicatdb59PLtiLc5dmAjb5nj4ihsLdZqQYq4mPXC9qQhv7Czz\nff/siBPzDUBPvRGjkzKkmGlTnxVfUhZH8YkSEeWXTMSJ5+RPAr72xokbrokcJ5784d/44gSAuOIE\nAMYJogLEpFEWiiVwUHSiLUJLROSVrM6NkR4qgvUcG0Bnxz4MvzuK6uWVmJqy4uk6gdFJQ+hN+Akr\ntu+4F11PPRKyn7b2nWj+Rjuq5nseIkYnpa8rTtV8AYMGuFNZGPAzg7pxfPt2ne84H5jd6PiFp6Aq\n4HmI0Go8tZC8I8wlWuAmxcTrKREVJMYJxgmiQsCkURaKJXDQ3MJ1tsAUGMCIKKJkdG6M5qGiXXb7\nRosP1Ams3FKGcxcmcPfhaaxcVq56E/6lu27H2Z//EhrNbaheXom29tnZRt7//vV3/wEbj09gnkHg\n4PrZB4nGPiv+0zkRkEz/UHGg/a5yfHahBs0nrXC4PaPGK5dpUP3UpG8wo7FGi8YaLc6OONHQa8ca\nVIa+6TgwuU9EuYhxIj1xgjGCKHOElHLurTJgiTDIb+ATmT6NjOGFMXn260ZwuEEbMHPr7IgTzb0O\n7FCqMnhmRPH7W5z/DynlrZk+j0zKpzjRLrtx84q16LpjIuBa9al/tuDHa42h16//o4XWpXgeHLwt\njQckOvc+GrD8AADm6W/DqYbAfex6yYb9v3L4bva9ywdabtFi92oDbt43ia662dp6PUMOPPKiLeCB\nornPhtqp5LRMDkzuJ3//RIWIcYJxIl/iBGMEUfLFEiM40yhLJWPUgjxYI4qIsonaoAAADL87ipVb\nygK2bb9Lj8Y+a8BNe8uARLFW4MCfi8DCpXVOtHbsC3kYsCgypF7Fqbec6KkPLHzaXW/ExuPTuLuq\nOKTGRWONFk63xLreaUwpUC3kmgg2gCAimsU4EYgxgiizmDSivMcaUUSUSrHMDFVbLtsyMIGeYwOo\nXl6JcxcCR5CvNxVh0gE88IIOF0YnUL28Ep17d2Jb82NYuSzwwWHlMg2Gj46GHHN+iSbkGhiu8KnZ\nDjT3OlCiDe1+c72pCPOhxXdRhSHF855PKKMw6QXMdjnzgBDfrFgm94konxVqnDirGcPPNKOYUoCF\nOg3uVBYyRhDloKJMnwBRqnlqRNlwdsQJh0v6tR1dkOlTI6Ic57u5b9DCtqschxu0GCy9jCGYVbf3\nHy3VajwjwE03uvDQ1/8Ww+9cwqZnrNj1ks13rWrpt+KvarUQDjuOHn4cb5w/g8atdTMPDq6AfZ+7\n4EL18tC6EVu3b0TTCWvANbB8piVy8M8v1WmxQ6nCTYoJTX1W1eum9z3fXyvwyfkCJ7cYYY/ivUfi\nTe4Hn88SnTbmfRERZZNCjRNn9R+hrMyN/oYS2HeVo7dBj1cYI4hyEpNGlPdqYELt1CI09zpg2G1B\nc68ja9ZAD8GM/boRPI7z2K8biSuQElHmqN3cH643YFA3rrq9Z7R0duS2Z8iB7iEH+u7Vw9ZWjhOb\njdj/Kwf0uy2of2Yav5+QOPWWE003utDZsc/3c23tO9EyIANu1lsGJNrad4Ycs+upR3Bvcz02HrdC\nv9uCjcetqLAbwybTh2DGxdJJtNyiReuADYZOCzYen8aSqTLUwOR7z6fecuLAOmPU7z0SJveJKF8V\napy4pgQ4uD4wRhxljCDKSVyeRgUhG2tEsasbUe6LNGVebTlC8HLZR1+y4el1gTUjeuqN2PTMNPo2\nl8zWp+i34ncTl3zH8NajaO3Yh+Gjo77lCP51KoLbMv/Lgcd9r3eIJgxNmVU79ezXjfgecHav9uzL\n0zzACiiz7znc0oV4lgskq201EVG2KdQ4AQcYI4jyBJNGFDV2dEsuFvUjyn3haqZV6DQY1IYmhZdM\nlaG5bxKH6w34wOzG76+GFh/11owIKF66zoj65+wB2zVurQspZuql1pa55eE9vp8DwifT56od4X3P\n1RVFSa0Xl43JfSKiRBVqnNCXOhkjiPIEl6dRVGJdj02hgpeifRg0/RjwBlxHhs6QiIDYlo2GmzLv\ndEF1OcJFnRVP/rADra/Mw87nbbjhGqFec6IiMDyvXKbBhDVwu0g6O/bhQJ0IOP6BOuFbutAuu9Eu\nu1XftwRQ/dQkeoZmr0X+tSO873nDjcVo6VevZ0FElK9iLS1QqHHi42lg++nAGLGNMYIoJ3GmEUWF\ns2ISo7YUbeNxB7u6EWWZWJeNhpsyfxKjYafle0d+NZrb0H6XHi39VhxYN9squbHPih23BBb3PHfB\nhepPXRf1+1Bryxyua0649739tBVOt8T1pqKZZNCigPd8aHAcHyoSG49b/bqncbkAEeWveEoLFGyc\nsANnnWNY1zvt1z2NMYIoF3GmEUUluCgfwFkxsVArgvjt23Vhu04QUWbEWrAU8Nwc71Cq8BhWYIdS\nhRqYwnZ6ma/R4OYVa6HR3IZ5hiL8dtyNztUGXyHRB89Y4XZLdA85Aq4NjX3WkOKlPccGfPu6ecVa\n9Bwb8L0WTdecnmMDvtHyF/Qfhbzvg+uN2Pm8TbV5gPc9b0IlymUxRFyfNhFRboknRgCFGyf+h2s5\n/kKpxFKdFlcUFwZ141ylQJSDmDSiqLDVZWLUkm7td+nx0ZTMyq5uRIUqWQlyteUI9x63wmCQ6Lpj\nArZHy9B3rx4Hfu3Ab8Zc+PU3SvHCfSWYcgBfv1UX8oCgLTf5akz0HBtA1dJ7sHXb92G7MoqD6/To\numMCbQ/v8T0QqHXN2XrShus/+UeeB4iiW7Fzx2O4v1bAtqscFkW9Zsa0At8DTjAuWyaiQpPMQVTG\nCSLKFUwaUVTY6jIx4ZJuS3XakJEnIsqcZCXIa2BC7dSigKRwsSzC0aBR2u5NRnS9qkC/24INx6dR\ns7AI3UMOVJYJ3wPCpAJs2PRl3LxiLYqKbsV3vtWOp+9RYN9Vjh+vNaL9X+0YnZQBtSgat9Zhxedr\nsPH4NAydFrQO2FC7ROC/XnnN8zDSVo6HbtPiqdcUGDotmKeH6vsu14uwN/fxjrgTEeWqZA6iMk4Q\nUa5g0oiiohbYOCsmeky6EeWGZP6tBi9HuKK4VEdpJxXAvqscp7aUYGjMjRXXFgUuQ9Aa8NNnf4qu\nOyZwU0URjm0MvAE/sM6IzpftnloU73pqUfQcG8C5f30VFSWzC8dev+hG9yZP2+bn3nSie8iBE5tL\nYGsrx87bdGg6EbhctumEFas+WRR2VJjLlomo0CT7fo5xgohyAQthU9TY6jJ+4YogMulGaoZgxqBu\nHBcVx8zvygL+rqRJKv9Ww7Vdrq4oglYjMDopUaoF/s97LnxinsDfrNSh+y0N9BodDvy5A6uqijF8\nxa16Az58xR1Qi+Kvv/sPKNMJ/HhtYOHUD8xuAEDny3YcWGf0ncvu1Z7WyfXPTGPCDlRXFKHlC1qc\nessZtulBuPfDYv5ElK9SfT/HOEFE2YhJI6I0YdKNohFPZxZKrlT9rXpGqL3/33pu0Fv6rehcbUDP\nkANtL9kCuuNsPWnDwk9cj9+9/R7uPgzMNwCLS4XqDXjVfIGWAYnOvZ4iqFf/MIH+hpKAjpc99UY8\neMaK+z6nU32oaL9Lj78/p8D1mOe9O1wSf39OwcplGnyoTGO/biQggan2fvy75xAR5aNU3s8xThBR\nNuLyNCKiLJKv6/+FEH8phPitEOIdIcQjKq/rhRDHZ14fFEJ8Mv1nmVrPyZ/gyR92oPWVeTDsmUT9\nc3Y01WjRWKMNGNH1/v9+bKMBv3/7PZzaUgL7rnL0bS6B1SFx30lrSMec9z6WkFq971hTClRHmt/7\n2PMz1RVF6l1zKopCvj53wYWbFhaFFDDlsmUiSibGCcYJIspOnGlERJRFPOv/DQHf86z/n87QGSVO\nCKEB8BSALwP4AMBrQoh+KeWbfpu1APhYSvkpIUQDgP8HwJZkn0sylv4lso/GrXUB3W2+86123F3l\nDLucwKIgYBT4xJYSrO2ZxqZnrDDbJUx6gYdu06L9Lj3OXVDQ8vAeAMAnlszHuQtK6JKAcoFNz0xj\nwgZsPD6NihKBkasSVfMFxqclHrpdB4dL+ka3m2q0vlFubwLTfwkCZ1ASUTIwTszKtjhhUTxL0Tbc\nWIwDv3ag5QtaxgmiAsOZRkREWSSZnVmyyO0A3pFSvielVAD0AlgftM16AIdm/v0cgLuFEAJJlIzW\nv0Mw45WgfbwSxT6GYPa0MNbchptXrEXPsQE0bq1D/X2bsLZnGmU69a40/iO6wEx7Ywewb//jqP7U\ndTix2Yjdqw2zxU5nOuPsefI72P4TZ8BIc0u/Ff/rywac2FwCvQYoMxTjx2uNsLV5uuuU6AT+6RVP\nh576Z6bxu6sSp95yonO1AY01Wt/xWcCUiFKAcSJMnPhvf3IrNhyfRok2fXHiodt0WFQqcHKLpwh2\nV50BT//agevLgadeZZwgKjRMGhERZZE87bS3FMD7fl9/MPM91W2klE4AEwBC3rQQ4utCiNeFEK9P\nwxX8ckTJWPr3sm4spB3y0XoDXtaNhf0Z70NI1x0TsD1ahq47JtD28B70HBvAF7/4OSwo16H1dh1a\n+kOXE2y4MXBC8LkLLswv0aBxax2G3x1VL3b67igat9bhiX/+Ptb1zrZS9t7Ur1ymQbEGOLJeF/g+\nNhpRrAE+MV+gb3MJblpYhK662QcB7/FzPIFJRNmJcUIlTrQ+9ATO/+cQTm0pwb41Bmw/nZ44ceot\nJ3rqg5bCbTLinY8ldIwTRAWHy9OIiLJInnbaUxsJlnFsAynljwD8CACWCEPI65EkY+nfWJh2yGNK\n+AcT/4cQADMjvU60duwDABz8ajFWVRXjsws1aB2wYfiKG/P0wO1LNDjwawfurir2FRBtOmHF1u31\nAIDq5ZU4d2EiZGnBPEMRNJrbUL28EuXlJej/CkK2CVfLwqIAhmKJxj4rdtziWXLgX3S1qc+KLymL\no/68wmGHQCIKwjihEifqD55E37163/eLiwQePOOpT3TTwiJ8fnFRSuJEuKVwZjvwwn0laOybTmmc\nYIwgyi5MGhERZZk8XP//AYA/8vv6egAXw2zzgRCiGMA8AH9I5knE0/o3+Ma1dOZngvdRqgOgqN/o\nhnsIGT466vn3ljIAQONMsVOHS8LQacGZphJsfnYaX+mehqbIU7S0ckEJvvjFzwEA2tp3ouXhPThQ\n5wx4WNj5x1q031WCcxcm0HDSgftOSxxZD98223/iDFvLYp4euDwF3AADfvCqFWb7bHvlch3wGbsp\n4Rt3dggkIhWMEypx4up0YAKqsUaLe28qhn63BV11no5kXzwwiQ3Hp2GxA+V6gTv+9DZ0PeWpIx5v\nnDDp1TuwlWiB1gFbSuMEYwRR9uHyNCIiSrXXAHxaCFElhNABaADQH7RNP4D7Z/59L4CXpJQxjRDP\nJdalf2q1LdxuhCwP2H7aCp1LE7YWRoVOo16HYnnlzChw6Gvz9ICh04LXL7qxoESgv8HTGefYV+Bb\n2ta4tQ6dex8N6LLT8gVtQO2K3o1aCGOpb5vWV+ZhXcM6ON2e2UTBtSx23qbD4lKBz2Me7rFXYqlO\niwkbsESrxT32SqxBZcL/P+Rrh0AiSgjjhEosmF+i/v0l5QKtAzbod1vwoQW+7mmnthhx/j+H0HNs\nAADijhO1d96GrSdtIe9h3xoDuuoMKY0TjBFE2Uck+VqbNEuEQX4Dn8j0aVCacToqUXT+Fuf/Q0p5\na6bPI1pCiDUA/gmABsDTUspOIcTjAF6XUvYLIQwAjgD4Ajwjxw1Syvci7TOeOBHLNWa/bgSHG7QB\nI627XrLhB68qAV3HPp4GVtkXe250g7Y/O+LEvcfsKDHImVFTzwNAy4BE595H8W//9l/oO3ICxzYa\nAkaBW77g6XRT/dQkfrzWGLLPDcetaG6pR9dTj6Dn2AD++rv/gKt/mMC0w9Plpu1O/eyspT2TcLle\nA+DpxNP28B4cqBP4wOxGxy/seO9jiU/MF9gzU8vi7IgTzb0O7FCqYvpso/U4zsO2qxxazexKE4dL\nwrDbgsewIiXHJCpEjBO5Hye+8rWvoL+3Hwe/Orv87L7TChxugd6NWrQO2NBVZwjZ37reaVRUzMee\nJ7+Dxq11ccWJphtdOPWWp2ubSQ9sq9Gia43Rd4xUxQnGCKL0iCVGcHkaZQ1ORyXKX1LK5wE8H/S9\nx/z+bQPwtVSfR6Slf8EPCh+qLBdov0uPPS/P/KAE7FPFWDXzQHFSGVVfXuByYdVUJVpfERg+Oorq\n5ZXo3LsTAPDMkdMQbjfW9U5jSgFMeoE/+dPbcOp37+Pv94xCuqVqXYlJReK5w304+L9PQ+N2YJ7B\nMxvJ97DRbwUAVJYJVC+fHfXt7NiHA3XC94Bx3+d0ODviROuALajzTfT1O2IVz/IPIsp/jBOVvnqG\n1Z++zhcnDj99EpueUTBhA+YZADc0aH5gA1p//ku8OTatGiOmHcDT9yi476EOfPuhPXDZrHHECQN2\nr/Z8zxsn/I+RqjjBGEGUfZg0oqyhVgTwcL0Bzb3js8GbiCgF1JLWTX1OdPzCjt2rZ2/wz11w4aaF\nRRgec3tGPJXZny/XCxg6LQEjuN4b3RrFhOfOdwcc84+uuxuGIicObpy9id9+2orfDP0W7196ET3H\nBrBzx2OqN8/VFZ6ONRuOT6OiRATMRhqdlCgSwNYTnoeEbQ+s8f3s8DuXsHJLecB5rFymwfAVd8D+\no7k5j3dmqGf5x+WAEXXP8o9Fc/4sEVGmpCNOeO9322fixR9ddzfm6904uD4wTpw68XO8f+lFVC29\nR7U+3bJ5nsGBI+uBTc/kVpxgjCDKPkwaUdZIRscKIqJ4qCWtu+uN2Hh8OqArTUu/FU01WkxMyIAH\ngcHSyzhZbwzY7jdjLhz6lTPsje7VP0ygv6Ek4JgH1xuxrncCgGe096HbQjvTbD1hxT/+uedm2mIH\nJpXZ2Ug9Qw60vWQL2L7l2Z/6imeHK25aNV/A4ZJR35wnMjM0TzsEElGey8Y44XRLbD9txcH1xoCk\nknsmv7NymQYTNsBsz504wRhBlH2YNKKswemoRJQu0Swx8LYX3nh8GhbFUwOiqUYbcoOv2ip5nREb\nj1txj31x2BvdcG3vp2aud8PvjuLXW8rw2YUatA7YMHzFjeqKIoxOSl/toXI9sLBk9ga/82U7Dqwz\nBp5LnROtHfsAQDUJ1XTCiuIyEwx7zKheXonaqcDON0Mw46xmDIrGhSkFWKjznHNvAjND87BDIBHl\nmVyIExcvm3FwnT4gRuxepcf2056lZOcuuDDPACwwJh4nFGsRDLstIUkc7+f0oeKASS9gtkss1Wmh\nwB13nGCMIMouTBpR0nHJAhFls1iWGCzVaVFrX4BB3TiGxxyYmJAhI57hZkla7DLitS9c2/tPLJkP\nADOd1SbQWKP11Rvy1pU4O+JE0wkrrApwBbMjzcNX3KoPGG8evuT54moRvvLp4oAHjI+mJNyWF33b\nd4imgM/qrP4jlBkQsDzi7sPqdTQ4M5SI8kEuxYnrTRN4Y2eZ7/WzI05UVxTh7IgT205aYXUAV2Ti\ncaJdLve87pfE8X5O999SjO4hEZBoYpwgyh9FmT4Byi/hWokOwTznz9bAhNqpRWjudcCw24LmXgdq\npzgdlYiSS62db3e9ET94VVFts1wDE2qVBVii0+Ki4sCgbjzgmuadJenPN0sygj1Pfgfbf+IMOGbT\nCSt+f+kqbl6xFqu+/CW0DMiA1xv7rHhzzI2Nz1hhsUn87L4SdNUZYHdKrOudRokWqudywzUC9l3l\n6Koz4KdvO9F2px6ux0zoqjPgpk9dF/GzuqYEOLjeGPB53XCNiOs9ExHlgnyIE1tOuTCtSAxsTV2c\n8H5Op95y+mYvMU4Q5R/ONKKkSrSYNaejElGqhRvxNduB5l5HSA2FueoyxDtLsnFrHQCgtWMfho9c\ngkkv8NBtWrTfpce5CxNoefan+MrXvoLWn//S13Vt7w//Bo1b63DzirXoumMipAta80mran2LJ+42\n+G7kD6wzonXAhsoygZYBic69OwNmFwV/VnCELo9ov0uPxj4revzqc3BmKBHlC8aJ2TjR3GdD7ZT6\nPbz3c1KbvcQ4QZQ/mDSipGIxayLKduHqpy3VabFDqfJ8wy9pPVcyPJGinY1b63w39xsqx3HqLSf+\n/pziqYtxYzFO/fyXeOP8mZCfG353FCu3lAV8b+UyDS5OSlxbosEDL+hwYXQCJcUS+9YYfMvbAOAD\nsxu/n3Dj7sPTviUOkT4rfakz5PO63lSEScUzaj2tgIVKiSiv5HucqCjTRh0nvHXsIn1O1RVFjBNE\neYxJI0qqQi1mHW8dJyJKv1hHfKNJhic6S/LNdy5heiywHkRLvxW/m7ikur233lHwtdakB5xOF35/\n6Spu+tR1mJqy4nrT7An1DDmw66wd/Q3e+kQKWh7eg1swT/WaVasswFnxUeio9Ckr/upPdPjBqw48\nhk/n9fWdiApPpuOE/+zPdtkNIHlxokwHjFkcuKnSiKOHv4POjn243jTh2yY0ToTveub9nO6/pTik\neHZLP+MEUb5gTSNKKk/wsKmu985XidRxIqL0i7V+Wry1KGIx36gJqQdxYJ0R843qI7xt7TtD6lg0\nPDeN+QYBswLM0wMbKscxbZkKqIfx/bO2kPpEB+oEBnXjqsepgQmr7ItxedIzWqzfbcED/VY8cY8B\n7XfpYbbLpH0GRETZIl/ixNaTtpA4Ua4TAICro6P4q289HlIXSS1OHK43qMYJ7+d0aFDid1cl6p+Z\nhqHTgtYBGzpXM04Q5QvONKKkSmT6ba5KtI4TEaVfLCO+6ejsOGF1qXaZuTrtQs+xAV9dCy/v1+se\n+D6mHcCSMgFDscDTQaO8D35ei0NvG/HACwK/v3jVt9/g40RaQlwDEwY14zjcoA0YsT474sTSPJ9F\nSkSFKx/ixNb7vu/rguaNEwc3BNYyOnXi53hy76N44K//Ma444f2c9utGcHgz4wRRPuJMI0q6Gpiw\nQ6nCY1iBHUpVXieMAO+UZLXg6sjQGRFRMiWrs2OHaPItOWh96AlcW1qLInErri2txXyTMWw3m7aH\n96Dn2EDI/rwPCC/cV4J5Bs+DQPAI9Km3nPjwowkIhx0vNpfgpoVFqscp1ws8jvPYrxtRnSVZiLNI\niYiilYoOwM9jFHv1b6NI3Ir5htviihM3feo6dNUZ4HrMpBonDq434uofPEvTGCeIKBzONCJKUKHW\ncSIqJMns7Pi5ms24/LsR9N07O9rbdMKKDc8U4dRmBMwU6lxtQGWZQGvHvpBRZACYf+08bD9txgdm\nqZq8Hr7i9ixpqPM8ILTdqQ+pO9F0wopv3+7txqNeu6IQZ5ESEcUimXHiXzACUebEyU2JxYm29p3Y\n+q12HNuo3uFs5TINphSgs2Mf4wQRhcWkEVGC0jElOV+wYDjlk1h/n4dgxr/qLsPxthuntpQELGnt\n3mTEpmdtni4zDqC6ogidqz3dbBwuieGjo6r7fPIfvotv7vhblOlcqslrk14ELGnwdsdpHbDhzTE3\nTHqBb9+uxe7VBt+5hFteG+6BKPhzWKIYcVFn5d85ERW8uOOEcOPUptA4sfG4NaY40bi1Dv/2b/+F\ntT9+DmWYH85MAAAYtklEQVQ6qMaJTyyZj+G3L2HllnLPzyQ5Tqh9BgB4P0iUQxJaniaEuFYI8XMh\nxNsz/71GZZvPCyFeEUL8Rgjxf4UQWxI5JlG2ScWU5HzEguGUT2L9ffZu/2yDARa7er2ICasb2mIN\nXrivBG/sLPPduJ+74EL18krftv5L2771YDuKhUTr7Tq09FsDlgVsPWnDtgfqUf2p6wKWGjTWaNFV\nZ8BSnRYWu0T7XfqQc4l2eW3w53B/rcCFMgv/zomo4MUbJ75ZWxw2TpjtMuY4ceR/n4C+uEg1Tmz/\niRN7nvxOSCHvZMUJtc/grP4jvML7QaKckmhNo0cAvCil/DSAF2e+DjYNoFlK+VkAfwngn4QQ8xM8\nLlFWKbQ6TvHwLxg+VzcOomw1BDP260bwM91oTL/P3t//0UmJcj1U60XMNwA7/1iDphOBN/UtAxJt\n7TsBeB4Enjvch7579bDvKsfJrxlQppP47EINOlcb0Dpgg6HTgvrn7PjHf+lA11OPqHZa89aZCNfx\nZ75Gg/26kYj1K/zfl/dzOPWWE92bouu6Q0SUjxKJE/ffUozuIQfmGdITJ5745++jcWtdxHpEicQJ\ntXu/a0qAo7wfJMopiS5PWw/gz2b+fQjAvwL4nv8GUsrzfv++KIS4DGAhgKsJHpuIcoinYLgh4Htz\ndW0iyia+EdN6A+45Eq4Avvrvs/f3/ws/nMLqT3pu+LuDalVsrZmd/l//nB0TNjeql1eic+9OX52K\nYwdPou9eY8CShYPrjWgdsPlGnR0uCcNuC85vO4KObUcAALdgnnqdCQVY1z2K4mJgwgbMMwA2BbjW\nWITD9VqsXGYIW7/C/315hauZEe3fOZewElEuSzROnHqrCAfWGXFi2DFnnNh43AqLXfquld5r/hH9\n2zi5JbY4Eake0fvKNDYcN8NiB0p1QKkWmLIDJsPccULt3m/kqnoNPsYJouyV6EyjxVLKSwAw89+I\nRVyEELcD0AF4N8HjElGOCTdStUSnzdAZEcXGf8S0ukK9u0y432fv7//wFTee+VoJ7q0uRv0z09Dv\ntqD+mWl8NCnRtcYIAGi/S48Jmxsu12toa9+Jzo590Ghuw80r1uLqdGDL5Z4hh6/uxM37JtEz5MC5\nCy5U6AJvyMPNhnwf0ygzCJzYXAL7rnKc2FyCeUaB/35LcVSjwMF/17F+Lv64hJWIcl2iccKbeO9a\nYwyIExuOT2NRCQLihMUusRGeJWknMeqb7WO2y6TFiSGY8UHpJE5t8cSI/oYS6IsF3IhutpDavV/V\nfME4QZRj5kwaCSFeEEK8ofK/9bEcSAhxHYAjAP67lNIdZpuvCyFeF0K8Pg2X2iZElKPYipVynWfE\n1HOT7e0uE+3vs/f333uz3LXGiD98zwR3uwl9mz0tjr28tSl6jg2g7eE96LpjArZHy9B1xwQWlQp0\n/MIOwPMg0PaSDV11Bth3laOrzoBHXrRh87PTcAp3VDfRv9VbQpaT9dQbceotZ8B24epXBP9db7ix\nOGTZRLR/51zCSkS5LtE4Ua6bXZbmjRMvNpfAoBH4r2+V+7b1Lg9TS6AYi2f3kWicGNSNhySHDq43\noqhIveZScJxQu/f7eBrYFuf9IOMEUWbMuTxNSnlPuNeEEB8JIa6TUl6aSQpdDrOdCcBPAeySUv57\nhGP9CMCPAGCJMMi5zo2IcgdbsVIqpHOaunfEdFVVsa/46INnrHjvYwmTXuAz9vKwx/b+/p+1jaGx\nz4qe+sAlBy1f8CwX8HVfnDLhrx94HIcbtAFLDHrqjdh4fBp3VxWj82U7DqwLXYLwQL8VT68zqna2\nCRY8Ig14bvyHrwSO7fhGgYPaSKv9XS9TytHca43575xLWIkoFXIpTrxvn0ZTnwXdfjFiW58NThdw\ndsQZ0KW3WCN8CRRgtqvZ13ptvqVticaJcNflKUW9E1twnFCLEauUxYA9vvtBxgmizEi0plE/gPsB\nPDHz39PBGwghdABOAjgspXw2weMRUQ4L17KbKB5WuHy1I+aqvZMMnhFT7/E0qCwTcLiBQxsMuN5U\nhOa+SQxNmSM+ENS4TBiaMockWQ4NWvH3L1sCbp5PKqOqN8dmu6eWRbiEz4UJGfVNtEkvVG/8y3Wh\nDyi1ivoKdNW/6+D/RmG+RoPqpyYxclWiuqIIbXfqUVkmVJNVRETRyLU4sQaVGJoqCYgRd8xce4OT\nLCcxqhoDPlbcuFUxYeNxS8Jxwj8J5nXuggtLygWa+qwBya1wcSLcvV8894OME0SZkWjS6AkAzwgh\nWgBcAPA1ABBC3Argm1LKHQA2A/hTAAuEENtnfm67lPI/Ezw2EREVsCnhwol6Y8goazQzbOLhP2L6\noTKNG64ReOJug280OdpjR5tkCXezvlSnxQ57Ffbq31Z9fZ4+/MygYJ+xl6PphCWk2GqF3YjmXkfa\nZgUOwQyDQeLHa2fPY/tpKyZt8IxKExHFIRfjRLRJlkHdeNjZPmuUSqyxVyYcJ2qVBdjWdxlHZ5Jg\n3muzVQE+ZY9vVmm8GCeIMiehpJGUchzA3Srffx3Ajpl/HwVwNJHjEBERBXPI9Hdg8d7MP47zGH6o\nDFqNiOvY0QgesQ4eyTXbJVr6rTiwbvYGuqXfiqs2RJwZ5G8NKvH8JHwj0t7lE2tQGddsoXj5180A\nZpdQNPTauYSViOKWz3FirhgBJB4nvEmwht4xjCkulOoAnUuDVa6Fvg6cABgniPJcojONiIiIMkIr\n1JdWRTPDxr8tcjxLFsJO2U/SFPnnMYrf6i0wT0lsOD4Nix1YGjSSu1SnRVONQOuADcNX3KiuKEJT\njRY/eNWB2qnoR3zXwDMiDQCwJ37u8QhXp+KKwqYYRBS/fI4T72MaFqfE3YenUa4H3IrAX8jFAeeW\njDiRLaUFGCeIMmfO7mlERETZqFRq4u7Il2gHllR2A3weo7hQZsHJLUbYd5Xj1JYSLC4TWKIYA27w\na5UFOPQrJ7rqDLC1ebriHPqVE/fYF+fcqKtaW+ZoWzATEYVTSHGirNSTSAo+B8YJIkoUZxoREVFO\nMkKD2qmKjHRgSWU3wN/qLTi5KbAGR/cmIzYet8zOCPI7h3uPjUHRuDClAAt1mnC7nVM6OwwFi2aZ\nBRFRrBgnGCeIKHFMGhERUc6Kd9p8MpYNJDplP9zNd7huN2a7VN1PiUHiufoSv5vo2DsDJboMI1Gp\nfLgiosLGOME4QUSJ4fI0IiIqOKlcNhAN3813gxa2XeU43KDFYOllDMEMk16oTsE36UXIfhJdPpHs\n/SSiBibsUKrwGFZgh1LFBwEiyijGidTsJxGME0SZwZlGRBS3TE5TJkpEpkcs/W++gcA20J+xl6Pp\nhAXdm2a73TSdsOIz9vKQ/SS6fCLZ+yEiyheME6nZDxHlHiaNiCgumZ6mTLTkj29A++tHotq2QzSF\nfC/SsoFUJ0Qj3XzvQBWenwQ2HrfAbJcw6QU+Yy/HGlSG7CdZ3XlS3eWHiCgXMU4kfz9ElHu4PI2I\n4pIN05SJUiHSkoBkidQFZghmXNRZYbFLLNVpcY99seqDAJC85ROZXoZBRJRLGCcYJ4gKCWcaEVFc\nOE2Z8lWkJQG+EecEhesCs0Qpi2kGX7KWT2R6GQYRUS5hnGCcICokTBoRUVw4TZlySbvsjmq7DtGU\nloRouJvveB5EEu3Ok+z9EBHlO8aJxPZDRLmFSSMiiku4EbBaZVGmT40oIYkkRGOpcaF2831SGU3o\nQYTF6YmIUi9X4wRjBBHFg0kjIooLpylTvoo3IZqM4vDxPogMwYyzmjFoDW701BtZnJ6IKIVyMU48\nj1FcKLWgmzGCiGLEQthEFLcamLBDqcJjWIEdShVvOijntctuPCd/gid/2IHWV+bBsNuC5l4Haqfm\nTogmozh8PIVGvQ8h15g8CSMWpyciSq0amFA7tQjNvY6ciRO/1ZvRzRhBRHHgTCMiIqIgjVvr0Li1\nDh2iKeq6DcmocRHPDD7vQ8g9R6axcpkmoeNnCy6hIKJsF099n0zGCYuCvIkRAOMEUToxaURERBSG\nfwHtDtEUcdtkFYeP9UHE+xBSXVGUF8Xpk7F8g4goG2UyTlQvzI8YATBOEKUbl6cRERElQTxLBpLB\n+xDSdqceLf3WtB8/2ZKxfIOIKBtlMk5suLE4JEY09VlzLkYAjBNE6caZRkREREkQ7ZKBZE+p9y/I\n2vFnejx4xor3PpZYqNPgzhwsTp+OVtZERJmQyThx6FeXcf8tWrQO2DB8xY1yHfAZuynnYgTAOEGU\nbkwaERERJclcSwZSMaU+8CHE84CxCQtmzyPHJGv5BhFRNspknDg0OI6LituTiLLnbg0gxgmi9GLS\niIiIKAXURor9p9QD8E2pb+4dTyjJE09B1mwVbytrIqJcwzgRH8YJovRi0oiIiCjJwo0UfzjlTtqU\n+nztHBNPZyAiolyT6jiRrzECYJwgSjcmjYiIiKLg7aQ2Vxc1AGFHijcetyZlSn2+d47JpxFxIsqc\nJX98A9pfP+L7Oprrd7qkMk7ke4wAGCeI0ond04iIKGWEENcKIX4uhHh75r/XqGzzeSHEK0KI3wgh\n/q8QYksmzjWZPEU6NQHfW7lMA7NdJqVzTro7xwzBjP26ETyO89ivG8EQzCk5DhEVHsaJWcmKE5no\nLsY4QZS/ONOIiIhS6REAL0opnxBCPDLz9feCtpkG0CylfFsIsQTAfwghfialvJruk02WcEU6l+q0\nqJ1akPCU+nR2jimEEWsiyqi0xQnvjFEg87OOUhkn0t1djHGCKL9xphEREaXSegCHZv59CMCG4A2k\nlOellG/P/PsigMsAFqbtDFPAU6RTfaS4BibsUKrwGFZgh1IV1w2192HDn2/5QpJlYsSaiAoK40SS\n40Q6YwTAOEGU7zjTiIiIUmmxlPISAEgpLwkhIrY2EULcDkAH4N10nFyqpLpIZzo7x6R7xJqICg7j\nRJLjRLq7izFOEOU3Jo2IiCghQogXAFSqvNQW436uA3AEwP1SSneYbb4O4OsAsGyZ2iGzRyqLdKaz\nc0y4JRSxFu8mosKVjXEiluYGqZKqOJHu7mKME0T5jUkjIiJKiJTynnCvCSE+EkJcNzN6fB08SwrU\ntjMB+CmAXVLKf49wrB8B+BEA3HrrTTKxM89t6eock+4RayLKP4wT6ZfO7mKME0T5jUkjIiJKpX4A\n9wN4Yua/p4M3EELoAJwEcFhK+Wx6T4+CDcGMQd04LiqOmdHpBaidWpS2EWsiKjgZjRPZMOMo1zBO\nEBUWJo2IiCiVngDwjBCiBcAFAF8DACHErQC+KaXcAWAzgD8FsEAIsX3m57ZLKf8zA+db0MJ1wKmd\nWoQdSpVnIy41IKLkYpzIIYwTRIWHSSMiIkoZKeU4gLtVvv86gB0z/z4K4GiaT41U+HfAAeDrgNPc\nOz67zIGIKIkYJ3IL4wRR4SnK9AkQERFRdvB0wNEEfM/TAceRoTMiIqJswjhBVHiYNCIiIiIAsx1w\n/Pk64BARUcFjnCAqPEwaEREREQBvBxwbzo444XBJnB1xznTAWZDpUyMioizAOEFUeFjTiOak1iGB\n3RCIqFDlc6edGpiAKbADDhEVHO+1HcjP63uyME4QFR4mjSiicB0SMAUGByKiPFQD02wxU3bAISKi\nIIwTRIWFy9MoIv8OCVqN8HVIGNSNZ/rUiIiIiIiIiCiFmDSiiNghgYiIiIiIiKgwcXkaReTtkLCq\navZXxdchgdNRiYh8WP+NiIgiYZwgolzEmUYUETskEBHNzVf/rUEL265yHG7QYrD0MoZgzvSpERFR\njNpld0Bh7GRgnCCiXMWkEUVUAxNqpxahudcBw24LmnsdqJ1ihwQiIn+s/0ZERJEwThBRruLyNJrT\n/9/e3YVaVpdxHP/+psGGQFObMad8mYQZcJAwmcRutFBqGEi7GGqCoQkGQYNuuhqwi6irggoCoSQi\nFSoxqAZ7gZwURTympI2OoDOa2eDgTC8Okb2MzNPF+o/sOXufc9Y+Z+/1X88+vw8sztpnLw6/Z629\n/s8566wXPyHBzGxxzf3f1p31veb+b29WSmRmZn3iPmFmWflMIzMzsxU6c/+3QW/f/83MzFY99wkz\ny8oHjczMzFbI938zM7PFuE+YWVaKiNoZRpJ0Avhz7RwrsB74a+0QFbju1cV113N5RGyonKGqCfaJ\nSW3Py9aIDacD1ghOByeAVyfwcxfSh8/hcmXNnjU35M2eNTfUz+4+4T5R+zO4ElmzZ80NebNnzQ11\ns7fuEb09aJSdpKciYlvtHF1z3auL67ZZkHV7Zs0NebNnzQ15s2fNDbmz29mybsusuSFv9qy5IW/2\nrLkhT3ZfnmZmZmZmZmZmZkN80MjMzMzMzMzMzIb4oNH03FU7QCWue3Vx3TYLsm7PrLkhb/asuSFv\n9qy5IXd2O1vWbZk1N+TNnjU35M2eNTckye57GpmZmZmZmZmZ2RCfaWRmZmZmZmZmZkN80GhCJF0o\n6beSDpevF4xY5mpJj0s6JOmgpM/UyDpJbeouy/1G0huSHug646RI2i7pBUlHJO0b8f47Jd1X3n9C\n0qbuU05ei7qvl/QHSW9J2lkj4zS0qPtLkp4v+/IBSZfXyGnjyzZeZx57su5HS+UeWG6npJDUmyef\ntMku6dNlvR+S9KOuM47S4rNymaSHJD1dPi87auScT9IPJB2X9NwC70vSd0pdByVd03VGG5/7RDey\n9gjI2yey9ghwn6gqIjxNYAK+Aewr8/uAr49YZguwucy/DzgGnF87+7TrLu/dCHwSeKB25mXW+Q7g\nJeAK4Bzgj8DWect8Afhumd8F3Fc7d0d1bwI+CNwD7KyducO6Pwa8q8zfPgvbe7VMmcbrzGNP1v2o\nTe6y3LnAI8AcsK127jHW+WbgaeCC8vqiJLnvAm4v81uBV2rnLlmuB64Bnlvg/R3ArwEB1wFP1M7s\nqdV2dZ/oR+7e9Yi22ctyveoTWXvEGNndJ6Y0+UyjybkFuLvM3w18av4CEfFiRBwu868Bx4ENnSWc\njiXrBoiIA8A/uwo1BdcCRyLi5Yj4H/ATmtoHDa6LnwI3SlKHGadhyboj4pWIOAicrhFwStrU/VBE\nvFlezgGXdJzRli/TeJ157Mm6H7VZ5wBfo/nD8j9dhltCm+y3AndGxD8AIuJ4xxlHaZM7gPPK/LuB\n1zrMt6CIeAT4+yKL3ALcE4054HxJG7tJZyvgPjF9WXsE5O0TWXsEuE9U5YNGk/PeiDgGUL5etNjC\nkq6lOUr6UgfZpmmsuhN7P/CXgddHy/dGLhMRbwEngfd0km562tQ9i8atey/Nfwgsh0zjdeaxJ+t+\ntGRuSR8CLo2Ivl1y3WadbwG2SHpM0pyk7Z2lW1ib3F8Bdks6CvwK+GI30VZstfbR7Nwnpi9rj4C8\nfSJrjwD3iarW1g6QiaQHgYtHvHXHmD9nI3AvsCcien92xqTqTm7Uf2PmP3qwzTLZzGJNbbSuW9Ju\nYBtww1QT2VhmaLzOPPZk3Y8WzS1pDfBt4PNdBRpDm3W+lubyg4/S/Nf+UUlXRcQbU862mDa5Pwv8\nMCK+KekjwL0ld99/j+rr/rnquU9U/xxm7RGQt09k7RHgPlGVDxqNISJuWug9Sa9L2hgRx0rzGHkq\nn6TzgF8CXy6nn/XeJOqeAUeBSwdeX8LwKY9nljkqaS3NaZGLnYqYQZu6Z1GruiXdRPPL5Q0R8d+O\nslkLMzReZx57su5HS+U+F7gKeLhc3XExsF/SzRHxVGcpR2v7eZmLiFPAnyS9QPMHwpPdRBypTe69\nwHaAiHhc0jpgPf3/vWO19tHec5+o3iey9gjI2yey9ghwn6jKl6dNzn5gT5nfA/xi/gKSzgF+RnPN\n4v0dZpumJeueEU8CmyV9oGzHXTS1DxpcFzuB30VEr44SL0ObumfRknWX046/B9zco+u9rZ1M43Xm\nsSfrfrRo7og4GRHrI2JTRGyiuc9G7T8Ezmjzefk5zc1lkbSe5lKElztNOaxN7ldpHqqBpCuBdcCJ\nTlMuz37gc+XpONcBJ89c9mS95j4xfVl7BOTtE1l7BLhP1BU9uBv3LEw01wUfAA6XrxeW728Dvl/m\ndwOngGcGpqtrZ5923eX1ozQ77b9pjqZ+onb2ZdS6A3iR5nr1O8r3vkrTBKAZmO4HjgC/B66onbmj\nuj9ctum/gL8Bh2pn7qjuB4HXB/bl/bUze2q9bVON15nHnqz70VK55y37MD14Ks4Y61zAt4DngWeB\nXbUzt8y9FXiM5ok5zwAfr5255PoxzVOzTpVeuBe4DbhtYH3fWep6tk+fFU+Lblf3iX7k7mWPaJN9\n3rK96RNZe0TL7O4TU5pUgpqZmZmZmZmZmb3Nl6eZmZmZmZmZmdkQHzQyMzMzMzMzM7MhPmhkZmZm\nZmZmZmZDfNDIzMzMzMzMzMyG+KCRmZmZmZmZmZkN8UEjMzMzMzMzMzMb4oNGZmZmZmZmZmY2xAeN\nzMzMzMzMzMxsyP8BpE+yWFC5TeIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10844d9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "step = 0.01\n",
    "nu = [0.1,0.05]\n",
    "\n",
    "\n",
    "plt.figure(figsize=(20,15))\n",
    "\n",
    "\n",
    "####### RBF ########\n",
    "\n",
    "\"\"\"sigma2=0.5\n",
    "\n",
    "plt.subplot(2,3,1)\n",
    "nu=0.1\n",
    "kernel = ['RBF',sigma2]\n",
    "alpha, rho = fit(X, nu, kernel)\n",
    "plt.title('kernel RBF \\n'+r'$ \\nu =$'+str(nu)+r'  $\\sigma^2 =$'+str(sigma2)+r' $\\rho$ = '+\\\n",
    " str(np.round(rho[0],2)),fontsize=15)\n",
    "x_axis, y_axis, my_grid = get_grid(X, step = step)\n",
    "pred = plot_pred_plan(X, alpha, rho, kernel, step = step)\n",
    "pred_bin = np.sign(pred)\n",
    "pred_100 = Normalize_Pred(pred_bin)\n",
    "x_delim, y_delim = get_delim(pred_100, x_axis, y_axis, eps = 0)\n",
    "plot_pred(X, x_axis, y_axis, pred_100, x_delim, y_delim, step = step)\n",
    "                       \n",
    "\n",
    "plt.subplot(2,3,2)\n",
    "kernel = ['RBF',sigma2]\n",
    "nu=0.1\n",
    "alpha, rho = fit(X2, nu, kernel)\n",
    "plt.title('Kernel RBF \\n'+r'$ \\nu =$'+str(nu)+r'  $\\sigma^2 =$'+str(sigma2)+r' $\\rho$ = '+\\\n",
    " str(np.round(rho[0],2)),fontsize=15)\n",
    "x_axis, y_axis, my_grid = get_grid(X2, step = step)\n",
    "pred = plot_pred_plan(X2, alpha, rho, kernel, step = step)\n",
    "pred_bin = np.sign(pred)\n",
    "pred_100 = Normalize_Pred(pred_bin)\n",
    "x_delim, y_delim = get_delim(pred_100, x_axis, y_axis, eps = 0)\n",
    "plot_pred(X2, x_axis, y_axis, pred_100, x_delim, y_delim, step = step)\n",
    "\n",
    "plt.subplot(2,3,3)\n",
    "nu=0.3\n",
    "kernel = ['RBF',sigma2]\n",
    "alpha, rho = fit(X2, nu, kernel)\n",
    "plt.title('Kernel RBF \\n'+r'$ \\nu =$'+str(nu)+r'  $\\sigma^2 =$'+str(sigma2)+r' $\\rho$ = '+\\\n",
    " str(np.round(rho[0],2)),fontsize=15)\n",
    "x_axis, y_axis, my_grid = get_grid(X2, step = step)\n",
    "pred = plot_pred_plan(X2, alpha, rho, kernel, step = step)\n",
    "pred_bin = np.sign(pred)\n",
    "pred_100 = Normalize_Pred(pred_bin)\n",
    "x_delim, y_delim = get_delim(pred_100, x_axis, y_axis, eps = 0)\n",
    "plot_pred(X2, x_axis, y_axis, pred_100, x_delim, y_delim, step = step)\n",
    "\"\"\"\n",
    "\n",
    "#### POLYNOMIAL  #######\n",
    "d=3\n",
    "c=0.001\n",
    "\n",
    "plt.subplot(2,3,4)\n",
    "nu=0.1\n",
    "kernel = ['Poly',d,c]\n",
    "alpha, rho = fit(X, nu, kernel)\n",
    "plt.title('kernel Polynomial \\n'+r'$ \\nu =$'+str(nu)+' d = '+str(d)+r' $\\rho$ = '+\\\n",
    " str(np.round(rho[0],2)),fontsize=15)\n",
    "x_axis, y_axis, my_grid = get_grid(X, step = step)\n",
    "pred = plot_pred_plan(X, alpha, rho, kernel, step = step)\n",
    "pred_bin = np.sign(pred)\n",
    "pred_100 = Normalize_Pred(pred_bin)\n",
    "x_delim, y_delim = get_delim(pred_100, x_axis, y_axis, eps = 0)\n",
    "plot_pred(X, x_axis, y_axis, pred_100, x_delim, y_delim, step = step)                    \n",
    "\n",
    "plt.subplot(2,3,5)\n",
    "nu=0.05\n",
    "kernel = ['Poly',d,c]\n",
    "alpha, rho = fit(X2, nu, kernel)\n",
    "plt.title('kernel Polynomial \\n'+r'$ \\nu =$'+str(nu)+' d = '+str(d)+r' $\\rho$ = '+\\\n",
    " str(np.round(rho[0],2)),fontsize=15)\n",
    "x_axis, y_axis, my_grid = get_grid(X2, step = step)\n",
    "pred = plot_pred_plan(X2, alpha, rho, kernel, step = step)\n",
    "pred_bin = np.sign(pred)\n",
    "pred_100 = Normalize_Pred(pred_bin)\n",
    "x_delim, y_delim = get_delim(pred_100, x_axis, y_axis, eps = 0)\n",
    "plot_pred(X2, x_axis, y_axis, pred_100, x_delim, y_delim, step = step)\n",
    "\n",
    "plt.subplot(2,3,6)\n",
    "nu=0.5\n",
    "kernel = ['Poly',d,c]\n",
    "alpha, rho = fit(X2, nu, kernel)\n",
    "plt.title('kernel Polynomial \\n'+r'$ \\nu =$'+str(nu)+' d = '+str(d)+r' $\\rho$ = '+\\\n",
    " str(np.round(rho[0],2)),fontsize=15)\n",
    "x_axis, y_axis, my_grid = get_grid(X2, step = step)\n",
    "pred = plot_pred_plan(X2, alpha, rho, kernel, step = step)\n",
    "pred_bin = np.sign(pred)\n",
    "pred_100 = Normalize_Pred(pred_bin)\n",
    "x_delim, y_delim = get_delim(pred_100, x_axis, y_axis, eps = 0)\n",
    "plot_pred(X2, x_axis, y_axis, pred_100, x_delim, y_delim, step = step)\n",
    "\n",
    "#plt.show()\n",
    "plt.savefig('fake_data_plot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### testing K means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class OCC:\n",
    "    \n",
    "    def __init__(self, X, step = 0.05, eps = 0):\n",
    "        import matplotlib.pyplot as plt\n",
    "        import numpy as np\n",
    "        \n",
    "        self.X = X\n",
    "        self.n = X.shape[0]\n",
    "        self.figsize = (10,5)\n",
    "        \n",
    "        # plot parameters\n",
    "        self.step = step\n",
    "        self.eps = eps\n",
    "        self.norm_colors = mpl.colors.Normalize(vmin=0,vmax=100)\n",
    "        self.set_grid()\n",
    "        \n",
    "        pass\n",
    "    \n",
    "    # Plot functions\n",
    "    \n",
    "    def plot(self):\n",
    "        plt.scatter(self.X[:,0], self.X[:,1], edgecolors  = 'black')\n",
    "        plt.xlim((min(self.X[:,0])-self.step,max(self.X[:,0])+self.step))\n",
    "        plt.ylim((min(self.X[:,1])-self.step,max(self.X[:,1])+self.step))\n",
    "        pass\n",
    "    \n",
    "    def set_grid(self):\n",
    "        self.x_axis = np.arange(min(self.X[:,0])-self.step,max(self.X[:,0])+2*self.step,self.step)\n",
    "        self.y_axis = np.arange(min(self.X[:,1])-self.step,max(self.X[:,1])+2*self.step,self.step)\n",
    "\n",
    "        self.my_grid = []\n",
    "        for i in self.x_axis:\n",
    "            for j in self.y_axis:\n",
    "                self.my_grid.append([i,j])\n",
    "        self.my_grid = np.array(self.my_grid)\n",
    "\n",
    "        pass\n",
    "\n",
    "    def Normalize_Pred(self):    \n",
    "        self.pred_100 = self.pred -np.min(self.pred)\n",
    "        self.pred_100 = (self.pred_100 / np.max(self.pred_100)) * 100\n",
    "        pass\n",
    "\n",
    "    def set_delim(self):\n",
    "        ix_delim = np.where((self.pred  < self.eps) & (self.pred  > -self.eps))[0]\n",
    "        self.x_delim = []\n",
    "        self.y_delim = []\n",
    "        for i in range(len(ix_delim)):\n",
    "            a, b = np.divmod(ix_delim[i],len(self.y_axis))\n",
    "            self.x_delim.append(self.x_axis[a])\n",
    "            self.y_delim.append(self.y_axis[b])\n",
    "        pass\n",
    "\n",
    "    def plot_pred(self, pred):\n",
    "        \n",
    "        X_axis, Y_axis = np.meshgrid(self.x_axis, self.y_axis)\n",
    "        C = np.transpose(pred.reshape((len(self.x_axis), len(self.y_axis))))\n",
    "        plt.pcolor(X_axis, Y_axis, C, norm = self.norm_colors, cmap = 'YlOrRd')\n",
    "        plt.scatter(self.x_delim, self.y_delim, c = 'black', s = 10)\n",
    "        self.plot()\n",
    "        pass\n",
    "\n",
    "    def plot_pred_plan(self):\n",
    "        self.pred = self.predict(self.my_grid)\n",
    "        self.pred_bin = np.sign(self.pred)\n",
    "        self.set_delim()\n",
    "        self.Normalize_Pred()\n",
    "        \n",
    "        plt.figure(figsize=self.figsize)\n",
    "        plt.subplot(1,2,1)\n",
    "        self.plot_pred(self.pred_100)\n",
    "        plt.subplot(1,2,2)\n",
    "        self.plot_pred((self.pred_bin+1)*100)\n",
    "        pass\n",
    "    \n",
    "    \n",
    "    # Skeletons for fit and predict\n",
    "    def fit(self):\n",
    "        pass\n",
    "    \n",
    "    def predict(self):\n",
    "        pass\n",
    "    \n",
    "    # Others methods\n",
    "    def RBF_Kernel(self, X, sigma2, Y = None):\n",
    "        \" Compute the RBF kernel matrix of X\"\n",
    "        from sklearn.metrics.pairwise import euclidean_distances\n",
    "\n",
    "        if type(Y)==type(None):\n",
    "            Y = X\n",
    "\n",
    "        K = euclidean_distances(X,Y, squared=True)\n",
    "        K *= -1./sigma2\n",
    "        K = np.exp(K)\n",
    "        return K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class OkMeans(OCC):\n",
    "    \" Visual Object Recognition through One-Class Learning \\\n",
    "      QingHua Wang, Luís Seabra Lopes, and David M. J. Tax \"\n",
    "    \n",
    "    def fit(self, thresh, k, kernel = False):\n",
    "        from sklearn.cluster import KMeans\n",
    "        \n",
    "        self.thresh = thresh\n",
    "        self.k = k\n",
    "        self.kernel = kernel\n",
    "        if kernel:\n",
    "            K = self.RBF_Kernel(self.X, 1)            \n",
    "        else:\n",
    "            K = self.X\n",
    "\n",
    "        kmeans = KMeans(n_clusters=k).fit(K)\n",
    "        self.centers = kmeans.cluster_centers_\n",
    "        \n",
    "        pass\n",
    "    \n",
    "    def predict(self, newData):\n",
    "        from sklearn.metrics.pairwise import euclidean_distances\n",
    "        if self.kernel:\n",
    "            newData = np.transpose(self.RBF_Kernel(self.X, 1, newData))\n",
    "        D = euclidean_distances(newData, self.centers, squared=True)\n",
    "        D = np.min(D, axis = 1)\n",
    "        pred = -D + self.thresh\n",
    "        return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class OkMeans(OCC):\n",
    "    \" Visual Object Recognition through One-Class Learning \\\n",
    "      QingHua Wang, Luís Seabra Lopes, and David M. J. Tax \"\n",
    "    \n",
    "    def fit(self, thresh, k, kernel = False):\n",
    "        from sklearn.cluster import KMeans\n",
    "        \n",
    "        self.thresh = thresh\n",
    "        self.k = k\n",
    "        self.kernel = kernel\n",
    "        if kernel:\n",
    "            K = self.RBF_Kernel(self.X, 1)            \n",
    "        else:\n",
    "            K = self.X\n",
    "\n",
    "        kmeans = KMeans(n_clusters=k).fit(K)\n",
    "        self.centers = kmeans.cluster_centers_\n",
    "        \n",
    "        pass\n",
    "    \n",
    "    def predict(self, newData):\n",
    "        from sklearn.metrics.pairwise import euclidean_distances\n",
    "        if self.kernel:\n",
    "            newData = np.transpose(self.RBF_Kernel(self.X, 1, newData))\n",
    "        D = euclidean_distances(newData, self.centers, squared=True)\n",
    "        D = np.min(D, axis = 1)\n",
    "        pred = -D + self.thresh\n",
    "        return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pOZ/3JaSR2bynwEXuAvnnS89Je5wT7k/CeJlwrxmZcJ+5DWMT7hXnFKivQ7gU9y9TDNzf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\nQRAEQRAKyP8D/kCVDTsTHj0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ad4feb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans = OkMeans(X2)\n",
    "\n",
    "kmeans.fit(0.3,k=1)\n",
    "\n",
    "pred = kmeans.predict(X2)\n",
    "\n",
    "kmeans.plot_pred_plan()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Application to real data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Thyroid data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "http://odds.cs.stonybrook.edu/thyroid-disease-dataset/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "share of outliers on test set: 0.01678445229681979\n"
     ]
    }
   ],
   "source": [
    "from scipy.io import loadmat\n",
    "x = loadmat('thyroid.mat')\n",
    "X=x['X']\n",
    "y=x['y'].flatten()\n",
    "y[y==1]=-1\n",
    "y[y==0]=1\n",
    "\n",
    "#normalize the data\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "X = StandardScaler().fit_transform(X)\n",
    "\n",
    "#split the data into train/test\n",
    "ind = np.random.choice(np.arange(0,len(X)),int(len(X)*0.7),replace=False)\n",
    "ind_test = np.setdiff1d(np.arange(0,len(X)),ind)\n",
    "#separate the data in train and test\n",
    "X_test,y_test=X[ind_test,:],y[ind_test]\n",
    "X_train,y_train=X[ind,:],y[ind]\n",
    "\n",
    "print(\"share of outliers on test set:\",len(y_test[y_test==-1])/len(y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### OSVM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cross_val_OSVM(list_sigma2,list_nu,X_train=X_train,X_test=X_test,y_train=y_train,y_test=y_test):\n",
    "    list_param = []\n",
    "    for sigma in list_sigma2:\n",
    "        for nu in list_nu:\n",
    "            list_param.append((sigma,nu))\n",
    "    false_pos = []\n",
    "    for sigma2_val,nu_val in list_param:\n",
    "        kernel = ['RBF',sigma2_val]\n",
    "        alpha, rho = fit(X_train, nu_val, kernel)\n",
    "        y_pred = np.sign(predict(X_train, X_test, alpha, rho, kernel)).flatten()\n",
    "        conf = confusion_matrix(y_test,y_pred)\n",
    "        #minimize false negatives ?\n",
    "        print(\"sigma2: \",sigma2_val,\"nu: \",nu_val,\"false pos\",np.round(conf[1][0]/np.sum(conf[0][0]+conf[1][0]),2) )\n",
    "        false_pos.append( np.round(conf[0][1]/np.sum(conf[0][1]+conf[0][0]),2) )\n",
    "    i_best = np.argmin(false_pos)\n",
    "    best_param = list_param[i_best]\n",
    "    sigma2_best, nu_best = [ best_param[0], best_param[1] ]\n",
    "    return( sigma2_best, nu_best )"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "list_sigma2 = [10,25]\n",
    "list_nu = [0.01,0.02]\n",
    "sigma2_best, nu_best = cross_val_OSVM(list_sigma2,list_nu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### RBF $\\nu$ = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nu_best = 0.1\n",
    "sigma2_best = 10\n",
    "kernel = ['RBF',sigma2_best]\n",
    "#kernel = ['Poly',3,1]\n",
    "alpha, rho = fit(X_train, nu_best, kernel)\n",
    "y_pred_base = predict(X_train, X_test, alpha, rho, kernel).flatten()\n",
    "y_pred = np.sign(y_pred_base)\n",
    "y_pred_train_base = predict(X_train, X_train, alpha, rho, kernel).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  13    6]\n",
      " [  62 1051]]\n",
      "             precision    recall  f1-score   support\n",
      "\n",
      "       -1.0       0.17      0.68      0.28        19\n",
      "        1.0       0.99      0.94      0.97      1113\n",
      "\n",
      "avg / total       0.98      0.94      0.96      1132\n",
      "\n",
      "false positive rate: 0.316\n",
      "true pos rate: 0.944\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix, classification_report\n",
    "conf = confusion_matrix(y_test,y_pred)\n",
    "print(conf)\n",
    "print(classification_report(y_test,y_pred))\n",
    "print(\"false positive rate:\",np.round(conf[0][1]/(conf[0][1]+conf[0][0]),3))\n",
    "print(\"true pos rate:\",np.round(conf[1][1]/(conf[1][0]+conf[1][1]),3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### RBF $\\nu$ = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nu_best = 0.5\n",
    "sigma2_best = 10\n",
    "kernel = ['RBF',sigma2_best]\n",
    "alpha_2, rho_2 = fit(X_train, nu_best, kernel)\n",
    "y_pred_base_2 = predict(X_train, X_test, alpha_2, rho_2, kernel).flatten()\n",
    "y_pred_2 = np.sign(y_pred_base_2)\n",
    "y_pred_train_base2 = predict(X_train, X_train, alpha_2, rho_2, kernel).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 19   0]\n",
      " [380 733]]\n",
      "             precision    recall  f1-score   support\n",
      "\n",
      "       -1.0       0.05      1.00      0.09        19\n",
      "        1.0       1.00      0.66      0.79      1113\n",
      "\n",
      "avg / total       0.98      0.66      0.78      1132\n",
      "\n",
      "false positive rate: 0.0\n",
      "true pos rate: 0.659\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix, classification_report\n",
    "conf = confusion_matrix(y_test,y_pred_2)\n",
    "print(conf)\n",
    "print(classification_report(y_test,y_pred_2))\n",
    "print(\"false positive rate:\",np.round(conf[0][1]/(conf[0][1]+conf[0][0]),3))\n",
    "print(\"true pos rate:\",np.round(conf[1][1]/(conf[1][0]+conf[1][1]),3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kmeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#cross validation\n",
    "def cross_val_kmeans(X_train,X_test,y_test):\n",
    "    thres_list = np.arange(10,50,1)\n",
    "    false_pos = []\n",
    "    for thres in thres_list:\n",
    "        kmeans = OkMeans(X_train)\n",
    "        kmeans.fit(thres,k=1,kernel=True)\n",
    "        y_pred_base = kmeans.predict(X_test)\n",
    "        y_pred = np.sign(y_pred_base)\n",
    "        conf = confusion_matrix(y_test,y_pred)\n",
    "        false_pos.append( np.round(conf[0][1]/(conf[0][0]+conf[0][1]),2) )\n",
    "    i_best = np.argmin(false_pos)\n",
    "    return thres_list[i_best]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "thres_val = cross_val_kmeans(X_train,X_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "kmeans = OkMeans(X_train)\n",
    "kmeans.fit(thres_val,k=1,kernel=True)\n",
    "y_pred_base_km = kmeans.predict(X_test)\n",
    "y_pred_km = np.sign(y_pred_base_km)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    }
   ],
   "source": [
    "print(thres_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  19    0]\n",
      " [1113    0]]\n",
      "             precision    recall  f1-score   support\n",
      "\n",
      "       -1.0       0.02      1.00      0.03        19\n",
      "        1.0       0.00      0.00      0.00      1113\n",
      "\n",
      "avg / total       0.00      0.02      0.00      1132\n",
      "\n",
      "false positive rate: 0.0\n",
      "true pos rate: 0.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/antoinegrelety/anaconda3/lib/python3.6/site-packages/sklearn/metrics/classification.py:1113: UndefinedMetricWarning: Precision and F-score are ill-defined and being set to 0.0 in labels with no predicted samples.\n",
      "  'precision', 'predicted', average, warn_for)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix, classification_report\n",
    "conf = confusion_matrix(y_test,y_pred_km)\n",
    "print(conf)\n",
    "print(classification_report(y_test,y_pred_km))\n",
    "print(\"false positive rate:\",np.round(conf[0,1]/np.sum(conf[0][0]+conf[0][1]),4))\n",
    "print(\"true pos rate:\",np.round(conf[1][1]/np.sum(conf[1][0]+conf[1][1]),4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Densité des valeurs de sortie"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
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5+L5vlwKvmNmgDKspxPdPnVjWgWH5Dmgfxm2F73v6H865kpB0D3z/uuncj+/L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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d9cf668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.distributions.empirical_distribution import ECDF\n",
    "\n",
    "plt.figure(figsize=(18,8))\n",
    "\n",
    "cdf_1 = ECDF(y_pred_base)\n",
    "cdf_2 = ECDF(y_pred_base_2)\n",
    "cdf_3 = ECDF(y_pred_base_km)\n",
    "\n",
    "plt.subplot(121)\n",
    "support = np.arange(-0.05,0.15,0.01)\n",
    "plt.plot(support,cdf_1(support))\n",
    "plt.plot(support,cdf_2(support))\n",
    "plt.axvline(0,color='red',linestyle='--')\n",
    "plt.legend([r'CDF $\\nu = 0.1$',r'CDF $\\nu = 0.5$'])\n",
    "plt.title('OSVM: fonctions de répartition empirique'+'\\n' + r'de $w^T\\phi(x)-\\rho$',fontsize=16)\n",
    "\n",
    "plt.subplot(122)\n",
    "support_km = np.arange(-3,15,0.01)\n",
    "plt.plot(support_km,cdf_3(support_km))\n",
    "plt.axvline(0,color='red',linestyle='--')\n",
    "plt.legend(['CDF OkMeans'])\n",
    "plt.title(r'OkMeans: fonction de répartition empirique'+'\\n'+ 'des distances au plus proche centre',fontsize=16)\n",
    "\n",
    "plt.savefig('cdf_plot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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taT/YhtpE3+NRHjNJI7bQbUJVvbvn4feS/Bz4RpJ7VtVE7xLbhImVzKxN+Ava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\nAAAAEyMhBAAAADAx/x8R1ZOtxY30SAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11451d128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,7))\n",
    "\n",
    "plt.subplot(131)\n",
    "plt.hist(y_pred_base,bins=40,fill=True,edgecolor='white',density=True)\n",
    "plt.title(\"Densité des valeurs de sortie \"+r'$\\nu$='+str(0.1) +'\\n'+ r' $\\rho$='+str(np.round(rho[0],2))+\"\\n\"+\\\n",
    "         \"SV: \"+str(np.round(len(alpha[alpha>10**(-6)])/len(alpha)*100)) + \"%, \"+\n",
    "          \" OL: \"+str(np.round(len(y_pred[y_pred==-1])/len(y_pred)*100))+\"%\",size=14)\n",
    "plt.xlim(-0.1,0.15)\n",
    "\n",
    "plt.subplot(132)\n",
    "plt.hist(y_pred_base_2,bins=60,fill=True,edgecolor='white',density=True)\n",
    "plt.title(\"Densité des valeurs de sortie \"+r'$\\nu$='+str(0.5) +'\\n'+ r' $\\rho$='+str(np.round(rho_2[0],2))+\"\\n\"+\\\n",
    "         \"SV: \"+str(np.round(len(alpha_2[alpha_2>10**(-6)])/len(alpha_2)*100)) + \"%, \"+\n",
    "          \" OL: \"+str(np.round(len(y_pred_2[y_pred_2==-1])/len(y_pred_2)*100))+\"%\",size=14)\n",
    "plt.xlim(-0.1,5)\n",
    "\n",
    "plt.subplot(133)\n",
    "plt.hist(y_pred_base_km,bins=400,edgecolor='white')\n",
    "plt.xlim(-1,30)\n",
    "plt.title(\"Densité des valeurs de sortie Kmeans \\n \\n\" ,size=14)\n",
    "plt.savefig('densite_OSVM_KMeans')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Letter recognition dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "data source: http://odds.cs.stonybrook.edu/letter-recognition-dataset/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.io import loadmat\n",
    "x = loadmat('letter.mat')\n",
    "X=x['X']\n",
    "y=x['y'].flatten()\n",
    "y=y.astype(float)\n",
    "X=X.astype(int)\n",
    "y[y==1]=-1\n",
    "y[y==0]=1\n",
    "#split the data into train/test\n",
    "ind = np.random.choice(np.arange(0,len(X)),int(len(X)*0.7),replace=False)\n",
    "ind_test = np.setdiff1d(np.arange(0,len(X)),ind)\n",
    "#separate the data in train and test\n",
    "X_test,y_test=X[ind_test,:],y[ind_test]\n",
    "X_train,y_train=X[ind,:],y[ind]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### OSVM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nu=0.05\n",
    "sigma2=0.5*256\n",
    "kernel = ['RBF',sigma2]\n",
    "alpha, rho = fit(X_train, nu, kernel)\n",
    "y_pred = np.sign(predict(X_train, X_test, alpha, rho, kernel)).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 11  15]\n",
      " [ 50 404]]\n",
      "             precision    recall  f1-score   support\n",
      "\n",
      "       -1.0       0.18      0.42      0.25        26\n",
      "        1.0       0.96      0.89      0.93       454\n",
      "\n",
      "avg / total       0.92      0.86      0.89       480\n",
      "\n",
      "false positive rate: 0.82\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix, classification_report\n",
    "conf=confusion_matrix(y_test,y_pred)\n",
    "print(conf)\n",
    "print(classification_report(y_test,y_pred))\n",
    "print(\"false positive rate:\",np.round(conf[1,0]/np.sum(conf[0][0]+conf[1][0]),2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nu_list = list(np.arange(0.05,0.15,0.01))+[0.30,0.40,0.50]\n",
    "nu_list = [np.round(n,2) for n in nu_list]\n",
    "OL_list, SV_list = OL_SV(nu_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NGzbou+++03PPPVfGI0V5ULlyZaWkpCg9PV1JSUnatm1bwPq5c+dq2LBhSk9P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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11aced780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,10))\n",
    "table = plt.table(cellText=data,colLabels=[r'$\\nu$','Fraction OLs (%)','Fraction SVs (%)'],loc='top')\n",
    "plt.axis('off')\n",
    "plt.grid('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import f1_score\n",
    "\n",
    "def cross_val(list_sigma2,list_nu,X_train,X_test):\n",
    "    t=0\n",
    "    list_score = []\n",
    "    for nu_val in list_nu:\n",
    "        for sigma2_val in list_sigma2:\n",
    "            kernel = ['RBF',sigma2_val]\n",
    "            alpha, rho = fit(X_train, nu_val, kernel)\n",
    "            y_pred = np.sign(predict(X_train, X_test, alpha, rho, kernel)).flatten()\n",
    "            #minimize false negatives ?\n",
    "            list_score.append([nu_val,sigma2_val,f1_score(y_test,y_pred)] )\n",
    "            t=t+1\n",
    "        print(100*t/(len(list_nu)*len(list_sigma2)))\n",
    "    return(list_score)\n",
    "\n",
    "def best_score(list_score):\n",
    "    scores = [n[2] for n in list_score]\n",
    "    index = np.argmax(scores)\n",
    "    return(list_score[index][0:2])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-44-790696969c95>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mlist_sigma2\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m30\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mlist_score\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcross_val\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlist_nu\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlist_sigma2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mX_train\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mX_test\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m \u001b[0mnu_best\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msigma2_best\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbest_score\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlist_score\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-43-a3de677bfe3f>\u001b[0m in \u001b[0;36mcross_val\u001b[0;34m(list_sigma2, list_nu, X_train, X_test)\u001b[0m\n\u001b[1;32m      7\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0msigma2_val\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mlist_sigma2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m             \u001b[0mkernel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m'RBF'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0msigma2_val\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m             \u001b[0malpha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrho\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnu_val\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkernel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m             \u001b[0my_pred\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msign\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX_test\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0malpha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrho\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkernel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mflatten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m             \u001b[0;31m#minimize false negatives ?\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-7-6259e1f5f3c4>\u001b[0m in \u001b[0;36mfit\u001b[0;34m(X, nu, kernel)\u001b[0m\n\u001b[1;32m     17\u001b[0m     \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'd'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 19\u001b[0;31m     \u001b[0msol\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msolvers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mqp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mG\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     20\u001b[0m     \u001b[0malpha\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msol\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'x'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m     \u001b[0mix_in\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwhere\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malpha\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1e-5\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m&\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0malpha\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m1.\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnu\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/cvxopt/coneprog.py\u001b[0m in \u001b[0;36mqp\u001b[0;34m(P, q, G, h, A, b, solver, kktsolver, initvals, **kwargs)\u001b[0m\n\u001b[1;32m   4485\u001b[0m             'residual as dual infeasibility certificate': dinfres}\n\u001b[1;32m   4486\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 4487\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mconeqp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mG\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m  \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minitvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkktsolver\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkktsolver\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/cvxopt/coneprog.py\u001b[0m in \u001b[0;36mconeqp\u001b[0;34m(P, q, G, h, dims, A, b, initvals, kktsolver, xnewcopy, xdot, xaxpy, xscal, ynewcopy, ydot, yaxpy, yscal, **kwargs)\u001b[0m\n\u001b[1;32m   2254\u001b[0m         \u001b[0;31m# On exit, they contain ux, uy, uz.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2255\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2256\u001b[0;31m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mf3\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkktsolver\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mW\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2257\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mArithmeticError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2258\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0miters\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/cvxopt/coneprog.py\u001b[0m in \u001b[0;36mkktsolver\u001b[0;34m(W)\u001b[0m\n\u001b[1;32m   1979\u001b[0m              \u001b[0mfactor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmisc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkkt_chol2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mG\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdims\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1980\u001b[0m          \u001b[0;32mdef\u001b[0m \u001b[0mkktsolver\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mW\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1981\u001b[0;31m              \u001b[0;32mreturn\u001b[0m \u001b[0mfactor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mW\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mP\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1982\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1983\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mxnewcopy\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mxnewcopy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmatrix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/cvxopt/misc.py\u001b[0m in \u001b[0;36mfactor\u001b[0;34m(W, H, Df)\u001b[0m\n\u001b[1;32m   1449\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1450\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1451\u001b[0;31m             \u001b[0mbase\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msyrk\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mF\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'Gs'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mF\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'S'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtrans\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'T'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpartial\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1452\u001b[0m             if mnl: base.syrk(F['Dfs'], F['S'], trans = 'T', beta = 1.0, \n\u001b[1;32m   1453\u001b[0m                 partial = True)\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "#cross validation\n",
    "list_nu=np.arange(0.1,0.8,0.1)\n",
    "list_sigma2=np.arange(30,100,10)\n",
    "\n",
    "list_score = cross_val(list_nu,list_sigma2,X_train,X_test)\n",
    "nu_best, sigma2_best = best_score(list_score)\n",
    "kernel = ['RBF',sigma2_best]\n",
    "\n",
    "#final model\n",
    "alpha, rho = fit(X_train, nu_best, kernel)\n",
    "y_pred = np.sign(predict(X_train, X_test, alpha, rho, kernel)).flatten()\n",
    "\n",
    "nu_best =0.1\n",
    "sigma2_best = 90\n",
    "\n",
    "from sklearn.metrics import confusion_matrix, classification_report\n",
    "print(confusion_matrix(y_test,y_pred))\n",
    "print(classification_report(y_test,y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### KMEANS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "kmeans = OkMeans(X_train)\n",
    "kmeans.fit(1,k=1)\n",
    "y_pred = kmeans.predict(X_test)\n",
    "y_pred = np.sign(y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 31   0]\n",
      " [449   0]]\n",
      "             precision    recall  f1-score   support\n",
      "\n",
      "       -1.0       0.06      1.00      0.12        31\n",
      "        1.0       0.00      0.00      0.00       449\n",
      "\n",
      "avg / total       0.00      0.06      0.01       480\n",
      "\n",
      "false positive rate: 0.94\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/antoinegrelety/anaconda3/lib/python3.6/site-packages/sklearn/metrics/classification.py:1113: UndefinedMetricWarning: Precision and F-score are ill-defined and being set to 0.0 in labels with no predicted samples.\n",
      "  'precision', 'predicted', average, warn_for)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix, classification_report\n",
    "conf = confusion_matrix(y_test,y_pred)\n",
    "print(conf)\n",
    "print(classification_report(y_test,y_pred))\n",
    "print(\"false positive rate:\",np.round(conf[1,0]/np.sum(conf[0][0]+conf[1][0]),2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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