hhllcks/supervisedlearninginanutshell.ipynb Secret

## supervisedlearninginanutshell.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Supervised Learning in a nutshell\n",
    "This notebook explains common machine learning algorithms used for [supervised learning](https://en.wikipedia.org/wiki/Supervised_learning). It is the first part of a series on machine learning algorithms. I try to explain them in very short texts to give an overview over the topic. It makes heavy use of the mglearn library that is provided by [Andreas Müller](https://github.com/amueller) over at [GitHub](https://github.com/amueller/introduction_to_ml_with_python). It is part of the great book [Introduction to Machine Learning with Python](http://shop.oreilly.com/product/0636920030515.do).\n",
    "\n",
    "This notebook covers the following algorithms and explains them briefly together with some images.\n",
    "\n",
    "* Linear Models\n",
    "    * Regression\n",
    "    * Classification\n",
    "* k-nearest Neighbors\n",
    "* Decision Trees\n",
    "    * Random Forests\n",
    "* Neural Networks (Deep Learning)\n",
    "    * Multilayer Perceptron"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import mglearn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A linear models tries to fit a linear function to the training data. The prediction is then just the result of this function for the given parameters. It can be compared to fitting a line to the data (in the two dimensional case). In its most basic variant the mean squared error for the training examples is minimized by the function. This is called **linear regression**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Regression with linear models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w[0]: 0.393906  b: -0.031804\n"
     ]
    },
    {
     "data": {
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yiEaPHq20tDRNmzZN+/fv7/Jzc3NT5Xa3/iveybs7vPjiixoxYoRGjx6t2bNn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\nIGMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e027b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.plots.plot_linear_regression_wave()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are also variants in computing the linear function. One is called **Ridge Regression**. Ridge Regression introduces the concept of *regularization*. This aims to avoid [*overfitting*](https://en.wikipedia.org/wiki/Overfitting). A linear model overfits, if the linear function fits to tightly to the training data. This results in a bad performance on the test (or productive) data. Ridge regression introduces the parameter *alpha*. *alpha* controls how much focus is on the performances on the training data vs the test data. Increasing *alpha* forces the algorithm to move the coefficients towards zero. This might help the model [generalize](https://en.wikipedia.org/wiki/Generalization_error). As you can see in the next figure a Ridge Regression model performs worse on the training data (since it tries to avoid overfitting). However it performs much better on the before unseen data of the test set. Notice, that if you have enough training samples (what \"enough\" means varies of course from project to project) the linear models will roughly perform the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PFxYWKlatWuXU6zLYP+POEBMTY9q/f/9Jp52wl6FE0QGNLS1dXl4umTNnTrR9ae277747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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b54af98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.plots.plot_ridge_n_samples()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Classification with linear models\n",
    "Linear Models can be used for classification, too. Usually you compute a *decision boundary* between two classes. Two examples of *Linear Classifiers* are **LinearSVC** (where SVC stands for *Support Vector Classifier*) and **Logistic Regression**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11d338dd8>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bktQiopRghtkUM4ysxkzR1KuqrQAyRCRDVf8bgGW74OljHe1tyOJ1pYiYYTbF\nDCOrMXPlyXYRcQF4GcBmEWmGcRkCsjheV4oIADPMtphhZDVmepquA3ACwAoAzwPwALgmkY1KBqtN\nYU0EXleKCEAaZpgT8gtghpH1jFg0qWo3gEkALlXVjQAeBdCT6IYlUl1dHWZW12Drvibkz1+LSV/5\nNfLnr8XWfU2YWV2Durr0GCPK60oRpV+GOSW/AGYYWc+Ip+dE5DYAtwMoAVAJYAKAH8EYTGk7Ho8H\nCxbVDpvCml1cgeyLlyD7jDlYsKg2LaawVlZWYttTm7FgUS16I1xXyu6vkyiSdMowJ+UXwAwj6zFz\nem4pgLkAOgBAVd8FEHlknoXFewqr1bvJeV0povTJMKflF8AMI2sxc+2511T1AhHZp6qzRCQLwF67\nXrepqLQM+fPXRhxY2HusAd3PrEZ7a3PEfT3++OO448t3o38AGOg5gYwxYzHmzBpk5+Siz/MqV6ol\nR7Hq4pbplGHxzK+6ujrMX7AQA4WnoqftQwyc7EJGngs5Jaci4/iHeGbb08wvcgyz+WVm9tyfRGQ1\ngDEicjmAuwBsj7WBqdLR3obCOExhffzxx3HrHXehYPY1cJ13JbJ8S/t3vfkCOt74PQov/HxadZMT\n2VjaZFi88svj8eCf5i9AzwDgmnQuSj7zlaAM62qtxz/NX4ADb+5nfhEFMHN67usAWgC8BeBLAH4H\n4N8S2ahE8k9hjWSkKawejwd3fPluuL/wLRRfejOyiysgGZnILq5A8SU3Yfz19+L4X36BrMqLuFIt\nUeqlTYbFI78A4Bv/8Z/w9g9g/PxvoPiSm4Zn2PxvwNs/gG/+533xbD6R7YUtmkTkNABQ1QFV/amq\nfl5V5/t+N3fBOguKxxTWdes3YMy5kccVuM67Ar29vVyplkyzw/gSO0nHDIvXFPxf/PJXKJh1VcQM\nK5g5D9ue+WXUbSXncUKGRepp+o3/FxGx1Tcn0gcXjymsm7dsgWvmVRHb4JpxJT7y7OJKtWSKk6aR\nJ1HaZdj1n7suLlPwe3t64JpxZcRtXOd9Gr09tl2ZgZLMKRkWaUyTBPx+ZqIbEi91dXVYsKgWuVVX\nIH/+WhT6ztNv3fciNlXXYNtTm2Oewmp2XMHARx0oLC6N90ukNOO0aeRJlH4Z9rP5+Oo9K/DddWti\nmoKvfb2mLk+i/b3xfGmUppyUYZF6mjTM75YV+MG5Ll4SdJ7edfESuK5ZjQWLanHWWWfFNIXV7LiC\njJwxXKlxA495AAAND0lEQVSWRsQruSdMWmbYd9etx29/9UxMU/BzTsk3lWG5Y/Lj9dIojTkpw8Iu\nOSAi/TCuzyQAxsC4DAF8f6uqjg2301RN1126bDm27muC6+IlYbfpenkTFlZX4OEN62N6nqf3NqLg\n728Mu82xPz6Bj954HocOvGH7ypoSK57TyFPJaksOMMPCu+Gmm7H9fzpQ/A//HHabY394DNeeU4if\nPflE1M9DzpAOGWY2v8L2NKlqpqqOVdUCVc3y/e7/O2zYpNLmLVuQO/2yiNvkVl0e8+Dse1bcjZ6D\nOyKOK+jc+xx+9MgGFkw0Il7JPTGYYeH9x7/fi563X4qYYT2HXsI377XlJENKMidlmJklB2wjWR+c\nf2n/ru1r0PnyRvQea4D296H3WAOO/eExtP7ym3j0Rz/ALbfcEtPzkDPEaxo52V8yM+xX255Gx2+/\njeN/fCIow47/8Ql0/Pbb+NW2p3nQR6Y4KcPSqmhK5gfnX9p/UfWpQeMKllx4Gg699QYLJjKNV3In\nv2Rn2Jv7dqP2/IlBGVZ7/kS8uW83VwMn05yUYWlVNCX7g6usrMTDG9ajvbUZ/f19aG9txsMb1vPo\nDM5YryNeeCV38mOGWQczzDwnZVhaFU1O+uCszCnrdcRL4Onerpc3BZ0q6Xp5E7q2r+GV3B2CGWYN\nzLDRcVKGjXjB3mik8mKXg2ucRFjDhN3OiePxeDCzumbYeh1+3iOH0LV9TVqs1xFvHo8HD37/Ifx8\n8xZ0trehoKgEN9Quxsrly2zxXllt9lwsmGHOxQyLnp0zzGx+pV3RBNj7g7O7ZE2ZJuth0RQ/zLDU\nYYY5k6OLJkqddFivg6LDoonSATPMmWJep4koGk5ar4OI0g8zjCJh0URx5aT1Oogo/TDDKBIWTRRX\nTlqvg4jSDzOMImHRRHHFKdNEZGfMMIokK9UNoPTiX69jwaJa9EaYMs0ZQERkRcwwioQ9TRR3/kvM\nLKyuCLo8w8LqCuzfs4trzBCRpTHDKBwuOUBEccElB4jIrrjkABEREVEcsWgiIiIiMoFFExEREZEJ\nLJqIiIiITEjakgO9vb2or6/HyZMnk/WUUcnLy8PEiRORnZ2d6qYQERGRhSStaKqvr0dBQQEmT54M\nEUnW046KqqK1tRX19fU444wzUt0cIiIispCknZ47efIkSktLLVswAYCIoLS01PK9YURERJR8SR3T\nZLZg8ng8WLpsOYpKy5CRmYmi0jIsXbYcHo8nwS0030YiIiJyFssNBK+rq8PM6hps3deE/PlrMekr\nv0b+/LXYuq8JM6trUFdXF9P+n3/+eUydOhVTpkzB/fffH6dWExERUbqz1LXnPB4PFiyqheua1cid\nMG3w9uziCmRfvATZZ8zBgkW12L9nV1TX/env78fSpUuxY8cOTJw4ETU1Nbj22mtxzjnnxPNlEBER\nURqyVE/TuvUbkFt1RVDBFCh3wjTkTr8cD37/oaj2//rrr2PKlCk488wzkZOTg4ULF+K3v/1tLE0m\nIiIih7BU0bR5yxbkTr8s4ja5VZfj55u3RLX/I0eOYNKkSYN/T5w4EUeOHIlqX0REROQsliqaOtrb\nkFU4PuI2WWPL0NnelqQWERERERksVTSNLSpB3/HmiNv0dbSgoKgkqv1PmDABH3zwweDf9fX1mDBh\nQlT7IiIiImexVNFUu3gxvAdfjLiN98AO3FC7OKr919TU4N1338Xhw4fR09ODp59+Gtdee21U+yIi\nIiJnsVTRdM+Ku+E98AK8Rw6FvN975BC8B3dg5fJlUe0/KysLDz/8MK688kpMmzYNCxYswPTp02Np\nctpI5dpYVsb3hcj6+D0Nje9L/Imqxn2nc+bM0d27dwfddujQIUybFnpWXKC6ujosWFSL3OmXI7fq\ncmSNLUNfRwu8B3bAe3AHtj21GfPmzYt7m6Npa7oYfM+rrkDu9MuQVTgefceb4T34IrwHXkjKe25F\nfF9GR0T2qOqcVLcjHkJlGFkTv6eh8X0ZHbP5ZbmiCTCq4we//xB+vnkLOtvbUFBUghtqF2Pl8mVR\nrc80WulWNHk8HqxbvwGbt2xBR3sbxhaVoHbxYtyz4m4AwMzqmmFrY/l5jxxC1/Y1Ua+NZVcej4fv\nyyixaKJECZdh13/uOlz3T/P5PR2C+TV6ZvPLUqfn/CorK/HwhvVob21Gf38f2lub8fCG9fxwozDS\nCuvLV96T0LWx7CrRa4YRkTmRMuzTV18LmXAuv6dDML8Sx5JFE8VH4ArrrouXILu4ApKRieziCrgu\nXgLXNavxu+d/j8xJMyLuJ5a1sewq0WuGEdHIRsqw0uu/ie739qH3WEPYfTjxe8r8ShwWTWnMzNGG\na+Y8fPTuaxH348S1sbhmGFHqmcqw865E597nwu7Did9T5lfisGhKY2aONgpmfQbdh/4UcZtY1say\nq0SvGUZEIzOTYa7zroyYYU78njK/EsfSRVNDQwM+/alL0NjYmOqm2JLZo42BjzojbhPL2lh2leg1\nw4hoZKYz7ERH2Pud+D1lfiWOpYumB9bch9f/vBMPrLkvLvu75ZZbMH78eFRVVcVlf1Zn9mhDsrIT\ntjaWXSV6zTAiGpnZDMvIc4W8z6nfU+ZX4li2aGpoaMDGjU/ipSV52Ljxibj0Nt188814/vnn49A6\nezB7tPGZq+aha/sadL28Cb3HGqD9feg91oCulzeha/sabHtqs+NmLlZWVmLbU5v5vhClkJkM++it\n3yNT+/k9DcD8ShzLFk0PrLkPN83IxKyKTNx4bmZceps++clPoqQkdedwk706q9mjjfXf+z/Yv2cX\nFlZXoPuZ1ahfdz26n1mNhdUV2L9nl2MXQJs3bx7fF6IAVsyw3rdfwvP/9Sy/p0MwvxLDkotbNjQ0\nYPrUShy8LRMVBRlo6BxA1aP9OPjOeygvL4+pbe+//z6uvvpqHDhwIOw2iVjcMlWrs1phhXVyBi5u\nmd6YYZTObL24pb+XqaLAaF5FQUbceptSwcx6SQsW1SbkaI1HG0QUK2YYkcFyRZN/LNOqC4JvX3UB\n4ja2KdlSvTorV1gnolgww4gMliuahvYy+dm5t4mrsxKRnTHDiAyWKprC9TL5xdrbtGjRIlx00UV4\n5513MHHiRDz22GMxtNY8rs5KRHbGDCMyZKW6AYHC9TL5Gb1NxnbrNjwy6v0/9dRTsTYxKv61RrKL\nK8Juw9VZiciqmGFEBksVTbte+zN27urC+p2Rt5vb82pyGhQntYsXY+u+F5F98ZKw23B1ViKyKmYY\nkcFSRdMrr+9LdRMS4p4Vd2NTdQ2yz5gTciDl4Oqsm3aloHVERJExw4gMliqa0pV/ddYFi2rRG2Gt\nEc4EISIrYoYRGZI6EDwRC2nGW6LayLVGiMjOmGFESVwR/PDhwygoKEBpaSlEJO7PGQ+qitbWVnR2\nduKMM85IdXOIbIUrghORXZnNr6Sdnps4cSLq6+vR0tKSrKeMSl5eHiZOnJjqZhAREZHFJK1oys7O\nZu8NERER2ZalFrckIiIisioWTUREREQmsGgiIiIiMiEhs+dEpAXA3+K+YyKystNVtSzVjYgHZhiR\n45jKr4QUTURERETphqfniIiIiExg0URERERkAosmBxKRfhHZH/AzOYp9FInIXfFv3eD+RUQ2iMhf\nReRNEZmdqOciIvtgflEq8YK9zvSRqs6McR9FAO4C8IPRPEhEMlW138Sm8wB8wvdzAYAf+v5LRM7G\n/KKUYU8TATDCQES+KyK7fEdGX/Ld7hKRl0Rkr4i8JSLX+R5yP4BK35Hed0XkUhF5LmB/D4vIzb7f\n3xeR74jIXgCfF5FKEXleRPaIyMsicnaIJl0HYJMa/gKgSEQqEvomEJEtMb8oWdjT5ExjRGS/7/fD\nqvo5AP8M4Liq1ohILoCdIvICgA8AfE5VO0RkHIC/iMizAL4OoMp/xCcil47wnK2qOtu37UsA7lDV\nd0XkAhhHe/84ZPsJvuf2q/fd1hDlayai9MD8opRh0eRMobq3rwAwQ0Tm+/4uhNG1XA9gjYh8EsAA\njC++O4rn3AoYR34A/g7AL0TEf19uFPsjImdiflHKsGgiPwGwTFV/H3Sj0UVdBqBaVXtF5H0AeSEe\n34fg071Dt+n2/TcDQLuJMQlHAEwK+Hui7zYioqGYX5QUHNNEfr8HcKeIZAOAiJwlIvkwjtiafYHz\nDwBO923fCaAg4PF/A3COiOSKSBGAT4V6ElXtAHBYRD7vex4RkfNCbPosgBt9918Io+udXdtEFArz\ni5KCPU3k9yiAyQD2itHv3ALgswA2A9guIm8B2A3gfwBAVVtFZKeIHABQp6pfFZFtAA4AOAxgX4Tn\nqgXwQxH5NwDZAJ4G8MaQbX4H4CoAfwVwAsAX4/IqiSgdMb8oKXgZFSIiIiITeHqOiIiIyAQWTURE\nREQmsGgiIiIiMoFFExEREZEJLJqIiIiITGDRRERERGQCiyYiIiIiE1g0EREREZnw/wFYo8lEmB/J\nbQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d3380f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.svm import LinearSVC\n",
    "\n",
    "X,y = mglearn.datasets.make_forge()\n",
    "fig, axes = plt.subplots(1,2,figsize=(10,3))\n",
    "\n",
    "for model, ax in zip([LinearSVC(), LogisticRegression()], axes):\n",
    "    clf = model.fit(X,y)\n",
    "    mglearn.plots.plot_2d_separator(clf, X, fill=False, eps=0.5, ax=ax, alpha=.7)\n",
    "    mglearn.discrete_scatter(X[:,0], X[:,1],y, ax=ax)\n",
    "    ax.set_title(f\"{clf.__class__.__name__}\")\n",
    "    ax.set_xlabel(\"Feature 0\")\n",
    "    ax.set_ylabel(\"Feature 1\")\n",
    "axes[0].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Multiclass Classifiction with linear models\n",
    "If there are more classes you have to compute a decision boundary for each class. The decision boundary for class X classifies \"X\" and \"NOT X\" ([one-vs-rest classifiction](https://en.wikipedia.org/wiki/Multiclass_classification#One-vs.-rest)). If you want to classify a new example the algorithm takes the class with the highest confidence. In the figure below you can see the three classes and the corresponding decision boundaries. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11b5a2b70>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+n/EtVk76GxYmnTqImDCWaW9tYVhr0DikvbV5gKBGC7FYTK1bt86joKCAy2Aw\nUFlZyQGA6dOnt69fv95TIpEwli1b1jRz5szOgICA7mvXrnFWr17tFhcX13L//fcPa+/V0JClWj0y\ncAnX+tYS7qOotPmNLOGOA8KFlwH0bbM3lDTFMiYOlE/BvGObEXT4bewomod7XHNxbvGHyHvgdTwX\ndIZIk6ASvrmFXNqi8ox+L9LWBvDNLbWuGAsNDe3Mzs7mDXXdu+++62Bvby8pLCwsyM3NLZBIJAwA\nuPvuu0Xnzp0rdnFxEa9du9briy++sLGzs5Pl5eUVzJ8/vy0hIcHu4Ycf9ux/PwcHB/HVq1dNAEAi\nkUAkEjEdHByMJtsEiDgNwgCBSi2R47nltkBhVH9HCFoQ0ZCGNrYZyi39h7z2apst/i/tAbgd+AiP\nnF2PqnZrfDD5R1x/eDO+m/8l5jiWku4+hEFZunRpY1de0qBHVrryTtL3L72vUdt7x8XFtYnFYmrr\n1q22itcuXbrEPXHihED5upaWFqaTk5OEyWRi+/btNjJZj6NLSkpMXF1dJZs2bRKuWrWqISMjg1db\nW8uSyWRYs2ZN8/vvv1+dm5s7QMyLFy9u3rt3rw0AJCYmWs2YMaONwTAuVZGlWgOivIR7w/wSSpz3\nIsdzy61pLLeWcMl/orEDTSO8IR05tlGQUz0rY/2zTZmcwvHrYdhROA8nrgeDooA4t2w8HXgWsS4F\nYFDkrDtBc/5386b6wzNm2Zh4T1FZINRdXYjO3JP0K7tSBk9LVcBgMPDrr7+WP/PMM27btm1z5HA4\ntKura/fnn3/eZ6/0+eefvxEfH+9z4MABmzvuuKOFy+XKAeCPP/4w++yzzxxZLBbN4/Fk33777dWK\nigr2unXrPOVyOQUAb7311oC5df/4xz+E8fHxXu7u7iEWFhaygwcPlmsbu64h8ziNCBp0r0Cb+YXg\ndjvBr3YVXBsXEYGOAVzaKrHj7GP4b+hL+MPzvj7SrO2wwJ7i2dhVPBfX2m3gxGvGk/7n8KT/ebjy\nmwwXNMGoUJ7HmZ2dXREeHj5kF4vb5zjvokxD7qIUjUO68k7Snbkn6ZGc45zIZGdn24aHh3uq+hr5\nNDYiKFBwaJ0O+9ZpvQLN9vwQJU5fE4GOASKEijFiU/Cr/VegaeB0bQASCufhSGUEpDQLsc75+HT6\nQcS5Z4PNII0KCCPnwQcfbA0ODi74cOvH9j//8IpNe2szk29uKbt/6X2Nr+xKuUE6B40+5FPYCOkr\n0L9R4pykmdluAAAgAElEQVRIBDoGiGhIRy3PGR84peCT3FjsLI5BSYsjbDhteD7kTzzlfw6+Flqv\nmBEIQxIcHNz9deLea9oeOSEMD/Lpa8T0CHQG7FunE4EaOQyZFCHCLFziL8A9B7aiW8bGTPsyvBaz\nG8s802HKIgVfBMJ4gXzqjgH6C7SYLOEaDVIpE9ev28Gp/Ar4snbsaX8Ia33/wobAZIRZD6h7mFDU\ndnTg8fNn8NWc+XDkDXmqgUAYM5BP2zFEX4FeRDHJQA1GaysPFRVOuH7dDjIZCytM9kAOCgnxf8LM\njJwhAYAtuZlIFdZjS24WPpk209DhEAijhnEdjiFoRI9AZ2JO0S5MLf0QJlILZHt+iDMhK1Blc4yc\nA9URMhmFa9fs8NdfYUhOjsK1a/ZwcmrE7NnZeMVyLxh2tkSat6jt6MC+0lKcWsXDvrJS1HUM2bmN\nMApUVlay586c4l9VVUV+gtYhRJxjmP4CZUstkO35ARHoKCMSmSI/3xNJSVORleUPsZiFoKAriI1N\nQ2RkKc57fQyqoQFwdjZ0qEbDltxMrI5gI9KJiVXhLGzJzRpwTW1HBxb9cYxIdRR5+/VXnfKyMgRv\nv/6vUfnLWFVVxVqyZIm3m5tbSHBwcGBMTMyknJwcTnFxsYmvr2/waDyjP7///rsgKCgokMViRScm\nJlrp4hkjhYhzHNBHoGUfgC01vyXQR4lAh4lcTqGmxgYXLwbjzJnJuHrVGba2zZgxIxfz52fAx6cG\nJibSnrOaNTU9QzJdxsa8UF2jyDZfntWT9Lw8i6Uy61ReyiWMnMrKSvbhHw/ZnlrJxeEff7Qdadap\nGCs2d+7ctmvXruXl5+cXfvDBB9U1NTU6bazt7e0tTkxMrIiLi9O625G+IOIcR1Cg4NAyC3OKvrwl\nUDMiUC3p7DRBUZE7/vxzMi5fDkR7Oxf+/hVYsCANkycXw9a2pbcNXm+Dg+pqgMUC7LWe3DQuUWSb\nTmY9Hy9OZowBWSdZyh193n79VafV4ayeLD+MiZFmnYYaK+bv7y+eNm1ap7G12VOGrIOPQxQCtW+Z\niRsWF1DslIhszw9Q6vQ1fGtXwbVxISkiUoKmgRs3rFBZ6Yj6emsAgL19Ezw8yuHgcFNlv9g+rfRq\nagAnJ4CpswEUYwaFEPOf5fZ5/eVZLIRsL8XLoRFw5PFULuWSAqLho8g2C9azKQB4ZTpFBe/60fa1\nN9+tcXd3H9ZPzIYaKzYWMF6lE0YMyUAHp7ubjdJSV5w+PRmpqcFoajLDpEnXceed6Zg2rQCOjhpI\ns60NaG0l+5u36J9tKlDOOjVdyiVojiLb7JPlj0LWqQlisZhasWKFp5+fX9Dy5ct9ysvLTYGesWLf\nf/+97YsvvuicmprKtbKykiuPFfvxxx/NraysxmT7LCLOCYBagQY/hms2xyeUQGkaaGw0x+XL/khK\nmoKiIk9wuV2IiipCbGwaAgMrweNp0aGsurrn3+Nwf1Pb4p3+QuyPQpBvZKYNuZRL0BxFtvnK9L4/\n5r0ynaJGstdpqLFiYwEizgmEskCnlH0AtoyPLM/3J4RAJRImrl51wtmzkbhwIQw3bljB07MW8+Zd\nxsyZeXBxEYLBGHrgwYDZmjU1AI8HWFrqJnADom3xjrpsU4GTGQPxgUx8V14+QK4k6xw+/bNNBSPN\nOg01VmwsMKyfRCiKEtA0LRr6SoIxQoGCY8ssOLTMRL3FBZQ47UWW5/socfwafnWr4NJ417jZA21u\nFqCy0hHV1XaQyZiwtGxDeHgpnJ0bwGLJtbrXAGnK5T3idHfHeBuc2Vu8s5qHBV/f3pscjDRhA1Ly\nuvDppS6115gwgSciTQZdyiV7nZrTf2+zPyPZ6zTUWLHk5GTegw8+OKm1tZV56tQpy3fffde5rKws\nX5vYdc2wxopRFFVF07S7uq+TsWJjCxp0r0Bb+CXgdbmMaYFKpQzU1NihosIRLS1mYDJlcHFpgIdH\nLSwt24d1zwHSBICGBuDXX4GYGGDSpJEFbWS8cCkF4FfgP4tM8MIJMah2rxELrbajA8E//YD8Z7kq\ns9LaNjlCtnch//7lE7ZFn7ZjxZ5Ys9JdUPqz7aexTLU/uT2fJKPb/e4Xfpm4v2q04x3PDGusGEVR\nL6r7EgCBmq8RxiDjJQNta+OistIJ167ZQyplwcysHSEh5XB1vQE2e/g1CCqlCfRkm8C429/sXxnb\nvyJ2uGiylEuyTu3IykjnX85tp7ZdGPQyKrotna+nkCYEg30avgfgI0DlxhfZGx2H9BVoCoqdlQRa\nuxouN2ONTqAyGYW6OhtUVDjh5k0LMBhyODkJ4eFRB2vr1hGvoKqVJtBTGGRtDXC56q8Zgwx2DlMb\nofVv8q7JUi4AzHIko9c0JT2nsNDQMUxEBvsUzABwhKbpy/2/QFHUE7oLiWBoegQ6Gw4ts24L1Os9\nlDjtMxqBdnRwUFnpiKoqB4jFJuDxOhEYeBVubvXgcEanyGlQaUqlQH09EBQ0Ks8yFjQ9h6kJ/Zu8\n/7V4qS5CJhD0zmCZ4+MAKtV8bbIOYiEYGQqBzi3cgyll74El5yHL672eKlzr3/VehSuXA3V11vj7\n7yCcOjUZZWWusLZuw7RpebjjjsuYNKl61KQ5JHV1PQHpeZlW1/1dNTmHqQmj1RmI9LMlGCNqxUnT\ndDFN0yo3pmmartddSARjo0egcwwm0K4uE5SUuOHUqSlISwtCWxsffn7XsGBBGqZMKYS9ffOoF7UO\nmm0CPcu0DAbg6Di6Dx4CXfZ31fQcpiYS06TJuyaQfrYEY8S4NqwIRo1CoA4ts1Fv8ReKnROR5fXe\nrVZ+q+Fyc8GoLeHSNCAUWqCiwgn19TagaQq2tk0ICbkCB4dG6LKN5ZDSBHrE6eDQ06NWTwzniIg2\naFq883pmOipFbWoHVI9WcZGu3+94YNv2bYHNDc1D/qFY2ll2/OOZf5D90FGCiJOgNaoF+i5KnfaN\nWKBiMQvXrjmgstIR7e1csNkSeHtXw8OjDnz+4EUlo4FG0uzoAJqagMn63bHQdX9XTYt3PM2uoUXS\nPeD5imIgd75gVIqLSD/boXF2cm7PFGdyL1tdVrvmEt0UTS9xWjKsc1hVVVWsZ555xj07O5tnbm4u\ns7W1lXz++efXOBwOvWTJEl9Fz9nR5I033nDYv3+/LZPJpG1sbKT79u2r8PPzE4/2c0YCqY4lDBvl\nJdzJZe+CKeciy+tdnA1eiWvWJzRewqVp4OZNM2Rm+iEpaSoKCrxgYiJGZGQxYmNTERRUYTzSBAxy\nDEUf/V3/WrwU9Lp1eD4kAFamFF4ICQS9bl2ff2oeeQQtYsmAvcusxkYE/3QQqcJ6HLg6sDPQ6nAG\ndpcUIadx8ElRij3N7MZG0s9WA2Lnx9Z6tXvBVGqq8uumUlN4tXsh9o7YGm3vbaixYtHR0R1ZWVmF\nJSUlBUuXLm164YUXXHX5vOEwpDgpivKjKOoURVF5t34fRlHUq7oPjTBWoEDBqWWu1gKVSpmoqHDE\nuXORSEkJR12dNdzd6xATk4HZs3Ph6toAJlP7Bh3DQWNpAj3LtKamgI2NzuLpjyajukaDoYp61O1d\nrj53Gl0yOU6t4gGgB+w578uWgsmg8URK8qDPV+xpPpmSPKz3O9GKiSwtLSVBQUHC4LZglf+jBLcF\n08FBwUILCwutCxEMNVYsLi6uzczMTA4As2fPFtXW1ppoG7uu0WQ97UsAmwHsBACapnMoivoOwDvq\nvoE/qQ3Tfz03OhHqib/vnWvoEMY8CoE6tsxBncV5lKhZwm1p4aOy0hHXr9tBJmPB3FyEsLBSuLho\n3wZP79D07TFiemqzN5pHRBT3Uz5fqcxgy6Pq9i7vcfVAWWsrnozu+b7HI9nYkiLGJwt7sqDaNjn2\nZYtxehUfs/c2IaexEWEqfuhQ3P/AclMsPdCEX2b17bOiyfvtfwRmIhA7P7a24L8Ftvlm+ehi3V6Z\nGUm2CRjHWLGdO3faLViwoGU48esSTcTJo2k6ler7ITHuuoGPNdGrwljkf1ugs1Fn8VevQAvtvgUz\n5f/QcWktGKDg4iK81QZPZNBWr1plm01NPXucelym1eSIiCpJqBOkOrkMVdSjLutdlXwKDAbwv7M4\nAHr+HbKjHS/PMoGjgIEtKWIsC2Tj/0514aEQFp5ISUbqvQ+ofZ+/l8qwLnJ473ciFhMpss6rlVdt\nlfc6R5JtaoNYLKbWrVvnUVBQwGUwGKisrOQAPWPF1q9f7ymRSBjLli1rmjlzZqfyWLG4uLiW+++/\nv1Xdfbdv326dnZ3N27lzZ7Eu4x8OmohTSFGUDwAaACiKWgagVqdREYaFMcpfWGINk4SvkX60Et2T\n3wcWrgf/7rexYMFcRE8LAJMx8jm2I/mBQStpAnrf31SXbSoYLAtTJcjB5DLYcvDm0Ai1We+uy114\nIrrv9z0UzILHpyKIZYApC1gZxkZqtQzLg9goaG5GXUdHn3gVcZ1ezcEdX3ch/xnVXT2Her8TtZio\nf9Y50mwT6BkrduTIEauhrlOMFTt8+PBVuVwOLpcbDdweK3b48GGLtWvXej333HP1zz33XGNeXl7B\nzz//bJ6QkGB38OBB60OHDlX0v+eRI0fMtm7d6nT+/PliLpern/0aLdBEnM8C2AUggKKoagBXATyq\n06gIYxqZhIHCX/xwaUcUrpz2BIMlQ/ADFpiy/CV0OZ3A6eTT+OXkd0i5bIv5c+cjNCR0RAId0Q8M\n2vbAqq4GLCwAgX7aNQ+3v6s6QaqTy2DLwUH/LcGRqgosCxo4ugpAn2xTwWtzOfg6WwoHLgdzPeX4\nsUCMU6v4WLC/AytCTAbEq4hrX7YUq8MHTk/R9P2Odn/dsUL/rHM0ss24uLi21157jdq6davtSy+9\nJAR6xoo1NTUxvby8eqtcW1pamK6urmImk4kvvviiz1gxb29v8aZNm4Td3d3UrbFiLRwOR75mzZrm\n4ODgrpUrV3r3f25KSgp348aNHsePHy91cXExytXNQcVJURQDwGSaphdQFMUHwKBpuk0/oRHGGs1V\n5kj7MgLpuyMgqhPA0r0Fse+eRfTabJg5KqrhgxEYEIjCokKcTj6NQz8fwplzZzB/7nyEhYSBocsD\nmiNFJuvpGOTrq7dHDre/qypB9s8aX57Fgt/nRVgzyR+JZUVql4M9LYGrzZ2gqIHFlFtSxIMuq36T\n04X8BgZWh5v0xBLGRodEjn1lt6WmLL3lhzqRck2GTy8NfvpA3fsd6RGYsYwi6yznlY842wQMN1Zs\n8+bNbh0dHczly5f7AICzs7P49OnTZSN5L6PNkGPFKIpKV4y50RSXyS70s+nPjigwwthALqNQ+oc3\nUhMiUXxsEkBT8FtchqnrM+F3dzkYg1TFyml5r0Dr6utga2NrEIH+84krml1YWwscPw4sWAB4eOg2\nqBHQf3yXYlzXMk9P8Cyu4z+LbhcpPnOsExev8lApEqkc91XbJoffFyKcW9OTLeY/w4ejgNH7teDt\nIuQ/I1A7Jix4uwidEuDvJ3gId2T1xLKjHfEBJhBIvPHJtJl9Rpj1R9VIs/57t+rGlY3FMWXajhXr\nz6GfD7ln52XbRYRENCy7fxkZIzYChjVWTIk/KYp6CcBBAL2HaGmavjk64RHGIqJ6Pi7vDUParkg0\nVVhC4CBCzP9dxOQnM2HloXa/vw8MioHgwDGUgVZX91TSOjkZOpJBUZV9xQcy8V1eOUo29p0u9dpc\nDnyyWvBoiOrl0S0pYqwM68lclfctgZ6h1KqyTQVOZj2Z5vlKKfZlS/GJY89Sr3LWuXqSv9Z7uP33\nbodbPDUeiZ0fWytsFHJHmm0SBkeTjPOqipdpmqYHrE0rIBnn+ISmgYpz7ri0IwoFP/lDJmHCe34F\npj6dgcD7SsAyGdlREkUGeursKdTfqNdbBqpxxvnLLz0benFxOotlpKjLvp76rRMsBrB98UBBPXus\nE7szJb1CVMaUBVz5H0Fv5ur/hQiPePki42YDGsQtqGwZum5jqgsDpY1yFDwrgKOA0SfrzLrOwyzv\nTpXZpgLlrFPx/k6tNsWCr7txetESzP/9t3EzHHukGSdh9BhRxknTtNeoR0QYU3Q2c5D5dShSE6LQ\nUGgLrlUnpj+XjilPZcEuYPBOMNqgnIEWFBb0yUDviLkDocGhOhHoe7u9h5ZndzcgFAKRkaP+/NFE\nVfZV2ybHjwUStZWqr87l4KssCdKWLkWYjU2vnBb7UTDjUH0y17WRbCRmloHNZKCxs0eapiyg61YJ\nhwkTCLFjYKYbE5/fc1vSG4939p7tVFTd7snshiVHhrRLUo33cPvv3fZvlNCfiZh1EnTPkOKkKGqV\nqtdpmv569MMhGAs0DVSnO+HSjijkHgiCpJMNt2nViE/8DaEPFYLN1V2xG4NiICQoBEGBQb0C/eGn\nH3A6+bROBTooBmizpy3qKmO3pIiHrFRdG8nuPV+5JTcTy4JYOFTYjYJ+sn1lFgd7MyWId/fGztlz\n8cKlFOwrK8bTAQHYHBqBwMMHcaVJjqMr+mZ3/5zDQfB2Ue/ZztfmcnAwj0b2fct79ynVNWVQ9/5e\nnsVCQFYz0i7RZDg2Qa9ossc5RenXpgDuRM+QayLOcYi4nY3s74OQuiMKNRlOMOGLEbEyD1M3ZMA5\nUr/T5PQp0CGzzupqgM0G7OxG5Xm6QN1eX1qNTKNKVXNOc2+P2GXBDDwaqnrfUJF1PhMY3OfIi0gi\nga8Nhemuqr/v0VB2n6xTORPUpOOPqr3btRGcAcVDBIKu0WSpdqPy7ymKsgRwQGcREQxCfb4tUhOi\nkPl1CLpbTeEQcgNx/z2BiMfyYGpu2MEERpGBKtrsGVOxUj80nm5iwcDV5wcu275wQownU872ZJsF\nA7NNBYqsc835M73LpivDmNidWQY2A/j1EdWFPv+cw4HPZyL85+/bf59mOd7oc+Z0bmLP8Zj+LflG\nu+0ggTAShjP7qR0A2fccB0i7mcg/7I9LO6JR+ZcbmCZShD5YiKkbMuE+87pB2+CpQp1AFVW4OhNo\nayvQ1gaEhIz+vUeRvxYvHfTrir3LC+vUV7BOutwMf0eWymxTgZMZA49HsrH7cguO3+on+8psNvZk\nduPRsCG+L8IEnC6fPhniC5dSbgs4XHVLPlI5axh4PF5kR0dHpvJrW7ZssePxePLnnntuxAUOhhhb\n1tnZSS1btswrNzeXZ2lpKT106NAVf39/rbIDTfY4f8OtdnvomaYSBOCQ9uESjIXGckuk7YrE5b3h\n6BDyYO1zE4u2nELU4zng23YaOrwh0ZVA1S7XVlf3/NuI9zc1QZMuRGsj2fi1WIqqVhr/TZMMej8X\nM+DxXzrx1dKeilZLLoX/pkmG/L6p9nW9v+6fSb42l4NJn/VtBD+StoOE0Ud5WspIUIwtW7FiRePR\no0evAMDFixe5NTU1bOXORKPNtm3bbC0sLKRVVVV5u3btsnrxxRddjx07pmFpfQ+aZJxblX4tBVBJ\n0/SAbg8E40YmpVB81BepCZEo/cMHDKYcAfeWYtrTl+F9Z4Uxr0CqRW8ZaHU1wOcD5uYjv5cB0XQp\n18OCgqcFhYpBjpqYsoB7fNn4sUDSu2959ySW2iMvCnqOljj2/l7lvqVSoZKqa/pDsk798uKLLzoL\nBALZW2+9VT916lT/6Oho0V9//WXe1tbGTEhIqFi0aJFIKpXi2WefdU1JSTETi8XUk08+eWPz5s19\njtaoG1sG9IwqU7xWXFxssmLFCq/Ozk4GAGzbtq0qNja2vbKykh0fH+8tEomYMpmM+vzzzysXLFgg\neuihhzxzcnL4FEXRjz76qPD111+/0e+5lm+88UYNADz++ONNr7zyirtcLtfqs0ITcd5D0/Qryi9Q\nFPVh/9cIxklrjQDpuyOQ/mUEWq6bw9ylFXe8cQ6Tn8iChYto6BuMAXQqULm8p2OQp6fexojpisGW\ncpW798ze246UayoOdd7ChAk8GMTCjwWS3v6zL88yQUGDHCnXZNiRPnjGqahwVZdJ/nMOB5Myb2ed\nw207OJ5YuxZueXkY1XQ6JAQde/fi2tBXDo5UKqVyc3MLDx48aPHWW285L1q0qOTTTz+1tbCwkOXl\n5RV2dnZSU6ZMCYiLi2sNCAjozSQNNbasvr7eRJHRstlsCAQCWX19PcvJyUnjowKaiDMWQH9J3q3i\nNYKRIJcDV055IjUhCoW/+EEuY8B3YTmWfH4S/ktKwWQZ3bCBUWEwgd4RcwdCgkKGFOiA5VqhEBCL\nx/wy7VBoKqcpdlYoa20Fh0X16T+7JUWMv9bye5sbKFrzqWqZp2CwfUvlrFMhfGW5D3Zfgn5Zvnx5\nEwDMnDmzffPmzSYA8Oeff5oXFRXxfv31VysAaGtrYxYUFJgqi1NTdDW2bCSoFSdFUU8DeAaAN0VR\nOUpfMgOQootgCCOjXchFxldhSNsZicYya/BsOzBr0yVMeSoTNj7Nhg5PbygLNL8gH6eTT+Pg4YO9\nVbiaCLQXxf6ms7PuAjYChiosUvDCpRREuHbgx4Lu3oYKL88y6Z2/qWipp1i+Vbf/ONS+Zf+sc6JP\nPxmNzFBXmJqa0gDAYrEgk8koAKBpmvr444+r4uPj1YrLUGPLHBwcxFevXjXx8fGRSCQSiEQipoOD\ng1YH0wf79PgOQByAX2/9W/FPNE3Tj2nzEILuoGmgMsUVh1bGYYvrRpzYfCcEju148NsjeOX651j0\n4ZkJJU1lGBQDocGh2Pj0Rjy87GFQFIWDhw/isx2fIScvB3K5Bi0Cq6sBGxvA1FT3AY8B0oQN2JfT\njYdDVM/fpN5sxaeXxEitlvV+bWUYE1tys/rcR9NCpSdSklVer7yvSTA+YmNjW3bs2GHX3d1NAUBO\nTg6ntbW1z3/suLi4NrFYTG3dutVW8dqlS5e4J06c6HMOqqWlhenk5CRhMpnYvn17n7Flrq6ukk2b\nNglXrVrVcGtsGUsmk2HNmjXN77//fnVubu6An6oWL17cvHfvXhsASExMtJoxY0abtls5ajNOmqZb\nALQAeAQAKIqyR08DBAFFUQKapknnfQPS1WqCrG9CkJoQhfpce3DMuhH9RBambciEQ8ioFL2NGxQC\nDQ4K1igD7V2uFYuBGzeA0FADRm9cHJp/F4J/+gGvzR04f/NAngSVzwt6p6coeGU2e0B2qOnSsHJT\nBnKGU/90dXUxHBwcwhS/f/rppzXqgvLCCy8IKyoqOKGhoYE0TVPW1taS48ePlytfY6ixZf/4xz+E\n8fHxXu7u7iEWFhaygwcPlve/Zig0afIeB+ATAM4AbgDwAFBI03Swuu8hTd51R02mA1ITopD9bTDE\n7SZwiqzDtKczEPZIPjiCwYsyCD3IaXmvQG803IC9nT3mz53fR6D/fOIKUFUFJCUBd9897pdqNWXw\nEWBdoCjgk4UDs/Pnf+8Go8N7wPlNdfe6fU8xUq5w1TaCH297naTJu/Ew0rFi7wCYDuBPmqYjKYqa\nD4As1eoRSScLuT8EInVHFK5dcgGbK0HowwWYuiEDrlNqx3qxp95Rl4EqqnBDgkJ6ss7giwCTCdjb\nGzpko2Do85QmAzoDKdO/6lXTrJPH7sYvs/gqv0ayToIh0EScEpqmGymKYlAUxaBp+gxFUZ/qPDIC\nGoqtkbYzEhlfhaGziQu7ACEWf5qEyFW54FoN/mFDGJqhBCqvqQbD0RFgDafB1vhDk33J9dGm6Ghx\nw6GrVwYM0v5x/l19rtekIEmRlZIznARjQpNPhGaKogQAzgP4lqKoG1AaaE0YXWQSBgqO+CE1IQpX\nTnuCyZYh6IFiTN2QAa+YKpJd6oBegQYGI68gD2fOncHBwweRuwJ4/botloEGA+QPXuNeuGbX1Bby\naCs3coaTYIxoIs77AHQCeB7AowAsALyly6AmIk2V5kj/MhLpe8IhqhPA0qMZd713BtFrcyBwID+n\n6AMGg4GwkDCEBIWgdcdvONqQioeiyhEsacS/WyKxrNNrQgtUkwxR0Q/35VmjU8ij6TEZAkGfaDId\npZ2iKA8AvjRN76MoigdgQDcGgvbIZRRKTngjNSEKJcd9AAD+i8swdUMmfBdeAYM5PhsVGDsMBgOr\nLnTj1VM8/L58Kt60yMJDtmcQLMkkAh0C0oydMBHQpMn7kwCeAmANwAeAC4AE9MzlJAwDUT0f6XvC\nkbYrAs2VlhA4ihDzzwuY8mQWLN110uiCoA1yObz+LMPVBb54qNMHyzq9cIh7FW8pCfT1lijEd3oS\ngSpBmrETJgqanPp8FsAsAK0AQNN0KQBSZqglNA1cOeuOAw8txYeuzyHpX/Ng7dOMRw79hJervkDs\n2+eINI0E+9x68G+04+pdk/Debm8wwcDDnT7Irbsf3wvnQQ7gQdvTCHP8CYe4VyEHWRkAtGvGThgb\n8Hi8yP6vbdmyxe6LL76wUXW9tlRVVbGWLFni7ebmFhIcHBwYExMzKScnh1NcXGzi6+ur9sjjSPj9\n998FQUFBgSwWKzoxMXHIzkWq0GSPs5umaTF1qyqFoigWQD4pNKWzyRQZ+0KRmhAFYbENuFadmLEx\nHVPWZ8LO/6ahwyOowOtkGQDg6gKfPq8rBLr8Vgb6pkUmHrQ9jWCJJclAQQp5JgpjfayYt7e3ODEx\nseKDDz5wGO49NBFnMkVR/wTApSgqFj39a38b7gMnAjQNXE9zQuqOKOQcCIK0iw236dcRn/gbQh8q\nBJurVVtEgp7xSipDQ5A9RC4WAAY2flcW6A+8q3jLnAgUIIU8E4WxPlZMMbR6JCMHNRHn/wJYByAX\nwHoAxwHsHvYTxzHdIjZyvg/GpR1RqM10hAlfjMjVuZi6PhPOkRp1qiIYGGaXBG7nK5C5furQ14KB\nRzp88GBHX4GGiK3wemskHpigAiXogLVr3ZCXN7obwyEhHdi7d8KNFRsNBpuO4k7TdBVN03IAX976\nh6CC+jw7XEqIRNb+EHS3msIh9Abu3X4C4Y/mwdRcZysOBB3g9lcl2F1SXI31GfriW6gS6HIiUMIE\ngbEq3YUAABumSURBVIwV68sRAFEAQFHUYZqm43URwFhF2s1E3o8BSE2IQuVfbmBxpAh5sBBTN2TA\nfUY1aVQwRvFKKoOMzURVjFef1wfM6VSBOoGG3hLo/USghOEyCpmhrhhrY8VGg8EWeZX/D/ce7QeP\nVRrLLXHi5fn40HUjDj12H0R1fNy99U+8fP1zLP/6N3jMJNIcy3gllaF6hhskAs7QF6tBIdC8ugfw\nXeM8SCg5ltmeRoTDzzhMqnAJEwBjHis2GgyWcdJqfj3hkEkpFP3mi9SEKJSd9AaDKUfgfSWY+nQG\nvO+owAj2mAlGBK+hHY6ZtUh+e8Go3E85Az3Iu4q3zTOxjGSghDHEeBwrlpyczHvwwQcntba2Mk+d\nOmX57rvvOpeVleVr8+eidqwYRVEy9PSkpQBwASg2cSkANE3T5upuOl7GirVUC5D+ZSTSvoxAW40Z\nzF1aMeWpLEx+IgvmziJDh0cYZYIO5GDpIwfx1d8bUDPNTeU1Qy3XDoYMchy8tYRbzG4hAiUMgIwV\nMx6GNVaMpukJ2VZPLgfK//TCpR1RKP7NF7ScwqSFV3Dv9hPwX1wGJmtCJ9/jGs+kMnRamqJ2sotO\n7s8EAys6fPDQrQz0rVsZaJjYGq+3RmJppwcRKIEwBiDzkm7RLuQiIzEMqTsjcbPcGjzbDsx+6W9M\nfjILNj7Nhg6PoGtoGl5JZai8wwc0U/3auyZFQkOhSqDxtqeIQAmEMcKEFidNA5UprkhNiELeoQDI\nxCx4zqnCgrfPIfiBYrA4MkOHSNAT1iVCWFxrwYV/xujtmUSgBMLYZEKKs6vVBFnfhCB1RxTq8+zB\nMe/C1PWZmLI+Ew7BZEthIuKVdKvNXuwkvT9bWaAHeFfwtnkWESiBYMRMKHHWZDrg0o4o5HwXDHG7\nCZyja3H/7mMIe7gAJnyJocMjGBCvpDI0eVuj2Wfo3tWjsVyrCiYYeLRjEh7u8MYB3hW8dUug4bcE\neh8RKIFgFIx7cYo7WMj7IRCXdkTheqoL2FwJwh7Jx9QNmXCdUmvo8AhGAEMig8eZq8hfETb0xXpA\nlUAfIAIlEIyGcXsCsaHIBsdeWIAPXTbi8ONx6G7jYPG2k3il5jM8sOc4kSahF+dL18Bp6zbIMu1g\nKASaX/cA9jfGoJOS4QHbU4hyOIKfuRWkkQJB54zHsWJvvPGGg4+PT7Cfn1/QjBkz/EpKSkyG/q6+\njKuMUypmoPCIPy7tiMLVsx5gsmUIji/C1A2Z8JxbRTr6EFTilVQGOYNC5R2a96fV1XKtKlhg4LE+\nGWgmHrA9hQilDJQiGShBT4z1sWLR0dEdmzZtKjQzM5N/+OGHdi+88ILrsWPHtPqfeVxknE0VFjj5\nrxh85P4cDjx0P5orLHDX+2fw8rUv8ND3v8ArhkiToB6vpHLUTnZBlxXX0KEMikKgBXXx+LpxLtop\nKe6/lYEe4VaAJhkoQQ+8+OKLzv/+978dAGDq1Kn+Tz/9tEtoaGigp6dniKJdnlQqxfr1611DQkIC\n/fz8gj766CPb/vdRN1Zs0aJFfbrLFBcXm0RHR/sHBQUFBgUFBSYlJfEBoLKykj158mT/gICAIF9f\n3+ATJ04IpFIp4uPjPX19fYP9/PyC3nzzTfv+z42Li2szMzOTA8Ds2bNFtbW1EyfjlMsolPzug9SE\nSJQcnwRQNPwXl2Hqhkz4LrwCBpN8iBCGhtPSBefU67j4v3O1/l59Zp3KsMDAyg5fPNLhg+955Xjb\nPAv3kwx0XLP2l7VueTdGd6xYiH1Ix977JvZYsZ07d9otWLCgRdv3PObE2VbHR/qecKTvikRzlQUE\njiLE/CsFU57MgqW7TibIEMYxHmeugCGTG93+piYQgRKMgbE6Vmz79u3W2dnZvJ07dxZrG9OYECdN\nA1fPeuDSjigU/OwHuZQJnzuv4u5P/kTgvaVgsuWGDpEwRvFKKoOYb4LrM1T3ph0LEIGOf0YjM9QV\nY3Gs2JEjR8y2bt3qdP78+WIul6v18qRR73F23DRFyqdT8Gngeuy541GU/+mJGf+TjheKE7D2z+8R\nEl9MpEkYEZ5JZaiK8YTcZHg/Q76323gm7ikEqmoP9BfTSrIHStAbxjxWLCUlhbtx40aPX375pczF\nxUU6nPdndBknTQPXU51xaUcUcg8GQtrFhvuM61i271eELC8Cmzus90kgDMC8sgk2pY3IeGaaoUMZ\nVZQz0O9uZaBL7f5EhNgab7RE4d4ud5KBEjRiPI4V27x5s1tHRwdz+fLlPgDg7OwsPn36dJk2fy5q\nx4qNhOGMFesWsZH9XTBSE6JQm+kIE0E3Ih7Lx9QNGXAKvzHqMRII4bvTsPjJI9iV9z8QBjsM+z6G\nKBDSBinkvQItY7cSgRoxZKyY8TCssWL6oi7XDqkJUcjaH4LuNg4cw+px747fEfFoPjhmOjvKQyDA\nK6kcbc5mEAYNqFjXCkNV12oKCwys6vDFin4ZaKTYBq+3RBKBEghaYhBxSrqYyP8xAJd2RKHqghtY\nHClCHizEtKcz4Da9mpy5JOgeuRyep8pRttgfE+UvnLJAv+WV423zTCJQAmEY6FWcjWVWSN0ZiYzE\nMHQ08mAz6Sbu3vonotbkgmfTqc9QCBMcx8xa8Bo7Ru0YirFnncqwwMDqDl88qkKgb7REIo4IlEAY\nFJ2LUyalUPSrH1ITIlGW5A0GU47ApSWY9nQGvOZXgGHUdb3Do2tXF5i1g567BQDInGQwfcpUDxER\n+qMYI1axQPM2e+MNVQK9jwjUmJDL5XKKwWCQcmg9c6u4SO2RDZ2Js+W6GdJ3RyDtywi01ZjBwrUV\nd76VjMnrsmHuLBr6BmMYhisD5Z3lyLTMVHtNZHMkvF2N5yjDRMPrZBnqwxzR7mhm6FAMjrJAv+GV\n4R3zLCJQ4yCvoaEhyM7OroXIU3/I5XKqoaHBAkCeumt0Is6b/9/evQY3dadnAH/ecyRL4CsYGwyy\nJXEzSgPGQJIliR0CBHK/TEM7093mtml2N9t86Uw7/dDpkNlkt51Mv2y2TdvJZtt0d3rjUzZclYTs\nLplNlyy3ZCAOMrbAIMf4gmzJtmzZpx90QVdLMralIz2/GSYgHx39IcDD+57/eY9rCd6wfh/QBOse\n7MQTbx3B+oddUA2l8f/e2GaE7YwNFyouYNwwnvR1c9AMm98GY7sxD6sjw+gELJ+48dkr2+f0vHpq\n16ZigILnRtfjW6Nr8fPFLvygOhSgWyZqsd+7BY+ONzJAF1AwGHyxt7f37d7e3ttR4PfcF5lpAF8E\ng8EX0x0wL8E54S9D2199ijteOo2l9pzHAOqeVAqUzQocFx0pq06HzwFlswKp4F9C+dD0624YJqZ0\nOWZvIUQC9Juja/GLcIA+XudkgC6wrVu39gF4PN/roGTz8q+YFZv6sPdHH5dkaEYY24yw+W0wB+Ov\nYbLazD+704VgmYorbdZ8L6WgGcMB+qXnafxsoA03lAk8XufEHcvfw/vmy5xERCVrfsp/4R+oaNXp\nc8S9zmoz/+xOF3rutSK4OOenCWVUSCP45kpsgL4z2IYhJYDHGKBUwtg3n0eJVSerzfwr7x1B/edf\ns007C0YoeN7PACXK++SgYpZ4rTOXapO3tMwP2wehcZnzGZx63ySUSSRAv+Vfi5+Xu/CDqjN4rM6J\nrRPLsN/bikd4DZSKHINznkV22HYt6sqp2uQtLfPD7nRhtHYxelsb8r0U3YsN0P8oD93GwgClUsBW\n7TyLVJ3tfe05XdtMt7kogm3fWdA02J0udO9ag6KcvJEnRih4wb8eHZ6n8dPBNgyGW7h3Ln8PB9nC\npSLEvz0WgLHNCEOjIaeQS7e5KIKbjHK37HwfKj0j6Hpg/qcFFeMmoUxiA/TtwXvRr4zjUQYoFSG2\nahdA4D8DUD0qgv8w87NEE69XphukwGpzdiJj9rgxaH4ZoeDb/mY841+Hd8sv4rWqM3i0zok7Asuw\nf3gLHhq3sIVLusbgXABZXa8caIXNY8Pkq5PR16YaplIOUmC1OTt2pwsD62oxbF2S76WUhFQB+kjd\nMQYo6R5btQsgm+uVFr8FhyyHcMB2AAdsB9BZ0wnFovCWljmiTATR9KtudC9gtVmK7dpUIgH6lWcf\n3h68F9fVcTxSdwx31b+HQ+YrbOGS7rDiXACZRvA1DzfDXeFGwBAAEB+OUnHzvdVj1VgWWAYAM7Z9\neYtKMstvr6DMP4FLe9imzZd0FeidgTrsH27Fg6xASScYnAtkpuuVTb4mHFt5LPpaYis28t6esh54\ny7w4XctbVHJlP3YR06qCyzv4a5NvkQD9U/9avFvuwutVZ/AwA5R0hMGZpWwHEgQlCIOW/pfV4XWg\neuJm5RjxWM9j8QeeBMY+G4OsEJhfMkPZrKDh9w1QoOBCNZ+6kiu704Wrd1kQqF7YSrzYhyHcijKo\neNHfjGcYoKQzDM4sZbPBZ/PAZkzLNM4tPYcdnh1J4ahCxZqR+Fsh+k39+Ljh46RztQy2oDZQiyWW\n0EYWY5sR2nUNUiNwdPOpK7kwD46i4bNrOPG39+d7KZRCYoC+xgClAsfgTCOxwhQI1mAN1txIHXzm\noBk2nw3HVxwHAAyZhjBkGsLZpWfTfkbLQAu0FAPxzUEzrD4rlGkFclIw3jMO80tmmJ41QRvRYHuT\nt6jkwvbRJYim5e02FFad2WGAkl4wONPIpsJsGWyJ7gh0eB1AHbB6bDVOm06jo6oDe67tQUdVR/q2\nqs+GI6uOJH2tebgZPoMP/eZ+qIoad80y3UajVNUm592G2J0uBCpNuHanJd9LoSykC9C7AnXYP7wF\ne8dXMUAprxicaaTbzBMRu6nHHDTDOmqF6U9MsL1z8z3uCjeah5uTqs7YNm7Stc0YAkGVVoWpy1Nx\n93cKBFaxRj/HHDTD6rVi2j0d937Ouw2xOV1w32/HtDHzPyKocMQG6L+XX8TrVWfxUN1RBijlHYMz\njUy3kGzwboBh2hAXfFP/MgUVKh7teTT6WlCCSVXnsHEYN8pu4EztmbSfv3lgM+wjdqhQMfX1FDor\nO+N207YMtkRDuXm4GcNlw1iScGN/NuFf7O3dms4BLOkawu/+4p68roPt2tkrg4o/82/As/51DFAq\nCCUdnJlamYmVXUTkGqS7wo1Ty06lfX/LYAtqx2qxwbshLiRFE1j9VnxZ/WX6atbfhEOWQwgYAjAH\nzdhzbU/cbtpIK9hd7obVZ4WqqEkBmCn8S2EzEcfsFY/EAH2t6gwDlPKipIMzm1bmTs9OOIYdOL30\n5jHN3tA1SMuoBeeD52ds5fYt7oPNZ4uGpDlohmXUAp/Bl7KNC4Sq2e6K7uhAhHHDOHoW98DhdUSr\nzkgruP3rdviMPizZtCRlAJb6vFu7sxPexmoMrl+W+WDShdgA/bfyi3idAUoLrKRH7mUzCq96qhq2\nsfiRd1a/FeXBcngWebDBuyHlex1eBzyLPFgZWAnlNiW0eQihjT+Xyy+jPFgOq8+a9NmRTUPrh9fj\n6e6no99W+1YnHd9R1YEbxhuonqpOG4DpnrJSCtWmTE3D+lFnqNqU/P88OYJvbpVBxUv+Dbjo2Yd/\nHrwHHnUUD9Udxd31v8RRcw9H+dG8KengzOrRXa1K3DEbvBvgM/jgrnSjYbQhbfhZR61YObYSymYF\nZXvLYPVbUROoQZOvCedrzsNd6Y5WnbGavc24VHkpOrM2Oru2shOoRdxaxw3jGFk0AqV15gAs1Xm3\nDZ9dxaIb4ws6n5YWXhlUfCcmQK+qo3iQAUrzqKSDE0hfdcaGS+SYmkANrD4rKiYr0F3ejUHTIC6X\nX04KP4fPAfV2FYam0DM4pVKgblTR3tuOnsU9CBgC6C7vRtVEVVzwRqrZjqqOpLVYR60w/aFpVgGY\n+A+EUqg2gZvXN7t3zf/zN7PFqnP+RALUlRCg99S/j2MmBijNnZIPzmxamZFj2r9uh4jAs9iD1b7V\nOLHiBC7UXEgKP5vfBuNuI0zPmm7Om91lhFKpQFVCm5FWj60G6gGf8WbVmXhtM7oWrwPqRhXKCmXW\nARgb/qVQbQKh4OxtbcBoXXm+l0ILKDFAe1Q/9tYzQGnulHxwAtm1Mo1tRhiaDFA3qWgYa4DVHwrL\n2I07QPowk0qB+UUzGscao+FlesqE6qlqWEdCbVybzwZ3uTvufZFq07jLGLfWXAMwGv597SVRbRp9\nAaz67RXupi1hiS1cBijNlZLeVRuReNtGqvCTSomOvNNuxM+MVRQFFp8FXRVdM4ZZNLxOtUMza9H7\nPgGgvbcdogke8DwQ9x6/6oe6UY2uJfYcypbcAjAy77YUqs2mX3VBnZxC1551+V5KEt7TubBM4QB9\nzr8OPyv/Cj+sOou99Udxd6Ae+71bsDuwkrtwKScMzrDIbRtdi9KHX+S+TyVcqCfOrt3t2Q0AGHtz\nDMaJNOEJQRnKAD/gN/hx2HIY5qAZ2/q34eSyk3Ft2paBFth8tmi1GbcGCc2xnTw5mepjUo7Ri4R/\nKVh9zIVJswFX7mnK91KoQJig4rt+B573r48G6J76IwxQyhmDM0wqBVqZhvbedkBL/6DoxAk+iVpv\ntMJaZkXnROZRd9bhm+3eEytOxH3dHDTD7rPDoBmS1pLNGop9jF4mdqcLV9ptmDIXf3VNuUkM0NcZ\noJQjBmcMda2K8fPjOL78eNIGHSAUZnuv7s34PMyyPy6Lm1mb7jhlk5L2EWHNw6HbUs4tPRf3+rbB\nbbD6rHwm5wwqe7xYduE6zr6wNd9LSYvt2vyLDdB3WIFSDhicMYy7jFh0ftGMf1hEBA7fzCPsortf\nY0bdpXo+J84kt3v7Tf34tO7T6AD5WOZgaHPRTIFbKreazMT2QScAjtmj7Jig4nt+B15ggFKWGJwx\nspntqm5UYTufeYRd4qi7bJ7P2TrQCtuILTokfvv17XEPuY6EorHNyGdyzsDudMFfX46+jcvzvZQZ\nseosLLEB+tOKDvyo8hz21B/BPYHl2O9txS4GKIXxdpQExjYjrN4004C8VshZASYRvf0kIrHSS7w/\ntKOqI+WUodjzW/wWHLIcwgHbAVysvIhB02Dc1yOhWMpj9DKanob9Axe6dq8FFP72ptyZoOJl321w\nefbhH4e2o1sdwQP1R9BWfxAfmK7yNhZicCaSSgHqkDSDNnLN8YDtAA5bDqPJ1xQ/8cdrDe1yfXUS\nk69OYvxfx+PuD0283zNR83Az3BXu6NNQbD5b3AShxFAs1TF6mdR//jXK+/xs09ItiwRop+eP4gK0\nvf4gPjRdY4CWMAZnCqYnTbD54kOpydcUF2QaNDR7QxN/YkP1gO0AOms6oViUpMpQUZTo4IRYied3\njDggItG2UKpQLNUxepncfIxY4YzZmwlH8BW+xADtUkewu/4wA7SEMThTUBqUuKozthoEQm3aa4uu\nxQ1uj4Reymud4Uk/jWONUDepSS3WpGpz1BZ3XLpQLMUxepnYnS70O+rgW1Wd76VQkUkXoPfVHcRH\nDNCSwuBMI1J1pgpG66gVMCD6PMy4UE1zrTMy6s64M7nFGldtRjYA7cwciqU2Ri8TdXwSjb/uZpuW\n5lVsgP5kaDsuGUawiwFaUhicaUSqzlTBqN6uonGsMfSElLLBtNVmhLHNCEOjIeXGHofXEX1iSqoN\nQJlCMfbcpa7xk8swjgd1F5xs1+qTCSq+H95ExAAtLQzOGZieNEGBEh28HvvkE2WzgtVjoSekpKs2\nIyKj7hI39tQEamAdtUafmJJqA1CmUEw8dymzOV2YMii4fJ8930uhEmKGgQFaYhicM1AaFKhb1dAj\nwBAfbLeyqzW2moxUr6lasgzF3NidLlzd3oSJSv3N42XVqX8M0NLB4Mwg3QacW93VGq0mw9Urr1Pe\nmkX9fqw47dHNbloqXukCdEfdIRxngBYFBmcGM11rvJVdrbHVJK9T3jrbh50QTSvIx4hRaYoN0DeH\ntsNlGMZOBmhRYHBmIV2wzdWuVrZkb539mAtjNWZ4tq3K91Jmje3a4mSGAX/uuw2daQKU9IfBmYWZ\ngo3VYgHQNNidLrh3roGm8rc0Fab0AXoQH5s8+V4e5YB/y9wiVov5t/SrflRf8fL6JulCYoBeNAzj\n/vpD2FF3MN9LoywxOEn3bo7Z09f9m6mwXVs6YgP0x0PfwFfG4XwvibLE4CTdsztdGLIvwY01tfle\nClHOzDDgFd8f4NK1ffleCmWJwUm6pkxOwXq8C91FUG1GsOosTWY+Hlk3GJykayt/1wPTSKAo2rRE\npA8MTtI1u9MFTQTdO1mlEdHCYHCSrtmcLni2rcT40sX5XsqcYruWqHAxOEm3TN5xrPq/HrZpiWhB\nMThJt5o+vgRlappj9ohoQTE4SbdWH3NhorwMPdsb872UecF2LVFhYnCSbtmcLly+z4bpMm7jJ6KF\nw+AkXapyD6H24kDRX99k1UlUeBicpEvFNGaPiPSFwUm6ZHd2YmRlJfpvq8/3UoioxDA4SX+mp2H7\nsBNdu9cCUvxPpWG7lqiwMDhJd1ac9mDxwCjbtESUFwxO0p3I9c3u3Xz+JhEtPAYn6Y7d6ULfxuXw\nr6jM91IWDNu1RIWDwUm6YhidgOWEm21aIsobBifpSuNv3DBMTDE4iShvRNO0uT+pyHUA7jk/MRFR\ncbNqmlaX70XQzOYlOImIiIoVW7VEREQ5YHASERHlgMFJBUlEpkTkTMw32yzOUSMiL8/96qLnFxH5\nsYi4ROSciGyZr88iosLB5zFRoRrTNG3zLZ6jBsDLAP4plzeJiKpp2lQWhz4EYF34210A3gr/l4iK\nGCtO0g0RUUXkDRE5Ga7wvhN+vUJEPhSRUyLyuYg8EX7L3wFYE65Y3xCRHSLyfsz5fiIiz4W/3y0i\nfy8ipwDsE5E1InJERH4vIr8RkQ0plvQEgHe1kE8B1IhIw7z+IhBR3rHipEK1SETOhL/fpWnaUwC+\nDcCradodImIC8ImIHANwBcBTmqYNi8gyAJ+KyHsA/hrA7ZHKVUR2ZPjMAU3TtoSP/RDAdzVNuygi\ndyFUte5MOH5V+LMjesKveWb5cyYiHWBwUqFK1ardA2CTiDwd/nE1Qm3SHgA/FJF2ANMIhdfyWXzm\nfwOhChbA3QD+V24+fcU0i/MRURFicJKeCIBXNE07GvdiqN1aB2CrpmmTItINwJzi/UHEX55IPMYf\n/q8C4EYW11ivAmiM+bEl/BoRFTFe4yQ9OQrgeyJiBAARWS8i5QhVnn3h0LwfgDV8/AiA2EnwbgC3\niYhJRGoA7Er1IZqmDQPoEpF94c8REWlJceh7AJ4Jf/0bCLWR2aYlKnKsOElP3gZgA3BKQj3U6wCe\nBPALAL8Ukc8BfAbgSwDQNG1ARD4RkS8AHNY07S9F5H8AfAGgC8DpGT7rmwDeEpG/AWAE8F8AziYc\ncwjAwwBcAEYBPD8nP0siKmgcuUdERJQDtmqJiIhywOAkIiLKAYOTiIgoBwxOIiKiHDA4iYiIcsDg\nJCIiygGDk4iIKAcMTiIiohz8P/Dmw6rMQ9ZMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b959400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "X, y = make_blobs(random_state=42)\n",
    "linear_svc = LinearSVC().fit(X, y)\n",
    "mglearn.plots.plot_2d_classification(linear_svc, X, fill=True, alpha=.7)\n",
    "mglearn.discrete_scatter(X[:,0],X[:,1],y)\n",
    "line = np.linspace(-15,15)\n",
    "for coef, intercept, color in zip(linear_svc.coef_, linear_svc.intercept_, ['b','r','g']):\n",
    "    plt.plot(line, -(line * coef[0] + intercept) / coef[1], c=color)\n",
    "plt.legend(['Class 0', 'Class 1', 'Class 2', 'Line Class 0', 'Line Class 1', 'Line Class 2'], loc=(1.01, 0.3))\n",
    "plt.xlabel(\"Feature 0\")\n",
    "plt.ylabel(\"Feature 1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### k-Nearest Neighbors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FwSp7dOscZrUYqlMErEivvv113dbhune/AbU+f+kiYNVVVYGsquTk5Jjd9u67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\nvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d32e5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.plots.plot_knn_classification(n_neighbors=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This image explains what a k-Nearest Neighbours classifier does. It looks at the existing examples in the training set and takes n of them with the shortest distance to the test example. The distance is often the [euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance). It can be used for regression, too. To do that the algorithm takes the mean of the target value of the n nearest neighbors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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x5MgRvPTSS/jDH/6gOyRCcDxAwWSMQpIZ6yER6WbG+yo3dzVuugmoqACiopre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\nxGSMiIiISKP/D6VFQDRmlnjmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b336fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.plots.plot_knn_regression(n_neighbors=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Decision Trees\n",
    "Decision Trees are conceptionally the easiest of the machine learning algorithms. The algorithms arrives at a prediction by just traversing a tree. Look at the following example for animal classification."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11dae20f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.plots.plot_animal_tree()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to predict which animal is in front of you, you can just start at the root node and move your way down. Has the animal feathers? Yes? Can it fly? No? It seems that you have a penguin in front of you.\n",
    "\n",
    "#### Building a decision tree\n",
    "An importang concept for building decision trees is [entropy](https://en.wikipedia.org/wiki/Diversity_index). What the algorithm tries to do while building the tree is picking the feature that splits the data into more homogeneous sets. \n",
    "You can find a great explanation [here](http://www.saedsayad.com/decision_tree.htm). \n",
    "\n",
    "#### Ensembles of Decision Trees (Random Forests)\n",
    "To prevent overfitting of a single decision tree often times multiple decision trees are used. The form an ensemble which is often called **Random Forest**. The single trees are restricted to have only a certain number of levels. This forces them to focus on few features. This results in very different decision boundaries for each tree. The random forest classifier then takes the results of the single trees and average the predictions to generate its own prediction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Neural Networks (or Deep Learning)\n",
    "Neural networks are used very often in several different areas. Here we take a look at a very simple neural network. The **Multilayer Perceptron** is roughly modeled after the human brain. First take a look at a perceptron. It has some inputs *x* with corresponding weights *w* and computes output *y*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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    "As you can see every input is connected to every perceptron of the next layer. Depending on the results of the computation (by forward propagating the results through the network) the weights are adjusted (using [backpropagation](https://en.wikipedia.org/wiki/Backpropagation)). Now think about image classification (a classical field in computer vision). Let the inputs be the RGB values of an image. If it has size 400x400 there are 16000 inputs. Usually in modern deep learning there are a lot of hidden layers. This results in high computing power requirements. However the results are often really good. Just take a look at the powers of the [Google Vision API](https://cloud.google.com/vision/). Upload a random image there and see what it can identify. Neural networks are the foundation of that."
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