notebooks/02-IntroMachineLearning_update.ipynb

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   "source": [
    "# 02 - Introduction to Machine Learning\n",
    "\n",
    "by [Alejandro Correa Bahnsen](albahnsen.com/)\n",
    "\n",
    "version 0.1, Feb 2016\n",
    "\n",
    "## Part of the class [Practical Machine Learning](https://github.com/albahnsen/PracticalMachineLearningClass)\n",
    "\n",
    "\n",
    "\n",
    "This notebook is licensed under a [Creative Commons Attribution-ShareAlike 3.0 Unported License](http://creativecommons.org/licenses/by-sa/3.0/deed.en_US). Special thanks goes to [Jake Vanderplas](http://www.vanderplas.com)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What is Machine Learning?\n",
    "\n",
    "In this section we will begin to explore the basic principles of machine learning.\n",
    "Machine Learning is about building programs with **tunable parameters** (typically an\n",
    "array of floating point values) that are adjusted automatically so as to improve\n",
    "their behavior by **adapting to previously seen data.**\n",
    "\n",
    "Machine Learning can be considered a subfield of **Artificial Intelligence** since those\n",
    "algorithms can be seen as building blocks to make computers learn to behave more\n",
    "intelligently by somehow **generalizing** rather that just storing and retrieving data items\n",
    "like a database system would do.\n",
    "\n",
    "We'll take a look at two very simple machine learning tasks here.\n",
    "The first is a **classification** task: the figure shows a\n",
    "collection of two-dimensional data, colored according to two different class\n",
    "labels. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Import libraries\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set();\n",
    "cmap = mpl.colors.ListedColormap(sns.color_palette(\"hls\", 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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qN8CU9gH8Nu76Bk6Qw+FQQp+ztStQ8WhWbllIaQMzLatn6J/u1pz6TbXAFa95Kafoopvv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\nwMYIagAAbIygBgDAxghqAABs7P8DII/Hg4HdEEoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xac094a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a random set of examples\n",
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, Y = make_blobs(n_samples=50, centers=2,random_state=23, cluster_std=2.90)\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=cmap)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A classification algorithm may be used to draw a dividing boundary\n",
    "between the two clusters of points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDClassifier(alpha=0.01, average=False, class_weight=None, epsilon=0.1,\n",
       "       eta0=0.0, fit_intercept=True, l1_ratio=0.15,\n",
       "       learning_rate='optimal', loss='hinge', n_iter=200, n_jobs=1,\n",
       "       penalty='l2', power_t=0.5, random_state=None, shuffle=True,\n",
       "       verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDClassifier\n",
    "clf = SGDClassifier(loss=\"hinge\", alpha=0.01, n_iter=200, fit_intercept=True)\n",
    "clf.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Plot the decision boundary. For that, we will assign a color to each\n",
    "# point in the mesh [x_min, m_max]x[y_min, y_max].\n",
    "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, .05), np.arange(y_min, y_max, .05))\n",
    "Z = clf.predict(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KOoI33ngdhYWFcDqdOHbsmGtWvT+o1WokJCQiJiYGs2e/hbCwMJkSE/kuFjKR\nlxBFO3JyjuG112a7nu+7f//+i+75ValUiI6ORmxsHGbMmIXQ0BAEBYXA399fxvRExEIm8kCCAOTm\nHsPHH8+DzWZDbm4udu/eDbPZfNGh59DQULRt2w6TJt0DnU6Hrl27ISKiuYzpieivsJCJPMCZM8fx\n00+r4HSK2Lx5E9LT01FaWgqLxVJrPb1ejy5duqBHj97QaLS4/fYJaNWqtUypiehasJCJFKas7Bzy\n8nJgs9kwb977OHz4ME6dOoXq6toz2wmCgPbt26NFi0jo9XpMnfos4uM7yJSaiK4XC5lIRg6HFVar\nGZWVlZg16yUcO3YMhw4dqvWMX6CmfGNiYuDvH4CgoCC88MJL6NAhwTVvPBF5PhYyUQMRhJr/SkuL\n8cYbc5CdnY3ffvsNFosFoii6zv0KggCTyQS1Wg2TyYQnnnganTsnITIySubvgIjqEwuZqB5VVpZh\n0aJPsW/fPmzZsgUOhwNWq7XWHrCfnx/UajViYmJxyy1jMHjwUCQmdpExNRHJgYVM5CZmcwV27NiG\n5cuXYuvWrRBFESUlJSgrK7to3ZiYGHTp0hXjx09CcvKAhg9LRIrDQiaqA7PZjPz8E/j3v/+F3bt3\nQ5IkHD9+HMXFxRet26JFC9xwQxQef3wabrxxEADI8rAFIlI2FjLRFUmwWqvxxhuvIivrKOx2O/bs\n2YPS0lI4HI5aa4aFhcFkMuGxx6aiY8dOMBoD0bx5C5lyE5EnYSET1SLBbrfhk0/eR0FBAcrKyrB+\n/XqUl5dfdOVzQEAAmjVrjokT74bJ1BhRUXHo27efTLmJyNOxkMmn2e1WrFu3CpWVlcjIyMCKFStQ\nVlZ20aFnlUqFZs2a4cYbB0Kr1WPw4BsxZMhNMqUmIm/EQiaf4XTacPLkcTidDixbthQrVqxAYWEh\nCgoKLlrXZDKhbdt2UKlUGD36FkyefO+f/tx3H65ORPWDhUxeSoLNZgEg4dNPP8KGDRtw5MgR5Ofn\nQ5KkWg9bCA0Ndd33O378RNx++wQ+apCIGhwLmbyABEEQIEkiFi36FLt27cQvv/yCc+fOAUCtKScD\nAgJgMBig1+sxfvydSE6+Eb169eFVz0QkOxYyeSRRFLFmzQ9IT9+DpUuXorKyEk6n01XCAKDRaKBS\nqdCoUSOMHDkaSUldMWHCZJYvESkSC5kUTxSdyMw8hF9//QVffLEIFosFZrMZp06dumjdwMBAdO/e\nAz169MabebLpAAAah0lEQVQTT0xj+RKRx2Ahk6JIkojq6gqsXLkcX331JZxOJwoLC5GTk1PrvC9Q\nc/g5NjYOAwcOwhNPTIdKpYKfnx9LmIg8EguZZCNJElQqYNmyb/HjjyshiiIOHjyIvLw8WK3WWgXs\n5+eHxo0bY/jwkRgzJhVqtQYdOnSCVquV8TsgInIfFjI1GEmSsHHjGuzatRN2ux1r167B6dOnUVZW\nBlEUXetpNBoEBwdj6NDhaNeuPYxGI8aPnwidTidjeiKi+sVCpnohiiIOHdqL06dPoLi4BPPnf4qi\noiKcPn26VvkCgJ+fP/r27YvQ0FA0aRKBZ575OwwGg0zJiYjkwUKm6/LHPb3l5cWwWi3IyDiMd955\nG4WFhcjOzobT6ay1vl6vR3x8PHQ6HVq2bIVXXnkDAQEBMqUnIlIOFjJdk5rzuk5IkoS0tB348MMP\nkJubi4yMDIiiCKfT6Tr3q9Pp0Lx5c6hUKiQmdsZTTz2D2NiW0Ov18n4TREQKxEKmy/rjguW9e3dh\nyZKvsWvXLmRmZkKSJJjNZtfTjjQaDQICAqBSqdC9e0/cfPNYDBkyDEFBwTKmJyLyHCxkqkWSJGRn\nZ+DXX3/FkiVf4/jx4wCAs2fPwm63A6h5lq9arYZarUbv3n2QkNAZjz76BEJDOd0kEVFdsZB9XHFx\nPjIzM/HWW2+gsLAQTqcTubm5sNlstdZTq9Xo3DkJsbFxmDXrdc71TETkZixkH+JwWJGTk4U5c2ah\nvLwc1dXVOHDgACwWS6311Go1YmNjERsbh5dffg2hoaEICDDy3C8RUT1iIXspQQBycrIwb95c2GxW\nnDx5Ert374bFYnEdegZqnvMbFhaGtm3bYsqUv0Gv16Njx0SEh4fLmJ6IyPewkL3EqVM5WLFiOZxO\nEVu3/or09HSUl5dftPfr5+eHxMRE9O3bH2q1Grfeejvi4lrKlJqIiP7AQvZAJSVFOHLkMBwOB+bP\n/y8OHTqE06dPw2w211pPEAR07NgRN9wQDb1eh8cffxrx8e1lSk1ERJfDQlY4m80Mi6UalZUVmDXr\nZWRnZyMjIwNVVVW11hMEAXFxcTAaAxEYGIgZM15G+/adoNFwiImIPAH/tVaUmikly8pK8Pe/T0VO\nTg527twJi8UCURRd9/wKgoDw8HBoNBo0bhyGqVOfRVJSFzRtGiFneCIiug4sZBkJAlBRUYb58z/C\n/v378euvv8Jut8Nms6G6utq1XkBAAARBQIsWLZCaejsGDBiMTp0SZExOREqzYP4P2PVbJQQB6NU3\nFHdMGCZ3JLpGLOQGZDZXYPPmDVi1ahW2bv0VkiShtLQU5eXlrnUEQYAgCIiNjUX37j0xfvxE9O7d\nV8bURKR0mzfvwK5tETDoIwEAWzceQ6vWe9G1Kz+4exIWcj2x2SwoKDiFuXP/g9270wAAeXl5KCkp\nuWjdyMhIxMTE4tFHn8SAAYMAACZTIIqKKho0MxF5ptycfBj0PV3Lel0sjmb+xkL2MCxkN5AkJ8zm\narzxxmwcPXoUDocDe/fuRWlp6UVPOzKZTGjSJBxPPjkNCQld4Ofnx3t+qd4dOpSJPWkZaNm6BXr0\nSJI7DrlZUlIb7Nx6AAZdBwCAxb4H3bt3lDkVXSsW8jWTYLfb8MEH/8aZM2dQWVmJjRs3uma+upDR\naITJZMJdd01BeHg4IiOj0L17z0u8L1H9WP/zdnz/dQUMuh7YviUH2Vk/4o47h8sdi9yoQ8e2uGVc\nCTZv3AQBwE1DYhHXMkbuWHSNWMhXYLdbsXLlUlRWVuDo0aNYtWoVysvLLzr0rFar0bx5cwwePAR6\nvQHdu/fATTeNlSk10Xkbf86DQdcfAGDQx2D71lzccafMocjtBg3uhUGDe8kdg64DC/kCDocNOTlH\n4XSKWLlyOVasWIGioiIUFhZetG6TJk3QoUNHqFQqjBgxGhMn3t3wgYmIyGv4bCGLohM2mxmSJGL+\n/E/w888/IysrC2fOnLlo3UaNGiE8PBxqtQbjx0/A+PET+Zxf8hgDBt2A777eDz9dR1isOejVnz+7\nRErkE4UsSSLUahWcThELF36MHTt2YPv27Th37hwkSao137PRaIS/vz/0ej3uuGMSBgwYhC5dukIQ\nBBm/A6K6GzioJ5pGZGJ32g60bNkCPXvx/DGREnltIYuiiFWrvkd6+h788MMPqKiogCiKKC4udq2j\n1WqhVqvRuHFjjB59C7p1647U1PEsX1KkgoJC7E47gDZtYhAbd20X7MTHt0Z8fOt6SkZE7uBVhbx4\n8QJ88ME8WCwWWCwWnD59+qJ1goKC0Lt3b3Tv3guPPPIky5c8wq5d+/HZx0ehUXXGD98dw5ARObhl\n7EC5YxGRG3lVIX/6ac2Tj/5gNBrRqlUrDBgwCFOnPguVSgWNRsMSJo+zcvkh+OkGAAC0mo5Yv+5n\n3OKDF/FvWL8D69bkQpIE9Ogdhptv5ocS8h5uLWRJkjBz5kwcOXIEOp0Os2bNQmRkpDs3cVlz536E\nRYvmY9y4O6DRaNG6dRs+7Yi8giSpay2LokqmJPLJzTmOJYvPwV8/AACwbtVRRDRNR/ceifIGI3IT\nt/5Wr1u3DjabDYsXL8a0adMwZ84cd779FbVu3RYvv/waOnVKRHx8e5YxeY2uPUwwWzMBAFZbEeI7\nqK/wCu+zc+cBGLTny9ega4VDB/NkTETkXm5trLS0NPTr1w8AkJCQgAMHDrjz7Yl81qhR/WEKS8f+\nfdsR0SwYI0eNkztSg+vYqQ02rj0Mf0PN9JBWWx5iWzaVORWR+7i1kCsrKxEYGHj+zTUaiKIIlcr3\nDq8RuVuPnono0dN3D8+2bdsSQ0edwKb16yGKArr3CURy8ki5YxG5jVsL2Wg0oqqqyrXMMiYid7rp\n5htx081ypyCqH24t5KSkJGzYsAHDhg1Deno6Wre+/H2PoaH+0Gh871zY1TKZAq+8EsmG46N8HCNl\n4/jUJkiSJLnrzS68yhoA5syZg5iYS09gwOf9Xhqfh6xsHB/l4xgpmy+Pz6U+iLh1D1kQBLz44ovu\nfEsiIo8jiiLOnDmN4OBgGI3cC6Srw/uCiIjcqKysFC/PXILyklio1CUYOjIUYzirGl0FXnFFRORG\nC+avAewjERzYHoH+fbF6ZRHMZrPcscgDcA+ZiBqcxWLBd9+uhdMp4aabkxEcHCJ3JLexWTUQhPP7\nOpIzBBUVFfDz85MxFXkCFjIRNSir1Yp/PrcIkm04BEGNnTu+w8uzxzZ4KWdnH8dXn2+D06FFuw6B\nGHfbELe8b2KXplh67Cj89K0gik6EhJ2AyeSe9ybvxkImoga1ds0WOCyDodVoAQA6DMfS7zfirrtv\nqdP72e12fPzhMpScE9DIJOH+B2654rS5VqsV7761ETrVMADA5nUnEOC/GSNGJdcpw4UGD+4NlbAd\n6Xu2Qm9w4u577uADbeiqsJCJqEFpNGpIosO1LEki1Oq6X87yztvf4MzxvlCr9Tibb8G773yDaU/f\ncdnXnDx5ApaqltD9fgG0QR+JzMytGFHnFLUNHNQTAwe56c3IZ/CiLiJqUClDkhEQshE2ewUcDgug\nWYWxtw6u8/vln9ZArdYDADQaAwpOX3k/o0mTJlBpzj8v3e6oRkgI/zkkeXEPmYgalFqtxkuz7sHq\n1ZvgsDswdNgkGAyGOr+fwc8GW9WFy9YrviYwMAip41tg+fdrYbdpEBltx6S7JtQ5A5E7uHWmrmvl\nq7O0XA1fnsXGE3B8lCMzMxsfvrcFFeUBCAyuxCOP34jY2KirHiNJkniOVwa+/DvUIDN1ERE1tNat\nY/HWu7GwWq3Q6/XX/HqWMSkFC5mIPFZ5eRk+eH8lKit1aNJEwt8eHnPFK6yJlIpXMRCRx3rz9aUo\nPHkjzGX9cOxwd8x7/3u5IxHVGQuZiDxWcZHeNSuWRmNA4RkefibPxUImIo8VEGh3/b8kSfDzv/IV\n1kRKxUImIo91z329Ae1qVFo2QG/8CQ8+PEzuSER1xqsfiMhjtW0bhzfejpM7BpFbcA+ZiIhIAVjI\nRERECsBCJiIiUgAWMhERkQKwkImIiBSAhUxERKQALGQiIiIFYCETEREpAAuZiIhIAVjIRERECsBC\nJiIiUgAWMhERkQLw4RJEbrJ5005sWJ8LAUDK0Jbo1buz3JGIyIOwkInc4NChTHz9ZQn8dMkAgC8X\npKFp00aIiY2SORkRXcjpdOLLz1ehuNiB1m3CMHxEP7kjufCQNZEbpO3KgJ8uwbWs1yZh+459MiYi\nor/y5utfIW1be5zM7o1VS/3wzddr5I7kwkImcoMboprAYjvlWrbYjiMutrmMiYjorxzP0UCrDQAA\nGPSROLivXOZE57GQidygf/+eSOx2AtW29ai2/YzufYrQvUeS3LGI6E+0WketZc2fluXEc8hEbjLl\nvptx7xQJACAIgsxpiOivjL4lDt9+vQWivTn0/lkYP6Gv3JFcWMhEbsQiJlK2wSm90L1HGc6cyUdU\n1DgYDAa5I7mwkImIyKcEBQUjKChY7hgX4TlkIiIiBeAeMhFdNavVijdf/xoFZ3Qw+Nkx8a6u6NSp\nrdyxiLwC95CJ6Kp9/OFynDszAHr1AEi2FPz3o98gSZLcsYi8AguZiK5aRbkaarXOtWypDoLZbJYx\nEZH34CFrIrpqTcJVKDhVAa0mEABgDCqBv7+/zKmUxel04p23/4eTeRro9Hbcfkcikrq0lzsWeQAW\nMhFdtXum3IQPrN/i5AnAYLDh7ilD5I6kOIsWrMSJYz2h1QZAtALzP1mLjp1aQ6vVyh2NFI6FTERX\nTaVS4eFHx8kdQ9HOFjlcUzMCgM0SgXPnzqJp0wgZU5EnYCETeTlJkvDvd/6HoxmASu3EkOGRGDU6\nWe5Y9cLhcMBiscBoNMqWIaK5HieyS6HThQAADP6nEBbWX7Y85DlYyERe7rtv1yL7SCL8dKEAgJVL\ndyGpy2k0a9ZM5mTutez7DfhpZT5Epx/Cm53Du3MfliXHhDtHoKL8O+TmOKHTOTBlYm9oNPynlq6M\nPyVEXq6wsBo6bahrWa2KwbFjeV5VyCUlxfhxRRkC/QcCACpLrJj33veYMHFEg2cRBAF/e/jWBt8u\neT7e9kTk5dq3bw6z9dj5L6j3e91kHmfPnoMkNnEtq9V6VFaKMiYiunbcQybycsn9u6GkdD327NwC\nldqBybcmIjg4RO5YbhUVFQV/4xZIUiwEQYDZehTdukfJHYvomgiSjNPsFBVVyLVpxTOZAvn3o2Ac\nH+UpKCjEogUb4HBokJgUjkmThnOMFMyXf4dMpsC//Lpb95CTk5MRHR0NAOjcuTOeeuopd749EdEl\nhYc3wdPP3C53DKI6c1sh5+XloX379pg3b5673pKIiMhnuO2irgMHDqCgoACTJ0/Ggw8+iJycHHe9\nNRERkder0x7ykiVLsGDBglpfmzFjBh588EEMHToUaWlpmD59OpYsWeKWkEREvuS/Hy9FZoYNao0D\nY25tj27dE+SORA3AbRd1WSwWqNVq13yt/fv3x6ZNmy77GofDCY1G7Y7NExF5hf8t/gnLvgmCTltz\nG5fVuRkf/jcVQUFBMiej+ua2c8hz585FSEgI7rvvPmRkZCAi4srztpaUVLtr817Hl69A9AQcH+Xz\n1DE6eKAQOm1L17LdEovfduxHQmInGVO5n6eOjzvU+1XWDzzwAKZPn45NmzZBo9Fgzpw57nprIiKf\n0byFEUcPnYNe1xgAoNJmIyaWT9XyBW4r5KCgIHz44YfuejsiIp80ZuxgFBV+h6NHnNBonbjzjrYI\nCgqWOxY1AM7URUSkIIIg4MGHOBe2L+Jc1kRERArAQiYiIlIAFjIREZEC8BwyEXmdgoIClJcXwmgM\ng0rF/Q7yDCxkIvIqH37wPdK26yEIgWjcZDlmvjwZOp1O7lhEV8SPjkTkNbKysrB7RwiCA7sgyNga\nloqh+PKLH+WORXRVWMhE5DXOFpVAow5zLavVOlgssj3yneiasJCJyGskdu4IrWEH/pii32zdib59\n28mciujq8BwyEXkNg8GAF14aiy+/WA+9zg/de8SiQ8c21/w+6ekHkb4nC9Ex4RgwoGc9JCW6mNue\n9lQXvjqx+NXw5YnXPQHHR/nqOkZrVv+C5d/Z4aeLh8V6Al17nsFd946uh4S+zZd/hy71cAkesiYi\nusAvW87ATxcPADDoI7F7V5XMichXsJCJiC4gQPzTF84fRJTxgCL5AJ5DJiK6wOAhcfjfF2kwaDvD\nYs1C8uDGyMg4hk8+/AWVFXqENrZg2vTRCAtrfMn3+ObrNdi1oxSCIGJgSiSGDO3TgN8BeSoWMhHR\nBfold0WLyOP4bXsa2sbHICGhPZ59ehEExzAE+gH2KgkfzVuNvz8/4S9fv3VrGjb/HASDLgEAsPzb\ndMS1zEFcXExDfhvkgVjIRER/EhMThZiYKNdydZUeht//tRQEAdXV2ku+9sjhkzDozl+Zrdd2wJ7d\ne1nIdEU8h0xEdAWNwsyQpJpzyw6HGeERl163dZvmsFhzXcsW+0EkJrat54TkDVjIRERX8PQzYxAe\nuQH+wVvQsv1OPPTwmEuu26dvV/S9sRTQbIKg24DRY/zRslVsA6YlT8X7kBXKl+/R8wQcH+XzlDES\nRREFBfkICgpGQECA3HEajKeMT3241H3IPIdMRFelqqoKX325Bg47kDK0M+LiouWO5PGKi4sx66Xv\nUVEaA7XmLEbdEoGRo/rJHYtkwkImoiuy2Wx44R9fAvaRUKnUOLB3C556Bizl6/TZp2shOEYiOFAA\nAKxY9jOGDLVDq730RWPkvXgOmYiuaNeudFgre0GlUgMA/HT98PO6dJlTeT67XQNBEFzLojMIZnO1\njIlITixkIrqioCAjnGK5a1kUHeBO3PXr1KkJzNYcADV/p41NNeeSyTfxkDURXVGHDvFoFf8lMg+K\nUKkC4R+0A7ePnyh3LI83fGQ/qNS/4OD+X2HwE3H3vX892Qj5Bl5lrVC+fAWiJ/DV8Tl8OAOVldVI\nTOyo+POcvjpGnsKXx4dXWRPRdWvXjhNcENUXnkMmIiJSABYyERGRArCQiYiIFICFTEREpAAsZCIi\nIgVgIRMRESkAC5mIiEgBWMhEREQKwEImIiJSABYyERGRArCQiYiIFICFTEREpAAsZCK6opzsXCxf\ntgYnT56SOwqR1+LTnojoslat3IIVS6th0LbD6pW7cfudp5Hcv1uDbLuwsBAVFeWIjo6BWq1ukG0S\nyYWFTESXtX7tKQQYbgQA+Ku7Y81PGxukkBfM/wFbN6sAKRjBjTdg5st3wt/fv963SyQXHrImossS\nRdVll+tDQUE+ft2sQZCxK4ICW8FpGYlFC36q9+0SyYmFTESXldDZDxZrzbljizUbXbqH1Ps2i4tL\nIUihrmWVSg2bTaj37RLJiYesieiy7rpnNFpEbkVOznbEx7dA7z4p9b7NVq1awhgyH5IjCoKgQrV1\nD3r1aVnv2yWSEwuZiK5o0ODeDbo9jUaDmS/fjkUL1sDpUKNnnzh07dqxQTMQNTQWMhEpUmBgEB5+\nNFXuGEQNhueQiYiIFICFTEREpADXVchr167FtGnTXMt79+7FbbfdhgkTJmDu3LnXHY6IiMhX1LmQ\nZ82ahX/961+1vjZjxgy8/fbb+PLLL7Fv3z5kZGRcd0AiIiJfUOdCTkpKwsyZM13LlZWVsNvtaNGi\nBQCgb9++2Lp163UHJCIi8gVXvMp6yZIlWLBgQa2vzZkzB8OHD8dvv/3m+lpVVRWMRqNrOSAgACdP\nnnRjVCIiIu91xUJOTU1FauqVbz0ICAhAZWWla7mqqgpBQUHXl46IiMhHuO0+ZKPRCJ1OhxMnTqBF\nixb45Zdf8Oijj172NaGh/tBo+ASXSzGZAuWOQJfB8VE+jpGycXxqc+vEIC+++CKefvppiKKIPn36\noFOnTpddv6Sk2p2b9yomUyCKiirkjkGXwPFRPo6Rsvny+Fzqg4ggSZLUwFlcfHUwroYv/7B6Ao6P\n8nGMlM2Xx+dShcyJQYiIiBSAhUxERKQALGQiIiIFYCETEREpAAuZiIhIAVjIRERECiDrbU9ERERU\ng3vIRERECsBCJiIiUgAWMhERkQKwkImIiBSAhUxERKQALGQiIiIFcOvjF8m9kpOTER0dDQDo3Lkz\nnnrqKXkDESRJwsyZM3HkyBHodDrMmjULkZGRcseiC4wdOxZGoxEA0KJFC8yePVvmRPSHvXv34s03\n38SiRYuQl5eH//u//4NKpUKrVq0wY8YMuePJjoWsUHl5eWjfvj3mzZsndxS6wLp162Cz2bB48WLs\n3bsXc+bMwfvvvy93LPqdzWYDACxcuFDmJPRnn3zyCZYtW4aAgAAAwJw5czB16lR07doVM2bMwLp1\n6zB48GCZU8qLh6wV6sCBAygoKMDkyZPx4IMPIicnR+5IBCAtLQ39+vUDACQkJODAgQMyJ6ILZWRk\noLq6GlOmTMHdd9+NvXv3yh2JfhcVFYX33nvPtXzw4EF07doVQM3RwG3btskVTTG4h6wAS5YswYIF\nC2p9bcaMGXjwwQcxdOhQpKWlYfr06ViyZIlMCekPlZWVCAw8/3BxjUYDURShUvGzrRIYDAZMmTIF\n48aNQ25uLu6//36sXr2a46MAKSkpOHXqlGv5wkkiAwICUFFRIUcsRWEhK0BqaipSU1Nrfc1isUCt\nVgMAunTpgqKiIjmi0Z8YjUZUVVW5llnGyhIdHY2oqCjX/4eEhKCoqAjh4eEyJ6M/u/D3pqqqCkFB\nQTKmUQb+S6JQc+fOde01Z2RkICIiQuZEBABJSUnYtGkTACA9PR2tW7eWORFd6Ntvv8Wrr74KACgo\nKEBVVRVMJpPMqeivxMfHY+fOnQCAzZs3o0uXLjInkh8fLqFQ5eXlmD59Oqqrq6HRaPDCCy8gJiZG\n7lg+78KrrIGaC1M4Lspht9vx3HPP4fTp01CpVHj66aeRmJgodyz63alTpzBt2jQsXrwYubm5eP75\n52G32xEXF4dXXnkFgiDIHVFWLGQiIiIF4CFrIiIiBWAhExERKQALmYiISAFYyERERArAQiYiIlIA\nFjIREZECsJCJiIgUgIVMRESkAP8PCdxHdDGu+XoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xabc4400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.contour(xx, yy, Z)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=cmap)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This may seem like a trivial task, but it is a simple version of a very important concept.\n",
    "By drawing this separating line, we have learned a model which can **generalize** to new\n",
    "data: if you were to drop another point onto the plane which is unlabeled, this algorithm\n",
    "could now **predict** whether it's a blue or a red point."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next simple task we'll look at is a **regression** task: a simple best-fit line\n",
    "to a set of data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xab424e0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kn8+nyZMny+v1qrCwUKNHj1YkEtHEiRM/85pAIDfhIjMB/dO/m7m5fzf3LtF/PBIK5KKi\nItXX12vJkiU6ffq0PvjgA/n9/ite09bWnVCBmSAQyKV/+ne6DMe4uX839y7Rf7x/jCQUyN/73vf0\n17/+VT/5yU9k27Y2btwoj8cT+0IAAHBZCR8MsmbNmmTWAQCAq3EwCAAABiCQAQAwAIEMAIABCGQA\nAAxAIAMAYAACGQAAAxDIAAAYgEAGAMAABDIAAAYgkAEAMACBDACAAQhkAAAMQCADAGAAAhkAAAMQ\nyAAAGIBABgDAAAQyAAAGIJABADCA1+kC4IxIpEPBYKNaWvJkWZ0KhYrl9/ucLgsAXItAdqlgsFHh\ncKkkj5qabEn12rVrntNlAYBrsWTtUi0teZI8/SNP/xgA4BQC2aUsq1OS3T+yZVldTpYDAK7HknUS\nxbMv6/QebihULKm+//27FArNGLH3BgB8GoGcRPHsyzq9h+v3+9gzBgCDsGSdRPHsy7KHCwAYjEBO\ngkikQ2VlL+idd/6loe7LsocLABhsWEvWZ8+e1R133KGnnnpKhYWFyaop7Xy0/Nwp6Vn5fB/ou9/1\nXnFflj1cAMBgCQdyX1+fNm7cqDFjxiSznrT00fKzT9JdKih4Ubt2/d8Vr2EPFwAwWMJL1o888ogW\nLFigz3/+88msJy2x/AwAGK6EPiE///zzuvrqq3XzzTfrt7/9bbJrSjssPwMAhstj27Yd+2Uft2jR\nInk8H35D+Pjx4yosLNSOHTt09dVXJ71AAADcIKFAHqy0tFSbN2+O+aWutrbu4bxNWgsEcumf/p0u\nwzFu7t/NvUv0HwjkxvX6Yd/29L9PygAAIHHDPqlr9+7dyagDAABX42AQAAAMQCADAGAAAhkAAAMQ\nyAAAGIBABgDAAAQyAAAGGPZtT24TiXQoGGzsPyazU6FQsfx+n9NlAQDSHIEcp48etehRU5MtqZ6n\nNgEAho0l6zh99KhFSfL0jwEAGB4COU4j9ajFSKRDZWUv6Lbb/qyysufV3t6RkvcBAJiBJes4jdSj\nFlkaBwB3IZDj5Pf7RiQYWRoHAHdhydpQI7U0DgAwA5+QDTVSS+MAADMQyMOUqvuSR2ppHABgBgJ5\nmPjyFQAgGdhDHia+fAUASAYCeZj48hUAIBlYsh4mvnwFAEgGAnmY+PIVACAZWLIGAMAABDIAAAYg\nkAEAMACBDACAAQhkAAAMQCADAGCAhG576uvr04YNG9Ta2qre3l4tW7ZMxcXFya7NEak6mxoAgCtJ\nKJD37t0rv9+vUCikzs5OzZ07N2MCmbOpAQBOSCiQZ8+erVmzZkmSotGovN7MOV+Es6kBAE5IaA95\n7NixGjdunM6dO6eVK1dq1apVya7LMZxNDQBwgse2bTv2yz7t3Xff1YoVK7Ro0SLNm5c5S7qRSIfu\nvfcVnTgxXoWF57Rjx2xNnMgeMgAgtRIK5DNnzmjx4sV66KGH9J3vfGdI17S1dcddXKYIBHLpn/6d\nLsMxbu7fzb1L9B8I5Mb1+oSWrHfu3Kmuri498cQTKi0t1eLFi3Xx4sVEfhUAAFCCX+oqLy9XeXl5\nsmsBAMC1OBgEAAADEMgAABiAQAYAwAAEMgAABiCQAQAwAIEMAIABCGQAAAxAIAMAYAACGQAAAxDI\nAAAYgEAGAMAABDIAAAYgkAEAMACBDACAAQhkAAAMQCADAGAAAhkAAAMQyAAAGIBABgDAAAQyAAAG\nIJABADAAgQwAgAEIZAAADEAgAwBgAAIZAAADEMgAABjAm8hFtm1r06ZN+uc//6lRo0apqqpKkyZN\nSnZtAAC4RkKfkPfv36+LFy+qoaFBq1evVnV1dbLrAgDAVRIK5L/97W+65ZZbJEnTpk3T22+/ndSi\nAABwm4QC+dy5c8rNzR0Ye71eRaPRpBUFAIDbJLSHPH78ePX09AyMo9GosrKunO2BQO4V/3umo3/6\ndzM39+/m3iX6j0dCn5C/9a1v6cCBA5KkpqYmTZkyJalFAQDgNh7btu14Lxr8LWtJqq6uVmFhYdKL\nAwDALRIKZAAAkFwcDAIAgAEIZAAADEAgAwBgAAIZAAADJHQf8lBx5rX04x//WOPHj5ckfelLX9LW\nrVsdrij1mpub9dhjj6m+vl4nT57UunXrlJWVpS9/+cvauHGj0+Wl3OD+jx07pnvuuUcFBQWSpAUL\nFmj27NnOFpgifX192rBhg1pbW9Xb26tly5bp+uuvd838X67/a665xjXzH41GVVFRoRMnTigrK0sP\nP/ywRo0a5Zr5v1z/vb29cc1/SgN58JnXzc3Nqq6u1hNPPJHKtzTKxYsXJUm7d+92uJKRU1dXp3A4\nrJycHEkf3hL3wAMPaPr06dq4caP279+vmTNnOlxl6nyy/7fffls/+9nPtGTJEmcLGwF79+6V3+9X\nKBRSV1eXfvSjH+mrX/2qa+Z/cP+dnZ2aO3eu7rvvPtfM/1/+8hd5PB49++yzOnTokH7961/Ltm3X\nzP/l+p8xY0Zc85/SJWu3n3l9/PhxnT9/XkuXLtWSJUvU3NzsdEkpZ1mWampqBsZHjhzR9OnTJUm3\n3nqrDh486FRpI+Jy/b/66qtatGiRysvLdf78eQerS63Zs2dr5cqVkqRLly4pOztbR48edc38D+4/\nGo3K6/XqyJEjamxsdMX8z5w5U5WVlZKkU6dOacKECa6a/8H9t7a2asKECXHPf0oD2e1nXo8ZM0ZL\nly7V7373O23atElr1qzJ+P5LSkqUnZ09MB58m3tOTo66u7udKGvEfLL/adOmae3atXr66ac1adIk\n/eY3v3GwutQaO3asxo0bp3PnzmnlypVatWqVq+b/k/3ff//9+uY3v6lgMOiK+ZekrKwsrVu3Tlu2\nbNEPfvADV82/9FH/VVVV+uEPf6hp06bFNf8pDeREzrzOJAUFBZozZ87Av30+n9ra2hyuamQNnu+e\nnh7l5eU5WM3ImzlzpqZOnSrpw7A+fvy4wxWl1rvvvqu7775b8+bN0+233+66+f9k/26bf0natm2b\n/vSnP6miokIXLlwY+Lkb5l/6eP8333xzXPOf0nR0+5nXe/bs0bZt2yRJp0+fVk9PjwKBgMNVjayp\nU6fq8OHDkqTXXntNRUVFDlc0spYuXap//OMfkqSDBw/qa1/7msMVpc6ZM2e0dOlS/epXv9K8efMk\nSTfccINr5v9y/btp/sPhsGprayVJo0ePVlZWlr7+9a/r0KFDkjJ//j/Zv8fj0S9/+Uv9/e9/lzS0\n+U/p0ZluP/O6t7dX69ev16lTp5SVlaU1a9boxhtvdLqslGttbdXq1avV0NCgd955Rw8++KB6e3s1\nefJkbdmyRR6Px+kSU2pw/0ePHlVlZaWuuuoqBQIBbd68eeALX5mmqqpKr7zyiq677jrZti2Px6Py\n8nJt2bLFFfN/uf5XrVqlUCjkivl///33tX79ep05c0Z9fX265557dN1116miosIV8//J/n/xi1/o\nmmuu0ebNm4c8/5xlDQCAAdyzoQsAgMEIZAAADEAgAwBgAAIZAAADEMgAABiAQAYAwAAEMgAABvh/\nEEMw/ci34DsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xabc7080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.5\n",
    "b = 1.0\n",
    "\n",
    "# x from 0 to 10\n",
    "x = 30 * np.random.random(20)\n",
    "\n",
    "# y = a*x + b with noise\n",
    "y = a * x + b + np.random.normal(size=x.shape)\n",
    "\n",
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "clf = LinearRegression()\n",
    "clf.fit(x[:, None], y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.52304358]\n",
      "0.848901732623\n"
     ]
    }
   ],
   "source": [
    "# underscore at the end indicates a fit parameter\n",
    "print(clf.coef_)\n",
    "print(clf.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3794b73320>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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r3yygodHJdZf04PbxKYSFdszaYm+npVYi7lMhi7iprqGZ59/cy0eOk4SHBjE3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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3794b73358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_new = np.linspace(0, 30, 100)\n",
    "y_new = clf.predict(x_new[:, None])\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x_new, y_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, this is an example of fitting a model to data, such that the model can make\n",
    "generalizations about new data.  The model has been **learned** from the training\n",
    "data, and can be used to predict the result of test data:\n",
    "here, we might be given an x-value, and the model would\n",
    "allow us to predict the y value.  Again, this might seem like a trivial problem,\n",
    "but it is a basic example of a type of operation that is fundamental to\n",
    "machine learning tasks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Representation of Data in Scikit-learn\n",
    "\n",
    "Machine learning is about creating models from data: for that reason, we'll start by\n",
    "discussing how data can be represented in order to be understood by the computer.  Along\n",
    "with this, we'll build on our matplotlib examples from the previous section and show some\n",
    "examples of how to visualize data.\n",
    "\n",
    "Most machine learning algorithms implemented in scikit-learn expect data to be stored in a\n",
    "**two-dimensional array or matrix**.  The arrays can be\n",
    "either ``numpy`` arrays, or in some cases ``scipy.sparse`` matrices.\n",
    "The size of the array is expected to be `[n_samples, n_features]`\n",
    "\n",
    "- **n_samples:**   The number of samples: each sample is an item to process (e.g. classify).\n",
    "  A sample can be a document, a picture, a sound, a video, an astronomical object,\n",
    "  a row in database or CSV file,\n",
    "  or whatever you can describe with a fixed set of quantitative traits.\n",
    "- **n_features:**  The number of features or distinct traits that can be used to describe each\n",
    "  item in a quantitative manner.  Features are generally real-valued, but may be boolean or\n",
    "  discrete-valued in some cases.\n",
    "\n",
    "The number of features must be fixed in advance. However it can be very high dimensional\n",
    "(e.g. millions of features) with most of them being zeros for a given sample. This is a case\n",
    "where `scipy.sparse` matrices can be useful, in that they are\n",
    "much more memory-efficient than numpy arrays."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Simple Example: the Iris Dataset\n",
    "\n",
    "As an example of a simple dataset, we're going to take a look at the\n",
    "iris data stored by scikit-learn.\n",
    "The data consists of measurements of three different species of irises.\n",
    "There are three species of iris in the dataset, which we can picture here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://raw.githubusercontent.com/jakevdp/sklearn_pycon2015/master/notebooks/images/iris_setosa.jpg\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iris Setosa\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img src=\"https://raw.githubusercontent.com/jakevdp/sklearn_pycon2015/master/notebooks/images/iris_versicolor.jpg\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iris Versicolor\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img src=\"https://raw.githubusercontent.com/jakevdp/sklearn_pycon2015/master/notebooks/images/iris_virginica.jpg\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iris Virginica\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img src=\"https://raw.githubusercontent.com/albahnsen/PracticalMachineLearningClass/6160065e1e574a20edddc47116a0512d20656e26/notebooks/iris_with_length.png\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iris versicolor and the petal and sepal width and length\n",
      "From, Python Data Analytics, Apress, 2015.\n"
     ]
    }
   ],
   "source": [
    "from IPython.core.display import Image, display\n",
    "imp_path = 'https://raw.githubusercontent.com/jakevdp/sklearn_pycon2015/master/notebooks/images/'\n",
    "display(Image(url=imp_path+'iris_setosa.jpg'))\n",
    "print(\"Iris Setosa\\n\")\n",
    "\n",
    "display(Image(url=imp_path+'iris_versicolor.jpg'))\n",
    "print(\"Iris Versicolor\\n\")\n",
    "\n",
    "display(Image(url=imp_path+'iris_virginica.jpg'))\n",
    "print(\"Iris Virginica\")\n",
    "\n",
    "display(Image(url='https://raw.githubusercontent.com/albahnsen/PracticalMachineLearningClass/6160065e1e574a20edddc47116a0512d20656e26/notebooks/iris_with_length.png'))\n",
    "print('Iris versicolor and the petal and sepal width and length')\n",
    "print('From, Python Data Analytics, Apress, 2015.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quick Question:\n",
    "\n",
    "**If we want to design an algorithm to recognize iris species, what might the data be?**\n",
    "\n",
    "Remember: we need a 2D array of size `[n_samples x n_features]`.\n",
    "\n",
    "- What would the `n_samples` refer to?\n",
    "\n",
    "- What might the `n_features` refer to?\n",
    "\n",
    "Remember that there must be a **fixed** number of features for each sample, and feature\n",
    "number ``i`` must be a similar kind of quantity for each sample."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading the Iris Data with Scikit-Learn\n",
    "\n",
    "Scikit-learn has a very straightforward set of data on these iris species.  The data consist of\n",
    "the following:\n",
    "\n",
    "- Features in the Iris dataset:\n",
    "\n",
    "  1. sepal length in cm\n",
    "  2. sepal width in cm\n",
    "  3. petal length in cm\n",
    "  4. petal width in cm\n",
    "\n",
    "- Target classes to predict:\n",
    "\n",
    "  1. Iris Setosa\n",
    "  2. Iris Versicolour\n",
    "  3. Iris Virginica\n",
    "  \n",
    "``scikit-learn`` embeds a copy of the iris CSV file along with a helper function to load it into numpy arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['target_names', 'DESCR', 'data', 'feature_names', 'target'])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "iris = load_iris()\n",
    "iris.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 4)\n",
      "[ 5.1  3.5  1.4  0.2]\n"
     ]
    }
   ],
   "source": [
    "n_samples, n_features = iris.data.shape\n",
    "print((n_samples, n_features))\n",
    "print(iris.data[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 4)\n",
      "(150,)\n"
     ]
    }
   ],
   "source": [
    "print(iris.data.shape)\n",
    "print(iris.target.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
      " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2\n",
      " 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
      " 2 2]\n",
      "['setosa' 'versicolor' 'virginica']\n"
     ]
    }
   ],
   "source": [
    "print(iris.target)\n",
    "print(iris.target_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This data is four dimensional, but we can visualize two of the dimensions\n",
    "at a time using a simple scatter-plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x7f37945cd080>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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F7fvuuw9r1qyJqIydO3fi29/+dtBjeJ6Pqn6EkNQQKgb3OHsUW7p/I2w36O5CJTcl0dUk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TsEy9kIV8eDqD/EPBV/7LHHMHz4cDz77LPQ6XSw2+247777tOxb3LkctSG3IxFoPXB/np9sz0NE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\nEWpk9uHx9//XFeVGAWfqLegar8XZs+cxbZYB55ot6NylNfeGJ7EWgsCc8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tYxV4HNtsYk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MgBp1/SrQWk+dvHCyT8JK0BcdiYmJqK6uth9XVlYiISHBXlZVVWUvq6ioQGJiopMMOdy++UmB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f379461c278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd  # Pandas is a topic of next session\n",
    "data_temp = pd.DataFrame(iris.data, columns=iris.feature_names)\n",
    "data_temp['target'] = iris.target\n",
    "data_temp['target'] = data_temp['target'].astype('category')\n",
    "data_temp['target'].cat.categories = iris.target_names\n",
    "sns.pairplot(data_temp, hue='target', palette=sns.color_palette(\"hls\", 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dimensionality Reduction: PCA\n",
    "\n",
    "Principal Component Analysis (PCA) is a dimension reduction technique that can find the combinations of variables that explain the most variance.\n",
    "\n",
    "Consider the iris dataset. It cannot be visualized in a single 2D plot, as it has 4 features. We are going to extract 2 combinations of sepal and petal dimensions to visualize it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xc2b6dd8>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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97hRvrHsNdYBnR63k2cm8M+5vGI3VZyDZbx09epwvPluPrUAlsgE8+dTIq3qv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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbc7e0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = iris.data, iris.target\n",
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=3)\n",
    "pca.fit(X)\n",
    "X_reduced = pca.transform(X)\n",
    "plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y, cmap=cmap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xc2ea208>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CAAW+2zvfrbZiY+ug2plbK2EV7zMiy5YF1QMl31Or62qwu2i317Lfi81mw4c7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\nCzUREZGD/QD1SO07NbhvZwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc465080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = iris.data, iris.target\n",
    "from sklearn.manifold import Isomap\n",
    "pca = Isomap(n_components=3)\n",
    "pca.fit(X)\n",
    "X_reduced = pca.transform(X)\n",
    "plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y, cmap=cmap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 3)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_reduced.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xc15f198>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CAAW+2zvfrbZiY+ug2plbK2EV7zMiy5YF1QMl31Or62qwu2i317Lfi81mw4c7\n30d2n1wU9CjC1thtWLR+caWcm6ouFmryGyNGJuGTz0aidq1GKCg873q92JSF+Hh9udpIHpmETj0u\nIyRyJ2Jqb8Hk14Zi2dLjCFIlIkQfB626B1YsO1VRXaD/stvtsGtKP7ZmV9jusve9yWQyvDPqn2i/\nvy2iVobDdNkIc3Vz6Z0q6dnsrKyrMNQrdm2ra2hw6uZvFXrOS1cz8J81X2PRhgV8hKyK4qVv8isK\nhQJRMRbI0AzpmT8DgoCata9j2PCXynW8IAhIGd2/1GsOu+Ke2+R9SqUSdYpicd2cA4VGActFM1qF\nu3+zlkqlwoSBT2Da8ncQmRiD3CPZyDmcjagHomHJMKOL9v6/o3ZHZGQUVIcUQOOSbbvZjgh5hMft\nZmZdwlc7voBRVYwa9ur4+8MToVQqceHSecw8/B6UPdWwm+w49sNRvPPYP92654Kkw58W+Z0XXh6C\neo3Oo1lLPfoPDMMnn77oUXsJjVWwWLMBAFZrLhokVPxayAS8NnIK2v3yAOrtiEeyZQQe7jbM80b/\nO8lZZOtoqMNUuPjFWYwxjca4fo973nY56HQ6pMSOhnODHea0YtRKq47nHnnG43Y/2fIR8h4qhDXR\njgvdM/B/a2YBANYcXQ1lTzUAQBGkwNXmWThz7rTH56PKxaEB+Z3IyEi8/EqK19p7/MmHsSI6DZnp\nZ1Gztg6PDH/Ea23T3SmVSjwx8M4zlrlj7a7VuFmYg/S551FjcC1o9EFIatAXPTomeu0c5ZHYtjcS\n2/Z2bSsUnv0adjqdyNPmQ4eSO4jlajmyZTkAAMFZ8n3/7yuTOc0i1OFqj85HlY+Fmugu0i9m4ODB\nE2jZshGGDu1d9gHkszbsXYefNMuhGRKEOLEecuZex7gHxqP/IwOljuYxmUyGEFMwfv9G32lzIswe\nBgAY2SUFf1vwHCKGx8B804TcbTfgHF2+GyvJd/DSN9EdbN68B+9PP4ndW1rhk/cvYM3q7VJHIg8c\nyz4GTYMgACX3IWg6BqFZvOdrihuNRqzasgI79m+DlFNS/LnTX6Fbr4GwVUSNTTF4bsBfAABhIWFQ\nhauRvf8aTNdMiH+2AZYc5l3mVQ1H1ER3sHl9BrTqkkuiWk1LbE3bgoGDJA5FbtOJOjhtTsiUJWMT\nebYc4c3uPV97WfLyb+KNVa/B0RewF9ixbcFWvJYyxXWZuTI1jE/AjPj3b3vdbrdDHqJA9S61XK+J\nMo6oqxowWUVCAAAgAElEQVSOqKnKWL1qGya/sAiTX1iMVSu2AgDS0zOwauVGXL58xctnK33DmNNZ\n+b98yXsm9H0CIT/rYNhbCNNGA4aEDfF4utNF2xcAg+RQaBTQVNPgfNOLOH7qVy8l9g6tVosGBQ1g\nKyp5tM16xIzusT0kTkX3iyNqqhKOHT2JdaucCFL3BACsX3saly9/j1+PRECjbIZ1qw9j5Jir6NGj\nvVfO165jOLasPw+Nuj7Mlgx07uGbc1hT+Wg0GkxPnQmDoQgaTZDHN3ABgCgrWXzld4JagMVqvscR\n0njl0dfw4+YluGm9iY71OqJ1kzZSR6L7xEJNVcKvv55DkLqjaztI1Qhb07agTs2SR1u08vbYsHaL\n1wr1I8P7oEaNQ/jt1F7Ub1gD3bv3L/sg8nl6vfcWQhnYZhCObjoKZR81HBYHovZH4IHH7n8Bl4om\nk8mQnPSo1DHIAyzUVCU0a14Pe7b/hiB1yUwRJutZaLWhpfZxOr37TU6nzm3QqTNHH3RndWrG4Y0u\nU7B+5zqo5WqMHD2qXAu/EN0vFmqqElq3bo6kAWnYtX0rRAC9E6NQVNQAB3ZlQqOOhdl6ET26hUkd\nkwJMreq18fjAJ6WOQX6OhZqqjIeH9sLDQ0v+vG/fEaxe/huMlm1QBgl4NLU7unbtK21AoipOFEUs\nSVuEq6YriA+ui6E9OLmPL2ChpionJycH8765AK06EZEhgMWcCauFiw0Qeeqz5f/CiQdOQRmuwm83\nzuDm2lw8PuApqWMFPD6eRVXOiRNnIENT17ZaFYszZ65JmIjIP5wVzkIZrgIAKGNUOGXjSnG+gIWa\nqpxGjerBIZ51bVus1xEby++niTyltCtLbStsvOjqC1ioqcqpXr06hiVHwinfDLuwDc0fOIeBg3pK\nHYuoyhvW4BFYtppQlFEI22YzkpvysS5fwI9LVCUl9e2MpL6dpY5B5Fe6tu6OVvVbI/NKJur0jYNe\nr5c6EoGFmoiI/iA4OARNGzeTOgb9AS99ExER+TAWaiIiP1BcXCzpUptUcdy69C2KIt566y2cPn0a\nKpUK06ZNQ2xsrOv9tLQ0zJ49GwqFAsOHD0dycrLXAhNR1ZKfdxObvp4NlcUEdd2G6Dt6nCRLQfqr\n69nX8d76fyIvMh+aQg3GN5uAjs0fdLs9k8mEz3/+DPmKAkQ7o/DMwD9DqVSWfSBVGLcK9aZNm2C1\nWrFw4UIcPXoU06dPx+zZswGUrH86Y8YMLFu2DGq1GikpKejduzciIiK8GpyIqoZVM97CYEcxBEFA\nzr7L2CSTISllrNSx/MbX276AdZADeqFkhbfv1s3zqFC/v2IGriflQKaQIcdyE899+jQe7ZyCPp04\n859U3Lr0ffDgQXTr1g0A0KpVKxw/ftz13vnz5xEXV3K3oFKpRNu2bXHgwAHvpCWiKsVkMiEyL8c1\ngo5Sq2C6eLaMo+h+mFWWUlcoTCqzR5fAs4OyIVOUlAa5Wo7cujexJHIpPlv+L4+zknvcGlEbDAYE\nB99aLk6hUMDpdEImk932nk6nQ1FRUbnajY723hJ0VRH7X9L/rKwsOJ1O1KxZM2Aukfrrz14U9TBp\nta5tpyhCERF+W3/9tf/l5Un/W4Q2RtrNnVBGqOC0OxHnqIWYGPfXTw91BqMAxa5th9kBVTU1th7e\nij7pPdGtfVe3276bQP/5l8WtQq3X62E0Gl3bvxfp398zGAyu94xGI0JCyvc/TXZ2+Qq6P4qODg74\n/t+4UYgP3/8BZ09GAYICdepdxquvj/X7Yu3vP/v6yan4/F8fQG4xQRdXD6ljnizVX3/vf1k87X9y\n98dg2eBAuiUDwXY9nh7wrEftjXvgCcxe+xkuC5dhsVkQ82B1AIBTKWLGhg8wd8/3KAgqQKgpFM/3\nnohqMdXdPhcQ2D//8n5AcevSd5s2bbBt2zYAwJEjR5CQkOB6r379+sjIyEBhYSGsVisOHDiA1q1b\nu3MaCjBpaTuRca4lQoJbI0TfHDeudMaqlZukjkUeOr17Bx6tEYmnE+oiVrQh+8plqSP5FUEQkPrQ\neLwx5E08/8gkaP9wBcMdDeMT8HHKp3i15WvQanXQRAfBeMUA0SnihvUGDANMkCeqUNS/GJ9t+dRL\nvaB7catQJyUlQaVSYdSoUZgxYwZeeeUVrF69GkuWLIFCocArr7yCxx9/HCkpKUhOTkZMTIy3c5Mf\nys0uhEoZ6dpWKUOQn198jyPI1+Xm5iL67AlEqEruGu6uUeDXtSslTkXl8UDTtnjQ+iAy16TDnG1C\n7aQ60Gg1rvcFQcDVoizsP7wPZrNZwqT+z61L34IgYOrUqaVeq1u3ruvPPXv2RM+ePT0KRoGnV58H\nsWPbOmhkfQAAJtt29OrVReJU5AlBAJwofWMTn/StOv4+6h+QLRWw9cAWXLt4BWKBE4ZLRdDXCcaV\nzZkIqq/Fl7ovoflRjTcfmoroqGipI/slTiFKPiMqKhIvTO6BFT/tBCCg/4C2qB1bU+pY5IGIiEjc\nbNQK2Rm/IUqlxFazA62HPCJ1LConQRBgldtQY0Ks607wrHmXERIVDGWQEhFtSq6AiQNFfL91Hp4f\nOknKuH6LhZp8Slxcbfzt+dpSxyAvSp44Gbs3b8C5nGx06tkL1arzw1dVkq/IdxVpAAitHYbJD76C\nV8+94npNEATY5Q4p4gUETiFKRBUqbelC5O7YDOOZkzDm50sdh+5TtD0KDsutIhxhCkf16jVQ/UI1\n1+uWwyZ0i+8uVUS/x0JNRBVmz/q1iNn2M3oU56FPUTYOzvoQxcW8QbAqeXbQX1BvexzUW5WIWB+K\nf/SeVHKfUsq76HCgLZrsbITnqj2Hji3cnw2N7o2XvomowuSeOYWmQWrXdmNbMdIvnkPTZi0lTEX3\nQ6VS4YURL9/x9fEDn5AgUeDhiJqIKkyuqRiFFotr+7TBhBo1eQ8C0f3giJqIKkyI6MS2K9egVSpg\nczqRKwpQqzVlH0hELizUVClWrdyKkyduQq2x44kn+yE42P25iKnqEAQZBteLc21vKzC6phsmovLh\nvxiqcKtXbcOG1TrkXO2Cy+e74d2pi7nAfYBoMfgRbDPZ4XA6cclkgdC2EzQajqgrytn0M3hz6et4\nZcVL+HbtN/x35ic4oqYKd+J4DjTqkhV3BEGG/NwaKCjIR1hYuMTJqKLVb9IM+tenYf/2rYipE4fB\nD3KmuYpis9nwr30fQ+hX8mt9b/Y+BG8NxojEkRInI09xRE0VTq12QBSdrm2ZogA6nV7CRFSZ0o8f\ngyPvJqxFhVJH8WvXrmXBUOfWo2+qaDUuGi5ImIi8hYWaKtzjTz4EmWYNCgy/wGDejKHD46BUKqWO\nRZVg/Xff4tqcz2HZshaWhd9i3fz/SB3Jb0VFRUOdpXJt24ttiJBFSJiIvIWXvqlctm3dj2NHrkAf\nIsNjqQPuq9CGhITivfefQH5+HvT6YBbpAHJ89U/oFRKE+JBo7M66jsvbNgGpj0sdyy8FBQVhbP2x\nWLJ+MSwqC2LNsRifzOec/QELNZVp3bqdWP0jEKTpDIfDgmnp3+GttyfcVxuCICA8nJ/uA4nT6YTW\nYsJveRZcLCiCSi6DrZCXvytSl1bd0KVVN6+1ZzQa8UPafNgEG/o064uEuo281jaVHy99U5kOH7yO\nIE1DAIBcrkbW5TCYTCaJU5GvE0URJpsNjcJCEa5Ro7Zeh0I+mlVl2Gw2vL70FRzp8itOdTuDD09+\ngDMXT0sdKyBxRE1lksvt//NKEQ4dOgq9ToeWrZpDEARJcpFvy83NhdNhh9nhQHxIMDZcugwxiDcR\nVhVHThxGYUcDtHIdAEDVVYPNOzfedVR94dJ5fH9gPmxKG5prm2Nkn5TKjOvX+PGWyjQmtTus4loU\nGdKRV7gNFmsWfvhWh88/LcbMGd/xWU26o+3btqBJRDiaRUYgQqPGow3rIfvqZaljUTntPrET1nyr\na9vpcELhvPPYzmKx4KM9H+BGn1zk9SjEpuppWL1zVWVF9Xss1FSmWrVqYOaHo/H3l0LRtqMTkaFj\noA2KQbAuHhnnmuDAgcNSRyQflF9QgDD1rbuQBUFAiEp1jyPIV+w4uA0nmp5C4YV85J/OQ3GWEc4l\nNozulXrH/S9fzoShwa1Hw9SxGpzJ42Vyb2GhpnJRq9Vo0qQxlEoNZLJbd20rFCEwGLhsId1u+PAR\nWHsxExZHyZrFWzOvwhTMSW6qglPXTkFdT4M6A+tCppTBeNWAfvX7Q6fT3XH/mJgYKK7IXdt2kx1h\nsrDKiuv3WKjpvjz0UHuYbVsAAE6nA3L1VnTu3E7iVOSLLqdfwIiEeth59Ro2X7qCuBA9OiT2ljoW\nlUO9qPqwXDEDAELqhSJYFoxWjR646/7BwSEYVX0UnBtsMKcZUWtLdYzrd39PhtDd8WYyui+xdWrh\nhVe6Yv3PeyCXi3g0ZTTnbqY7unr5MqqLInQKBWSCgFi9Dofy86SOReXQp2MSLq3NwJHThyFzyjCs\nxjDEx8bf+5gOfdGnQ1+IosgbTL2MhZruW1xcbTz9DNcUpnvbuPgHGM7+hnqhwbA6nVhzIQOquPpS\nx6JyenzAk24dxyLtfSzURFQhLh49jAH16iA2WI9QlQo7rmZh8/FjUsciqnJYqImoQoSqlVDKZWgS\nEYZskxnVtFo4/3tjGQWm69nX8e32b2BTWtE0pBmG90yWOlKVwEJNRBVCKZdjSN0412NZeWYLblgt\nUsciiTidTvxz3TtwDC65PJ6ZuQHKHUo88cidH/miW3jXNxFViBCVqtT3lUEKOcKr1ZIwEUnpxo3r\nKIwvcv0/oY7V4Lf83yROVTVwRE1EFeKKsRhzT5xG7WA9LA4HTubmYcq7/5Q6FlWg9XvXYWXmCtiV\ndjSw1sekES9B9t/53UNDw6DIuVVynDYntE6tVFGrFI6o6a5EUcTePb9g7do0GI1GqeNQFROlUaN3\nnVqu/+wQERdXT+pYVEFu3szFkrzFkPVVQJWowfnO6Vi46QfX+0FBQUiumQzrehOM2wsR+rMeTz70\ntISJqw6OqOmuPpj5PdLPNoNSWRcbfl6EKVOHIiKCS1VS+cSHBqN2cMkiHGq5HM0jwxEUxBGUv7p0\n9RKccbfm/VcGK5Fryym1T9+O/ZDU4SFYrVao1erKjlhlcURNd3TmzFmc+y0O2qCaUCq0UIgDsGTR\nVqljURWSazKX2s4zW1GtWjWJ0lBFa1g3AepTt+Zyt2SY0Siy8W37CYLAIn2fOKKmO7KYLRBw6x+T\nIAhwOjmRAZWfMSwS/znxG9rGRONiYRGO3MzjZBh+TKfT4a+t/4bFmxbCrrSjpb4L+vbqJ3Usv8BC\nTXfUtFkThMf8B5ai6pDL1TBZt6Jf/weljkVVyHsLV+Cj55/Bj2dPIyg8HP9ctk7qSFTBmtZvhrfq\nvyN1DL/DQk13JJfL8fa747Fk8XpYLE706t0FcXGcNpTKT61W45XPv5U6BlGVx0JNd6VUKjF6zCCp\nYxARBTTeTEYAAKPRiIyMdFitVqmjEBHRH3BETdiStg9LFlyE3VYTQfrteH5iD9StFyd1LCLyE5v2\nb8CKjOUlE6HYG2Li8BdcNxYajUb8Z/XXcMCOQe2HoEa1mvdsa9XOFVh2fDnyjoYgAtUwdmRv9Ezs\nWBndkIxbhdpiseDFF19Ebm4u9Ho9ZsyYgfDw8FL7TJs2DYcOHYJOpwMAzJ49G3q93vPE5HUrlp2F\nTpMEaACgEb7/Lg2vT2GhJiLP3byZi0U5C6Hpq4MCcpwtOIfFmxfi0T4pJbXkh5dR3M8GmVyGQxsO\nYUr3t+5arC9dzsCPhUtRdLgFGqrGAQB+mH8YOv0xtG/fsjK7VancuvS9YMECJCQk4Pvvv8fDDz+M\n2bNn37bPiRMn8M0332DevHmYN28ei7QPs1pKf16zW5USJSEif5NxJQOO+D9MhBKqwg3LdQDA9gNb\nUdjNBJm8pBTJk1RYfWDVXds6nf4bDGYHajpv3TsTqnsAh365UEHpfYNbhfrgwYPo3r07AKB79+7Y\ns2dPqfdFUURGRgamTJmClJQU/Pjjj54npQoTG2+D3W4CAJitWWjUVCdxIiLyFyUTodz68G/JNKOW\nuhbSdm9CYUEhnMZbS5+KDhFK4e4DhdaN2yAoT0Ch/azrNZutCKGhqrse4w8EURTFe+2wdOlSzJ07\nt9RrUVFReOONN1CvXj2IoojExERs3brV9b7RaMT8+fMxYcIE2O12jB07FtOnT0dCQkKFdII8Y7fb\n8X+zl+HmTTuaNI1C8si+UkciIj9y+ORhzN33HWxyG2raauCo+CtsrUU4L9kgHBAh9pdDFiRD+J5g\nzHrqUwQFBd21rb1H9+Hd2V/CdKERguThaNbCgenvPe1a/MMflVmo7+Svf/0rnn76abRo0QIGgwEp\nKSlYterW5Qqn0wmTyeT6fvr9999Ho0aNMGTIkHu2m51ddL9R/EZ0dDD7H6D9D+S+A+x/oPX/3Z/e\nxvVe2a5t+xYzxsaOh8liQtd23aFSlW90bLfbYbPZ7lnUfV10dHC59nPrI0ibNm2wbds2AMC2bdvQ\nrl27Uu9fvHgRKSkpEEURNpsNBw8eRLNmzdw5FRER+RGn3FFq26FwokPrB9Grc59yF2kAUCgUVbpI\n3w+37vpOSUnByy+/jNGjR0OlUuHDDz8EAMyZMwdxcXFITEzE0KFDkZycDKVSiWHDhqF+/fpeDU5E\nRFVPp2qdseTkUqibamArsKK5swnkcrnUsXyaW5e+K0ogXf75X4F2+et/BXL/A7nvAPsfiP3f9+te\nHLp0ENGaaDzz6OPIyTFIHUkS5b30zQlPiIioUnVs8SA6tihZ5Of3iU9EUeTqanfBQh0gDAYDsrNv\noFat2vf1PRARUUXKvJqJ15dMRZ42HyGmYDzX6S9oGM8nhP6IhToAbN60Bz8uugyHrQY0uh34x4u9\nEB8fK3UsIiJ8tPYTWAbaoYUedoj4av2XmBn/gdSxfIr/PnhGLiuWnYdO0x0hwQ2hkvXDD/N3SR2J\niAgAYFAVl9ouVhklSuK7WKj9nCiKsFpLXzix2ThFKBH5htpiTTgsJY9sOe1OxJhjJE7ke1io/Zwg\nCIitY7k1RajlMpo0L9+dhkREFe3V0ZPRZHcCwreFoN62OLz48GSpI/kcfkcdAF5+dQzmz12Dgnwn\nGjaKxMBBnCKUiKR39foVvL38c+QgDxHFEXhqwJ8CZhKT+8FCHQAUCgUmPPGw1DGIiEr5d9q/YBhg\nAiBDjjMP/173L7w2corUsXwOL30TEZEkCoIKXX8WZAIK1IX32DtwsVATEZEkws1h+H1yTKfDiXBL\nmMSJfBMLNRERSeL5pEmovS0a6q0K1NxYDX8fNFHqSD6J31ETEZEkoiOj8eGTHwTcXOf3iyNqIiIi\nH8ZCTURE5MNYqImIiHwYCzUREZEPY6EmIiLyYSzUREREPoyFmoiIyIexUBMREfkwFmoiIiIfxkJN\nRETkw1ioiYiIfBgLNRERkQ9joSYiIvJhLNREREQ+jIWaiIjIh7FQExER+TAWaiIiIh/GQk1EROTD\nWKiJiIh8GAs1ERGRD2OhJiIi8mEs1ERERD6MhZqIiMiHeVSoN27ciEmTJt3xvcWLF2P48OEYNWoU\ntm7d6slpiIiIApbC3QOnTZuGXbt2oUmTJre9l5OTg/nz5+Onn36C2WxGSkoKunTpAqVS6VFYIiKi\nQOP2iLpNmzZ466237vjesWPH0LZtWygUCuj1esTHx+P06dPunoqIiChglTmiXrp0KebOnVvqtenT\np6N///7Yv3//HY8xGAwIDg52bWu1WhQVFXkYlYiIKPCUWahHjBiBESNG3Fejer0eBoPBtW00GhES\nElLmcdHRwWXu4y9EUcTynzbhWlY+eiS2RnR0cED1/04Cuf+B3HeA/Wf/A7v/ZXH7O+p7admyJT75\n5BNYrVZYLBZcuHABDRs2LPO47OzAGXV/8tFCXDjdEmpVXWzbfBB/nViIhEYJUseSTHR0cED9/P8o\nkPsOsP/sf+D2v7wfULxaqOfMmYO4uDgkJiYiNTUVo0ePhiiKmDhxIlQqlTdPVaVZLBacOq5AiC4S\nAKBRtcXaNXsDulATEdGdeVSoO3TogA4dOri2x48f7/pzcnIykpOTPWnebwmCAMBR+jWI0oQhIiKf\nxglPJKBSqdCuoxrF5gw4nQ6YbTuRPKqd1LGIiMgHVch31FS2p/40FPtaH0JG+mF079EVLVo0CNjv\naYiI6O5YqCtJcXEx5s9dB6tVQKcuDdCuXQt07NgGHTtKnYyIiHwZC7WbbDYb3pu+AFczVVBp7Eh+\ntCm6dG1zx30dDgfeeuMHOMwDIJPJcfrEEYiiiPbtW1ZyaiIiqmr4HbWb/vPNKty81hM6TSKUSML3\n836D1Wq9476XLqWjILcxZDI5ACBI3Rp7dp2vzLhERFRFsVC7qagAkMvVrm2HNRp5eTfvuK9eHwJR\nyHdti6ITCoXjjvsSERH9EQu1m+Lr6WGx3nBta4MvIyoq+o77RkdHo0t3oNBwEEWGixCVa5A6rm9l\nRSUioiqM31G7afiIJJjNa3H29GmoVHakjkuCXC6/6/7jJgxCvwHXkJdXgAYNxkOh4F89ERGVjdXC\nTYIg4LHUgfd1TLVq1VGtWvUKSkRERP6IhbqciouL8eHMpcjNUUOrteHxp7ugQYO6UsciIiI/x++o\ny+nzWSuRn90HSqEnbKYkfDFru9SRiIgoALBQl1NRgcL1eBUAFBWpIYqcn5uIiCoWC3U5RcaIcDgs\nru3wcPN/F9cgIiKqOPyOupyeeXYoPvv0R9y4JkeQzoqnn+kvdSQiIvKQ0WjE8u0/AgCGdh8OnU4n\ncaLbsVCXk1KpxD8mjZI6BhEReUlxcTEmL30RzsElV0f3Lt2L95I/gFarlThZabz0TUREAWnl9uWw\nJTmRuTYdWVsvI0Oegbkrv5E61m1YqImIKCDJZXJcTbuM2P7xqNW7DuIG18Oe3L1Sx7oNCzUREQWk\nh3sOg6pICZniVilU11Df4whpsFATEVFAUqlU6BDZAU670/VamCVcwkR3xkJNREQB66+Dn0fNTdUg\n3yIgZL0Of+3xN6kj3YZ3fRMRUcAKCgrCa49OkTrGPXFETURE9Ad2ux0mk0nqGC4cURMREf3X4rSF\n2JC3AU6NE3H5dfD6qDfvuYRxZeCImoiICEBW1lWswzoE9dFB1zUY13rdwA8b5ksdi4WaiIgIAC5f\nvwyh5q2yqNAqUeAokDBRCRZqIiIiAM0SmkNzVOXatpwyoU3tthImKsHvqImIiABotVq81HUyFqT9\nAIfCgQ4xHdC5dVepY7FQExER/S6uVjwmD3tV6hil8NI3ERGRD2OhJiIi8mG89F2GSxmXsW7dL5DL\nRDyakgS9Xi91JCIiCiAcUd9D5qUrmDl9B84e74STRzpiymsLYDabpY5FREQBhIX6HjZs+AVByl4A\nAJlMDoe5J3bvOiBxKiIiCiS89H0PSgXgdNogkykBAHZHEXR6rcSpiIiosq3YvgxnC84hQhaOsQ9N\ngEJReeWTI+p7GDnqIcg0P8NkyobBmIHYusfRoUMbqWMREVEl+m7DPKyNWYeM7pk40OYg3ls6vVLP\nzxH1PWg0GvxzxngcOHAYWq0GrVqlQhAEqWMREVEl+s18CqoaagAl04pe0mRU6vk9KtQbN27EunXr\n8OGHH9723rRp03Do0CHodDoAwOzZs6vkHdNKpRKdO3eQOgYREUlEaVOW2lZZVXfZs2K4XainTZuG\nXbt2oUmTJnd8/8SJE/jmm28QFhbmdjgiIiKpPdZuLD5e9yEM8cVQXlVgTP0xlXp+twt1mzZtkJSU\nhEWLFt32niiKyMjIwJQpU5CdnY0RI0Zg+PDhHgUlIiKSQv24Bvioxr+QlXUVUc2jXVeKK0uZhXrp\n0qWYO3duqdemT5+O/v37Y//+/Xc8pri4GKmpqZgwYQLsdjvGjh2LFi1aICEhwTupiYiIKpFKpUJc\nXLwk5xZEURTdPXj//v1YtGjRbd9RO51OmEwm16eO999/H40aNcKQIUM8S0tERBRgKuSu74sXL+If\n//gHVqxYAbvdjoMHD+KRRx4p87js7KKKiFMlREcHs/8B2v9A7jvA/rP/gdv/6Ojgcu3n1UI9Z84c\nxMXFITExEUOHDkVycjKUSiWGDRuG+vXre/NUREREAcGjS9/eFqifqoDA/lQJBHb/A7nvAPvP/gdu\n/8s7oubMZERERD6MhZqIiMiHsVATERH5MBZqIiIiH8ZCTURE5MNYqImIiHwYCzUREZEPY6EmIiLy\nYSzUREREPoyFmoiIyIexUBMREfkwFmoiIiIfxkJNRETkw1ioiYiIfBgLNRERkQ9joSYiIvJhLNRE\nREQ+jIWaiIjIh7FQExER+TAWaiIiIh/GQk1EROTDWKiJiIh8GAs1ERGRD2OhJiIi8mEs1ERERD6M\nhZqIiMiHsVATERH5MBZqIiIiH8ZCTURE5MNYqImIiHwYCzUREZEPY6EmIiLyYSzUREREPoyFmoiI\nyIexUBMREfkwFmoiIiIfpnDnIIPBgBdeeAFGoxE2mw2TJ09G69atS+2zePFiLFq0CEqlEs888wx6\n9uzpjbxEREQBxa1C/e2336Jz584YO3YsLl68iEmTJmHZsmWu93NycjB//nz89NNPMJvNSElJQZcu\nXaBUKr0WnIiIKBC4VagnTJgAlUoFALDb7VCr1aXeP3bsGNq2bQuFQgG9Xo/4+HicPn0azZs39zwx\nERFRACmzUC9duhRz584t9dr06dPRvHlzZGdn46WXXsJrr71W6n2DwYDg4GDXtlarRVFRkZciExER\nBY4yC/WIESMwYsSI214/ffo0XnjhBbz88sto165dqff0ej0MBoNr22g0IiQkpMww0dHBZe7jz9j/\nwO1/IPcdYP/Z/8Duf1ncuuv73LlzeP755/HBBx+ga9eut73fsmVLHDx4EFarFUVFRbhw4QIaNmzo\ncesmv9EAAAQ6SURBVFgiIqJAI4iiKN7vQc899xxOnz6NWrVqQRRFhISEYNasWZgzZw7i4uKQmJiI\nJUuWYNGiRRBFEc8++yz69OlTEfmJiIj8mluFmoiIiCoHJzwhIiLyYSzUREREPoyFmoiIyIexUBMR\nEfkwnyvU58+fR7t27WC1WqWOUqlMJhOee+45PPbYY3j88cdx48YNqSNVGoPBgGeeeQapqakYNWoU\njhw5InUkSWzcuBGTJk2SOkalEUURb775JkaNGoWxY8ciMzNT6kiV7ujRo0hNTZU6RqWz2+146aWX\nMGbMGIwcORJpaWlSR6pUTqcTr776KlJSUjBmzBicO3funvv7VKE2GAyYOXPmbVOSBoLFixejefPm\n+O677zB48GB89dVXUkeqNL/PHT9//nxMnz4db7/9ttSRKt20adPw8ccfSx2jUm3atAlWqxULFy7E\npEmTMH36dKkjVaqvv/4ar7/+Omw2m9RRKt3KlSsRHh6O77//Hl999RXeeecdqSNVqrS0NAiCgAUL\nFuDvf/87Pvroo3vu79Zc3xVlypQpmDhxIp577jmpo1S6cePG4fcn5a5evYrQ0FCJE1WesuaODwRt\n2rRBUlISFi1aJHWUSnPw4EF069YNANCqVSscP35c4kSVKy4uDrNmzcJLL70kdZRK179/f/Tr1w9A\nyehS8f/t3TFr6lAYBuA3qVD0Dwj9AWZycXIrBhVFQWgHHSIOBVexiy2CW3ETEVqwSH9BEToVQXAQ\nhzo5CqVbFQpOLoKI5w6XW3ov1QsXzJer7zMlcIY34ZCPHE6+uBxVinYuHA7DNE0AwGQy+evzXuTu\nfNc//OTkBIlEAoZhYN8/7d7WPz2Xy+H19RUPDw9C6XbrX3rH75NN1x+PxzEcDoVSyfjznwAulwvr\n9Rq67qiFvp2JRCKYTCbSMUS43W4AP+dAoVBAsVgUTmQ/XddxdXWFbreLRqOxfbByiGg0qrLZrLIs\nS/n9fmVZlnQkMW9vbyocDkvHsNV4PFbJZFL1+33pKGJeXl7U5eWldAzbVKtV9fz8/Hl+enoqF0bI\n+/u7SqfT0jFETKdTdXZ2ptrttnQUUbPZTIVCIbVYLDaOccx6Q6fT+Tw2TXNv3yg3ub+/h9frRSqV\ngsfjwdHRkXQk2/zqHV+v12EYhnQcskkgEECv10MsFsNoNILP55OOJELt+Qrid2azGS4uLlCpVBAM\nBqXj2O7p6QkfHx/I5/M4Pj6GrutbV5IcU6i/0jTt4Cbv+fk5SqUSHh8foZQ6qI01tVoNy+USNzc3\nv/WOp/0WiUQwGAyQyWQA4KDm/FeapklHsF2z2cR8Psfd3R1ub2+haRpardbnXpV9F41GcX19Dcuy\nsFqtUC6Xt147e30TERE52GHs2iAiIvpPsVATERE5GAs1ERGRg7FQExERORgLNRERkYOxUBMRETkY\nCzUREZGD/QD1SO07NbhvZwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc18bdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y, cmap=cmap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KXqeePptMUmmpkCjdGK8BL8cl20+OlBMxOAInRB+DdsDv9w0QTnUz6rBnwx7s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\nhFCTFE5CCCGEEGqSwkkIIYQQQk3/D6axoEnBnoFwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc483390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "fig = plt.figure()\n",
    "ax = Axes3D(fig)\n",
    "ax.set_title('Iris Dataset by PCA', size=14)\n",
    "ax.scatter(X_reduced[:,0],X_reduced[:,1],X_reduced[:,2], c=y, cmap=cmap)\n",
    "ax.set_xlabel('First eigenvector')\n",
    "ax.set_ylabel('Second eigenvector')\n",
    "ax.set_zlabel('Third eigenvector')\n",
    "ax.w_xaxis.set_ticklabels(())\n",
    "ax.w_yaxis.set_ticklabels(())\n",
    "ax.w_zaxis.set_ticklabels(())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clustering: K-means\n",
    "\n",
    "Clustering groups together observations that are homogeneous with respect to a given criterion, finding ''clusters'' in the data.\n",
    "\n",
    "Note that these clusters will uncover relevent hidden structure of the data only if the criterion used highlights it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LUANGKUXsXTTPo7aaNm2Gk9EN3Sth/Wg0w37xPG7VVkyt2lyjQtm+XT5KfmN2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\nnfTW9WAR/wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc240320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "k_means = KMeans(n_clusters=3, random_state=0) # Fixing the RNG in kmeans\n",
    "k_means.fit(X)\n",
    "y_pred = k_means.predict(X)\n",
    "\n",
    "plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y_pred, cmap=cmap);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets then evaluate the performance of the clustering versus the ground truth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0 50  0]\n",
      " [48  0  2]\n",
      " [14  0 36]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "\n",
    "# Compute confusion matrix\n",
    "cm = confusion_matrix(y, y_pred)\n",
    "np.set_printoptions(precision=2)\n",
    "print(cm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_confusion_matrix(cm, title='Confusion matrix', cmap=plt.cm.Blues):\n",
    "    plt.imshow(cm, interpolation='nearest', cmap=cmap)\n",
    "    plt.title(title)\n",
    "    plt.colorbar()\n",
    "    tick_marks = np.arange(len(iris.target_names))\n",
    "    plt.xticks(tick_marks, iris.target_names, rotation=45)\n",
    "    plt.yticks(tick_marks, iris.target_names)\n",
    "    plt.tight_layout()\n",
    "    plt.ylabel('True label')\n",
    "    plt.xlabel('Predicted label')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GERER06hjFBER02gqVURExEHxj0UFo4iImEgdowf49M+vubqEIuGp70uKp5bT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\nvTsqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc136eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plot_confusion_matrix(cm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classification Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.266666666667 0.0 0.06025 0.0380525039328\n"
     ]
    },
    {
     "data": {
      "image/png": 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wwpjWWQm418BHg6r2HdfBGTNXBT2txo/yAUVF7mss07rKPvm8teMVP0du4Zym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\nl5/X5MpDFMRGkFuItiCVVRen+UpkMvSuW7RMUvbyGYV6Kaq8LC9Sb57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mUGjQxs6jhqVj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\njBDkAoFAIBAMYf4fRizxaG6B9j0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd4a4ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "from sklearn import cross_validation\n",
    "\n",
    "errors = []\n",
    "for i in range(1000):\n",
    "    X_train, X_test, y_train, y_test = cross_validation.train_test_split(iris.data, iris.target, test_size=0.4, random_state=i)\n",
    "\n",
    "    clf = LogisticRegression()\n",
    "    clf.fit(X_train, y_train)\n",
    "    y_pred = clf.predict(X_test)\n",
    "\n",
    "    acc = (y_pred == y_test).sum()\n",
    "    err = 1- acc / n_samples\n",
    "    errors.append(err)\n",
    "\n",
    "plt.plot(list(range(1000)), errors)\n",
    "\n",
    "errors = np.array(errors)\n",
    "print(errors.max(), errors.min(), errors.mean(), errors.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.15 0.0 0.0511333333333 0.0227020312356\n"
     ]
    },
    {
     "data": {
      "image/png": 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YF+55aANOdCalymiRGkrju4+8gfUtmbobSqfx/d9vwrqtR33jPb+hFT/94xZ5HxaG8P3D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\nRgpyiUQikUhKGCnIJRKJRCIpYf4f40IKex0HEcgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd7773c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "errors = []\n",
    "for i in range(1000):\n",
    "    X_train, X_test, y_train, y_test = cross_validation.train_test_split(iris.data, iris.target, test_size=0.4, random_state=i)\n",
    "\n",
    "    clf = RandomForestClassifier()\n",
    "    clf.fit(X_train, y_train)\n",
    "    y_pred = clf.predict(X_test)\n",
    "\n",
    "    acc = (y_pred == y_test).sum()\n",
    "    err = 1- acc / n_samples\n",
    "    errors.append(err)\n",
    "plt.plot(list(range(1000)), errors)\n",
    "\n",
    "errors = np.array(errors)\n",
    "print(errors.max(), errors.min(), errors.mean(), errors.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Recap: Scikit-learn's estimator interface\n",
    "\n",
    "Scikit-learn strives to have a uniform interface across all methods,\n",
    "and we'll see examples of these below. Given a scikit-learn *estimator*\n",
    "object named `model`, the following methods are available:\n",
    "\n",
    "- Available in **all Estimators**\n",
    "  + `model.fit()` : fit training data. For supervised learning applications,\n",
    "    this accepts two arguments: the data `X` and the labels `y` (e.g. `model.fit(X, y)`).\n",
    "    For unsupervised learning applications, this accepts only a single argument,\n",
    "    the data `X` (e.g. `model.fit(X)`).\n",
    "- Available in **supervised estimators**\n",
    "  + `model.predict()` : given a trained model, predict the label of a new set of data.\n",
    "    This method accepts one argument, the new data `X_new` (e.g. `model.predict(X_new)`),\n",
    "    and returns the learned label for each object in the array.\n",
    "  + `model.predict_proba()` : For classification problems, some estimators also provide\n",
    "    this method, which returns the probability that a new observation has each categorical label.\n",
    "    In this case, the label with the highest probability is returned by `model.predict()`.\n",
    "  + `model.score()` : for classification or regression problems, most (all?) estimators implement\n",
    "    a score method.  Scores are between 0 and 1, with a larger score indicating a better fit.\n",
    "- Available in **unsupervised estimators**\n",
    "  + `model.predict()` : predict labels in clustering algorithms.\n",
    "  + `model.transform()` : given an unsupervised model, transform new data into the new basis.\n",
    "    This also accepts one argument `X_new`, and returns the new representation of the data based\n",
    "    on the unsupervised model.\n",
    "  + `model.fit_transform()` : some estimators implement this method,\n",
    "    which more efficiently performs a fit and a transform on the same input data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Flow Chart: How to Choose your Estimator\n",
    "\n",
    "This is a flow chart created by scikit-learn super-contributor [Andreas Mueller](https://github.com/amueller) which gives a nice summary of which algorithms to choose in various situations. Keep it around as a handy reference!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"http://scikit-learn.org/dev/_static/ml_map.png\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(url=\"http://scikit-learn.org/dev/_static/ml_map.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Original source on the [scikit-learn website](http://scikit-learn.org/stable/tutorial/machine_learning_map/)"
   ]
  }
 ],
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   "language": "python",
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   "pygments_lexer": "ipython3",
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