{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.spatial.distance as distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Create a function to compute f from the sheet, the kernel is by default the canonic scalar product.\n",
    "def f (z, beta, x, y, kernel = np.inner):\n",
    "    r = np.multiply(beta[:-1], y)\n",
    "    s = kernel(z, x)\n",
    "    return np.sum(r * s, axis = -1) + beta[-1]\n",
    "\n",
    "#Create a function for the given feature map in Task 2.6.\n",
    "def phi(x):\n",
    "    return np.column_stack((x[:,0],x[:,1], x[:,0]**2+x[:,1]**2))\n",
    "\n",
    "#The identity function, which we use as default feature map.\n",
    "def id(x):\n",
    "    return x\n",
    "#Task 2.1\n",
    "#OneStep algorithm from the sheet, with the possibility to pass a kernel, by default it's the canonic scalar product.\n",
    "#There is not much to explain here since the algorithm is given on the sheet.\n",
    "def OneStep (i, j, beta, x, y, C, kernel = np.inner):\n",
    "    delta = y[i]*(( f(x[j], beta, x, y, kernel) - y[j] ) - ( f(x[i], beta, x, y, kernel) - y[i] ))\n",
    "    s = y[i]*y[j]\n",
    "    chi = kernel(x[i],x[i]) + kernel(x[j],x[j]) - 2*kernel(x[i],x[j])\n",
    "    gamma = s*beta[i] + beta[j]\n",
    "    if s==1:\n",
    "        L = np.maximum(0, gamma - C)\n",
    "        H = np.minimum(gamma, C)\n",
    "    else:\n",
    "        L = np.maximum(0, -gamma)\n",
    "        H = np.minimum(C, C-gamma)\n",
    "    \n",
    "    if chi > 0:\n",
    "        beta[i] = np.minimum( np.maximum( beta[i] + delta/2, L ), H)\n",
    "    elif delta > 0:\n",
    "        beta[i] = L\n",
    "    else:\n",
    "        beta[i] = H\n",
    "        \n",
    "    beta[j] = gamma - s*beta[i]\n",
    "    beta[-1] = beta[-1] - ( f(x[i], beta, x, y, kernel) - y[i] + f(x[j], beta, x, y, kernel) - y[j] )\n",
    "    return beta\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Task 2.2\n",
    "x22 = np.array([np.random.exponential(1/4, 40), np.random.exponential(2, 40)]) #Here we generate an array of 80 exponential distributed values (first 40 with scale parameter 4 and the rest with scale parameter 1/2). \n",
    "x22 = x22.reshape(40,2) #Here we reshape x22 to an 2x40 matrix so the first 20 tuples have scale parameter 4 and the last 20 have scale parameter 1/2.\n",
    "y22 = np.array([-np.ones(20), np.ones(20)]).flatten() #Create an array to label x22."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Task 2.3\n",
    "#SMO algorithm with kernel argument, so we can later pass the gaussian kernel.\n",
    "def SMO (x, y, C, k, kernel = np.inner):\n",
    "    beta = np.zeros(len(y)+1) #create an array to save the beta in the first len(y) entries, in the last entry we save b.\n",
    "    for l in np.arange(k):\n",
    "        ind = np.random.choice(len(y), 2, replace = False) #Find randomly two indices from 0 to len(y) - 1.\n",
    "        beta = OneStep(ind[0], ind[1], beta, x, y, C, kernel) #Run OneStep and save the output in beta.\n",
    "    support = beta[:-1] > 0 #Check at which position beta is bigger than 0, so we know which vector is a support vector.\n",
    "    supp_num = support.sum() #Save the number of support vectors.\n",
    "    med = np.median(f(x[support], beta, x, y, kernel) - y[support])#calculate the median of f(x_i) - y_i\n",
    "    beta[-1] = beta[-1] - med #Change b \n",
    "    return beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#LLS algorithm from the last sheet\n",
    "def LLS (xtrain, ytrain): \n",
    "    z = np.insert(xtrain, 0, 1, axis=1)\n",
    "    M = np.matmul( z.T, z )\n",
    "    b = np.matmul( z.T, ytrain )\n",
    "    return np.linalg.solve(M, b)\n",
    "\n",
    "#Contour function for LLS from the last sheet\n",
    "def contour_LLS (x, y, alpha):\n",
    "# generating a grid for the contourplot\n",
    "    samplenum = 400\n",
    "    xmax = np.ceil(np.amax(x[:,0]))\n",
    "    xmin = np.floor(np.amin(x[:,0]))\n",
    "    ymax = np.ceil(np.amax(x[:,1]))\n",
    "    ymin = np.floor(np.amin(x[:,1]))\n",
    "    plt.xlim(xmin, xmax)\n",
    "    plt.ylim(ymin, ymax)\n",
    "    xrange = np.arange(xmin, xmax+(xmax-xmin)/samplenum, (xmax-xmin)/samplenum)\n",
    "    yrange = np.arange(ymin, ymax+(ymax-ymin)/samplenum, (ymax-ymin)/samplenum)\n",
    "    X, Y = np.meshgrid(xrange, yrange)\n",
    "\n",
    "# evaluating classifier f at the points of the grid and drawing the contours of the two classes\n",
    "    arg = np.array([X.flatten(),Y.flatten()]).T\n",
    "    Z = alpha[0] + np.matmul(alpha[1:], arg.T)\n",
    "    Z = np.where(Z>0, 1, -1)\n",
    "    Z = np.reshape(Z,X.shape)\n",
    "    plt.contourf(X, Y, Z, levels=[-1, 0, 1], colors = ['blue', 'red'], alpha=0.2)\n",
    "\n",
    "# drawing in the data points\n",
    "    plt.scatter(x[y<0, 0], x[y<0, 1], color = 'blue', label = 'Class -1')\n",
    "    plt.scatter(x[y>0, 0], x[y>0, 1], color = 'red', label = 'Class 1')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Contour function, we can use different kernels and we pass the feature function so we can transform the values of the grid\n",
    "def contour_SVM (x, y, beta, xtrain, ytrain, C, feat = id, kernel = np.inner):\n",
    "# generating a grid for the contourplot\n",
    "    samplenum = 400\n",
    "    xmax = np.ceil(np.amax(x[:,0]))\n",
    "    xmin = np.floor(np.amin(x[:,0]))\n",
    "    ymax = np.ceil(np.amax(x[:,1]))\n",
    "    ymin = np.floor(np.amin(x[:,1]))\n",
    "    plt.xlim(xmin, xmax)\n",
    "    plt.ylim(ymin, ymax)\n",
    "    xrange = np.arange(xmin, xmax+(xmax-xmin)/samplenum, (xmax-xmin)/samplenum)\n",
    "    yrange = np.arange(ymin, ymax+(ymax-ymin)/samplenum, (ymax-ymin)/samplenum)\n",
    "    X, Y = np.meshgrid(xrange, yrange)\n",
    "\n",
    "# evaluating classifier f at the points of the grid and drawing the contours of the two classes\n",
    "    arg = np.array([X.flatten(),Y.flatten()]).T\n",
    "    Z = f(feat(arg), beta, xtrain, ytrain, kernel)\n",
    "    Z = np.where(Z>0, 1, -1)\n",
    "    Z = np.reshape(Z,X.shape)\n",
    "    plt.contourf(X, Y, Z, levels=[-1, 0, 1], colors = ['blue', 'red'], alpha=0.2)\n",
    "\n",
    "# drawing in the data points\n",
    "    margin = np.logical_and(C > beta[:-1], beta[:-1] > 0) #Find all margin verctors.\n",
    "    support = np.logical_and(beta[:-1] > 0, beta[:-1] >= C) #Find all support vectors, that aren't margin vectros.\n",
    "    minus = y < 0\n",
    "    plus =  y > 0\n",
    "    print('# Support Vectors = {}, \\n# Margin Vectors = {}'.format(support.sum() + margin.sum(), margin.sum()))\n",
    "    plt.scatter(x[minus, 0], x[minus, 1], color = 'blue', label = 'Class -1')\n",
    "    plt.scatter(x[plus, 0], x[plus, 1], color = 'red', label = 'Class 1')\n",
    "    plt.scatter(x[support, 0], x[support, 1], alpha = 0.7, color = 'grey', marker = 'D', label = 'Support Vectors')\n",
    "    plt.scatter(x[margin, 0], x[margin, 1], alpha = 0.7, color = 'black', marker = 'x', label = 'Margin Vectors')\n",
    "    plt.title('C = {}'.format(C))\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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XbhcJWORAd/dX3f3JzNd/AzqAOXF1bLQ5bS1U9vWOaKvs62VOW0vO761QD0xPT3btIoGI\npYZuZvXA8cBjY3xvtZltMLMNu3btjHyOGT3bsmrPlkI9IDU12bWLBCLnQDez9wD3Ap939zdHf9/d\n17p7o7s3VlcfGvk8/TVzs2qPQqEeiOZmqKoa2VZVlW4XCVhOgW5m00mHebu7/ySeLo1te3MrA1Wz\nRrQNVM1ie3NrrOdRqAegqQlaWqC2FszSjy0t6XaRgE2L+kIzM+BWoMPdvx5fl8a2q+kCIF1Ln9Gz\njf6auWxvbn23PU69DUuY1bGRjg5oaIj97aUQmpoU4FJ2zN2jvdDsJGA9sBkYzDRf5+6/GO81CxY0\n+h13bIh0vmKY1bERUKiLSHFZY+NGd2+c7LjII3R3fwiwqK9PgqGRuogUWCqVnmba05O+mN3crN+4\npqBsV4pOVW/DEjo6ClBT18pGkTQtDItMgT4Feb9Qqh9gkWFaGBaZAn2KhkI9L/QDLDJMC8MiU6Bn\nIW/lF/0AiwzTwrDISibQ4954K1/yUn7RD7DIMC0Mi6wkAj1fG2/lS+zlF/0AiwzTwrDIIk9bjNNE\nG2/lY+FQXIZG6TnPUx/6QdU0LZE0LQyLpCQCPd8bb+XD0Cg9tnnq+gEem+Yji0xZSZRcCrHxVr4M\nXSiVPNB0TpGslESgF2rjrXxKfKiX4sImTecUyUpJBPqupgvobFnLntp5uBl7aufR2bK2pOvn+0r8\nDo2lOhLWdE6RrJREDR3SoZ6UAB/LcKhvTN5mXhONhItZr66pSf/jMla7iOynJEbooyVlTvp4EjdS\nL9WRsKZzimSl5AI9aXPSR0tk+aVUFzZpPrJIVkou0PN5M+hC6W1YkqzZL6U8Em5qgvvvhyeeSD8q\nzEXGVXKBnsQ56RNJRKhrJCwShMh3LIp0Mmv02toNE64NWbiyngO6O/dr31M7jy33b81vB/NAdz0S\nkVxN9Y5FBR+hTzYjLoQ56ftKXPlFRBKrKCWXvj644YaxQz3pc9InolAXkXwqeMkFhm8SXVUVrVRb\nnWpnTlsLM3q20V8zl+3NrYkIfJVfRCSKki257CvKKu4kT2tM5JRGEUmMos9y6e7ObvuQpE9rVKiL\nSL4UPdAhu+1DQpjWqFAXkXwoiUAfMpUSTJK32t2XQl1E4lZSgQ6Tbx8S0rRGhbqIxKnkAn2y7UNC\nm9aoUBeRuBR12uJoUacxhkBTGkVkPImYtmgGBx2U6UjFcA292PdVKAaN1EUkVwUdoVdUNLr78Ah9\n+nQ45xz46U/hnXfG6JzBAQfAnj3lc39gjdRFZLSSHKGP/rdj7164996xw3zo+L6+0rorWr5ppC4i\nURW85LKKdv5MPQNU8GfqOd+nvsKzXO4PrFAXkSgKGugH8zrfZTX1dFKBU08n32U1q5h6qBf7rmiF\nsl+op1Lp5bTZLKsVkbJS0ECfw3ZmM3LZ/mx6+QpTX7Zf7LuiFdJQqG+/JZWuN3V3l1f9SUSyUtBA\nn0H/mO1z2X/Z/ujSzCraS+auaIXU27CEQ3/clq437SuJ9Sf9liGSVwUN9H5mjNm+jZHL9lfRPmZp\n5qZj2mOb5TJRtpRC7lSn2lm4sp7FSyuY/tfusQ9KUv0pNcZvGddfDzfdVOyeiQQjp0A3s7PM7E9m\n9pKZXTvZ8b3Vc3iLkcv232IW1zFy2f5XaBmzNHPu4y2xhOtY2TJUwZjoe4UyeotgG+/AJNWf2sb4\nLQPgnns0UheJSeRAN7NKoA1oAhYAq8xswUSvmVF7ML/+1FpeqZjHIMZW5nEZa7mLkcv2xyrBABzB\ntliqDGNly1AFY6LvFcpYWwTvJ2n1p4l+m0ha6UikROUyQj8BeMndX3b3fuBu4JzJXjT32gvY8fhW\nntowyLHv3bpfmMP+JZh92+OoMoz3Hj09E3+vUMbbCtgBN6P//bVsvzhheyRM9NtEkkpHIiUs8kpR\nM/sUcJa7X5p5/hngn9z9ylHHrQZWZ54uBLYMf/eQg2HekaPf+2BeZx6dVDD4btsgFXQyj9c5sB+e\n2Ryp0+86ZhFMH6Ogvzdz1Xa870163kOA13LrGxwDi6az/wWHvdD/DOT42XMS+fMdAgfPg/3+rqEk\nPhfE9HdXwvT5km2+ux842UHT8t0Ld18LrAUwsw1TWb6aVPp8yRXyZwN9vqQzs/F3NdxHLiWX7cAR\n+zyvy7SJiEgR5BLoTwBHmdmRZjYDOB/4WTzdEhGRbEUuubj7O2Z2JfAroBK4zd2fneRla6OeLyH0\n+ZIr5M8G+nxJN6XPV9Dtc0VEJH9K7hZ0IiISjQJdRCQQBQn0bLcISBozu83MdpjZlsmPThYzO8LM\nHjCz58zsWTO7qth9ipOZVZnZ42b2dObz3VjsPsXNzCrN7Ckzu7/YfckHM9tqZpvNbNNUp/clhZm9\nz8zuMbPnzazDzJZNeHy+a+iZLQJeAM4AukjPjlnl7s/l9cQFZGanAH8HfuDuC4vdnziZ2eHA4e7+\npJkdCGwEzg3l78/MDJjt7n83s+nAQ8BV7v5okbsWGzP7AtAIvNfdVxa7P3Ezs61Ao7sHt7DIzG4H\n1rv7LZnZhLPc/Y3xji/ECD3SFgFJ4u5/BF4vdj/ywd1fdfcnM1//DegA5hS3V/HxtL9nnk7P/BfM\nTAEzqwM+CtxS7L5IdszsIOAU4FYAd++fKMyhMIE+B3hln+ddBBQI5cTM6oHjgceK25N4ZUoSm4Ad\nwG/cPaTP903gGthnH43wOPBbM9uY2WokFEcCO4HvZUpmt5jZ7IleoIuiMiVm9h7gXuDz7v5msfsT\nJ3cfcPfjSK92PsHMgiibmdlKYIe7byx2X/LspMzfXxPQnCmBhmAasBj4trsfD7wFTHgNshCBri0C\nEi5TW74XaHf3nxS7P/mS+XX2AeCsYvclJsuBj2dqzHcDp5rZD4vbpfi5+/bM4w7gPtJl3hB0AV37\n/MZ4D+mAH1chAl1bBCRY5qLhrUCHu3+92P2Jm5kdambvy3w9k/TF++eL26t4uPsX3b3O3etJ/3/3\ne3e/sMjdipWZzc5crCdTjjiTETu6Jpe7dwOvmNn8TNNpwISTEQqx22KULQISxczuAlYAh5hZF3CD\nu99a3F7FZjnwGWBzps4McJ27/6KIfYrT4cDtmdlYFcCP3D3I6X2BqgHuS487mAbc6e6/LG6XYvU5\noD0zGH4ZuGSig7X0X0QkELooKiISCAW6iEggFOgiIoFQoIuIBEKBLiISCAW6iEggFOgiIoH4f/gX\nB+DMm8M/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22bc1359240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Support Vectors = 38, \n",
      "# Margin Vectors = 5\n"
     ]
    },
    {
     "data": {
      "image/png": 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/QNeq9+fROHSllFL+o0PXclFKKdV+NNCVUipIdEigi8hUEflSRApE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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22bc12a0320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Support Vectors = 17, \n",
      "# Margin Vectors = 5\n"
     ]
    },
    {
     "data": {
      "image/png": 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0LREPnRjmk6AEeoVve13OztWraZ+XVxnmFVxlZbTJyyN97156XHgh0TV7sE6j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\nLiLiEAp0ERGHUKCLiDjE/weNYd4f1CKACAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22bc0c2b1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Support Vectors = 18, \n",
      "# Margin Vectors = 15\n"
     ]
    },
    {
     "data": {
      "image/png": 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CitasaRgjdZ00JfINnRgWsqiP0M2M7FWrwO9nAbAg2D7a7w+M2K0BrIzUSVMi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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22bc0c2b2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Run LLS for the created data\n",
    "alpha = LLS(x22, y22)\n",
    "contour_LLS(x22, y22, alpha)\n",
    "\n",
    "#Run SMO with C=0.01 for the created data\n",
    "beta0 = SMO(x22, y22 , 0.01, 10000)\n",
    "contour_SVM(x22, y22, beta0, x22, y22, 0.01)\n",
    "\n",
    "#Run SMO with C=1 for the created data\n",
    "beta1 = SMO(x22, y22 , 1, 10000)\n",
    "contour_SVM(x22, y22, beta1, x22, y22, 1)\n",
    "\n",
    "#Run SMO with C=100 for the created data\n",
    "beta2 = SMO(x22, y22 , 100, 10000)\n",
    "contour_SVM(x22, y22, beta2, x22, y22, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Task 2.4\n",
    "#Create data the same way we did in task 2.2\n",
    "x24 = np.array([np.random.exponential(1/4, 2000), np.random.exponential(2, 2000)])\n",
    "x24 = x24.reshape(2000,2)\n",
    "y24 = np.array([-np.ones(1000), np.ones(1000)]).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy of LLS = 0.832\n",
      "C = 0.01, accuracy of SVM = 0.6565\n",
      "C = 1, accuracy of SVM = 0.9145\n",
      "C = 100, accuracy of SVM = 0.8975\n"
     ]
    }
   ],
   "source": [
    "#Run LLS for data x25 with the alpha computed in task 2.3\n",
    "pred_LLS = alpha[0] + np.matmul(alpha[1:], x24.T)\n",
    "pred_LLS = np.where(pred_LLS > 0, 1, -1) #Classify our prediction data\n",
    "acc_LLS = np.sum(pred_LLS == y24)/2000\n",
    "print('accuracy of LLS =',acc_LLS)\n",
    "\n",
    "#Run SVM for the data x24 with the betas computed in task 2.3\n",
    "pred_SVM0 = f(x24, beta0, x22, y22, np.inner)\n",
    "pred_SVM0 = np.where(pred_SVM0 > 0, 1, -1) #Classify our prediction data\n",
    "acc_SVM0 = np.sum(pred_SVM0 == y24)/2000 #Calculate the accuracy\n",
    "print('C = 0.01, accuracy of SVM =',acc_SVM0)\n",
    "\n",
    "pred_SVM1 = f(x24, beta1, x22, y22, np.inner)\n",
    "pred_SVM1 = np.where(pred_SVM1 > 0, 1, -1)\n",
    "acc_SVM1 = np.sum(pred_SVM1 == y24)/2000\n",
    "print('C = 1, accuracy of SVM =',acc_SVM1)\n",
    "\n",
    "pred_SVM2 = f(x24, beta2, x22, y22, np.inner)\n",
    "pred_SVM2 = np.where(pred_SVM2 > 0, 1, -1)\n",
    "acc_SVM2 = np.sum(pred_SVM2 == y24)/2000\n",
    "print('C = 100, accuracy of SVM =',acc_SVM2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Support Vectors = 100, \n",
      "# Margin Vectors = 55\n"
     ]
    },
    {
     "data": {
      "image/png": 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Fgw/+iEmTLu2y3eFwUFAwElOehVcq1qMkjX4DhpHWv2uJ6OLi2axd+yqdnZ00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\nHASR2wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22bc4c985f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Support Vectors = 12, \n",
      "# Margin Vectors = 11\n"
     ]
    },
    {
     "data": {
      "image/png": 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IigvwhS4e9g8btSNtr77aUFNTim+xmEUxPXqU8Nprlphv3Rr4uq1F9KVRJGBC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\nAI4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22bc4c98630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Task 2.6\n",
    "x26 = np.zeros((100, 2)) #Create an array to save our data points\n",
    "y26 = np.append(-1 * np.ones(50), np.ones(50), 0) #Create an array to classify our data\n",
    "k = 0\n",
    "while k < len(x26):\n",
    "    if k < len(x26) / 2:\n",
    "        temp = np.random.uniform(-1, 1, 2) #Create a two uniformly distributed numbers  in [-1,1)\n",
    "        if np.inner(temp, temp) < 1: #Check if the created vector is in the unit sphere\n",
    "            x26[k] = temp\n",
    "            k += 1\n",
    "    else:\n",
    "        temp = np.random.uniform(-2, 2, 2) #Create two uniformly distributed number in [-2,2)\n",
    "        if 1 < np.inner(temp, temp) < 4: #Check if norm of the vector is  in (1,2)\n",
    "            x26[k] = temp\n",
    "            k += 1\n",
    "#Task 2.6 a.)\n",
    "#Run SMO and plot the scattered data and the hyperplane corresponding to f=0, as seen before\n",
    "beta3 = SMO(x26, y26 , 10, 10000)\n",
    "contour_SVM(x26, y26, beta3, x26, y26, 10)\n",
    "\n",
    "#Task 2.6 b.)\n",
    "x26_transf = phi(x26) #Transform data with given feature function\n",
    "beta4 = SMO(x26_transf, y26, 10, 10000) #Here we just need the transformed training data, so we don't pass the feature function  \n",
    "contour_SVM(x26_transf, y26, beta4, x26_transf, y26, 10, phi) #Here we need to pass the feature function, so we can later transform the grid\n",
    "'''The feature map increases the dimension of the data, therefore the problem is now posed in an higher dimension. This can \n",
    "be an advantage if the data is in the lower dimension not seperable by a hyperplane, in the higher dimensions this could \n",
    "be possible and so we compute a hyperplane in the higher dimension to classify the data. In the example it is obvious that\n",
    "the data is in two dimensions not seperable by an hyperplane, but in three dimensions it is possible and so we get \n",
    "a better classification result'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Support Vectors = 8, \n",
      "# Margin Vectors = 8\n"
     ]
    },
    {
     "data": {
      "image/png": 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CQAw6tG9Pbm4uHdq3T1gUrrjsMj7dto1zhw7l/m99i78uXRrV69atX89f3niDFX/+Mz/8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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22bbe02fda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Task 2.7\n",
    "#gaussian kernel\n",
    "def gaussian_kernel(t, x, sigma = 1):\n",
    "    if t.ndim == 1: #Check if t is a vector\n",
    "        t = np.array([t])\n",
    "    if x.ndim == 1: #Check if x is a vector\n",
    "        x = np.array([x])\n",
    "    M = distance.cdist(t,x) \n",
    "    return np.exp(-np.square(M)/(2*sigma)) #Return the gaussian kernel\n",
    "    \n",
    "#Here we run SMO and plot the scattered data and the hyperplane corresponding to f=0 with the gaussian kernel\n",
    "beta5 = SMO(x26, y26, 10000, 10, gaussian_kernel)\n",
    "contour_SVM(x26, y26, beta5, x26, y26, 10, kernel = gaussian_kernel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy: 0.9376\n",
      "confusion Matrix:\n",
      " [[ 958    0    3    0    0    4    7    2    3    3]\n",
      " [   0 1124    1    2    0    2    4    1    1    0]\n",
      " [  11   19  930   11    5    0    7   21   25    3]\n",
      " [   1    2   14  933    0   23    2   10   16    9]\n",
      " [   2    2    8    1  924    2    9    2    2   30]\n",
      " [   9    1    6   17    2  825   13    5    8    6]\n",
      " [   7    3   11    0    7   21  905    1    3    0]\n",
      " [   0   15   18    4    5    1    1  960    1   23]\n",
      " [   5    5   11   13   10   15    9   13  882   11]\n",
      " [   7    6    4    8   22   10    1   12    4  935]]\n"
     ]
    }
   ],
   "source": [
    "#Task 2.8\n",
    "#This is just the code from the sheet\n",
    "#Load MNIST Data\n",
    "#!pip install urllib3\n",
    "#!python -m pip install --upgrade pip\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.metrics import confusion_matrix\n",
    "import os\n",
    "import gzip\n",
    "from sklearn import svm\n",
    "from urllib.request import urlretrieve\n",
    "def download(filename , source='http://yann.lecun.com/exdb/mnist/'):\n",
    "    print(\"Downloading %s\" % filename)\n",
    "    urlretrieve(source + filename , filename)\n",
    "def load_mnist_images(filename):\n",
    "    if not os.path.exists(filename):\n",
    "        download(filename)\n",
    "    with gzip.open(filename, 'rb') as f:\n",
    "        data = np.frombuffer(f.read(), np.uint8, offset=16)\n",
    "    data = data.reshape(-1, 28, 28)\n",
    "    return data / np.float32(256)\n",
    "def load_mnist_labels(filename):\n",
    "    if not os.path.exists(filename):\n",
    "        download(filename)\n",
    "    with gzip.open(filename, 'rb') as f:\n",
    "        data = np.frombuffer(f.read(), np.uint8, offset=8)\n",
    "    return data\n",
    "\n",
    "X_train = load_mnist_images('train-images-idx3-ubyte.gz')\n",
    "y_train = load_mnist_labels('train-labels-idx1-ubyte.gz')\n",
    "X_test = load_mnist_images('t10k-images-idx3-ubyte.gz')\n",
    "y_test = load_mnist_labels('t10k-labels-idx1-ubyte.gz')\n",
    "\n",
    "#Task 2.8 a.)\n",
    "\n",
    "#At first we create 500 indices without repetition\n",
    "a = np.arange(len(X_train)) #Therefore we create at first an interval from 0 to len(X_train)-1\n",
    "np.random.shuffle(a) #then shuflle it\n",
    "indizes = a[:500] #and then take the first 500 entries\n",
    "\n",
    "#Here we create a dictionary, so GridSearchCV knows for which gamma and C values it has to run SVC \n",
    "tuned_parameter = [{'kernel':['rbf'],'gamma':[0.1,0.01,0.001], 'C':[1, 10, 100]}]\n",
    "clf = GridSearchCV(svm.SVC(), tuned_parameter, cv = 5, iid = False) #Pass which classification Algorithm we want to use (SVC) and for which parameters we want to run it\n",
    "nsamples, nx, ny = X_train[indizes].shape \n",
    "d2_X_train = X_train[indizes].reshape((nsamples,nx*ny)) #Reshape the training data, so it has the right shape for the fit function\n",
    "clf.fit(d2_X_train, y_train[indizes]) #Run the 5-fold crossvalidation with the training data\n",
    "C_best = clf.best_params_['C'] #Return the best choice for C \n",
    "gamma_best = clf.best_params_['gamma'] #Return the best choice for gamma\n",
    "\n",
    "#Task 2.8 b.)\n",
    "#Create again random indices as seen before\n",
    "b = np.arange(len(X_train))\n",
    "np.random.shuffle(b)\n",
    "indizes_b = b[:2000]\n",
    "\n",
    "nsamples, nx, ny = X_train[indizes_b].shape\n",
    "d2_X_train_b = X_train[indizes_b].reshape((nsamples,nx*ny)) #Reshape our training data as seen before\n",
    "\n",
    "clf_2 = svm.SVC(C = C_best, gamma = gamma_best) #Create the classifier\n",
    "clf_2.fit(d2_X_train_b,y_train[indizes_b]) #Give the classifier the training data\n",
    "\n",
    "n_tests, nx, ny = X_test.shape\n",
    "d2_X_test = X_test.reshape((n_tests,nx*ny)) #Reshape our test data\n",
    "\n",
    "y_pred = clf_2.predict(d2_X_test) \n",
    "\n",
    "print('accuracy:', accuracy_score(y_test,y_pred))\n",
    "print('confusion Matrix:\\n', confusion_matrix(y_test,y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
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