{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Sebastian Raschka](http://sebastianraschka.com)  \n",
    "\n",
    "- [Open in IPython nbviewer](http://nbviewer.ipython.org/github/rasbt/pattern_classification/blob/master/python_howtos/scikit_linear_classificationreate=1)  \n",
    "\n",
    "- [Link to this IPython notebook on Github](http://nbviewer.ipython.org/github/rasbt/pattern_classification/blob/master/machine_learning/scikit-learn/scikit_linear_classification.ipynb)  \n",
    "\n",
    "- [Link to the GitHub Repository pattern_classification](https://github.com/rasbt/pattern_classification)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sebastian Raschka \n",
      "last updated: 2016-07-16 \n",
      "\n",
      "CPython 3.5.1\n",
      "IPython 5.0.0\n",
      "\n",
      "numpy 1.11.0\n",
      "scikit-learn 0.17.1\n",
      "matplotlib 1.5.1\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -a 'Sebastian Raschka' -u -d -v -p numpy,scikit-learn,matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "I would be happy to hear your comments and suggestions.  \n",
    "Please feel free to drop me a note via\n",
    "[twitter](https://twitter.com/rasbt), [email](mailto:bluewoodtree@gmail.com), or [google+](https://plus.google.com/+SebastianRaschka).\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# An Introduction to simple linear supervised classification using `scikit-learn`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this introduction I want to give a brief overview of how Python's `scikit-learn` machine learning library can be used for simple linear classification."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sections"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [About the dataset](#About-the-dataset)\n",
    "- [Reading in a dataset from a CSV file](#Reading-in-a-dataset-from-a-CSV-file)\n",
    "- [Visualizing the Wine dataset](#Visualizing-the-Wine-dataset)\n",
    "- [Splitting into training and test dataset](#Splitting-into-training-and-test-dataset)\n",
    "- [Feature Scaling](#Feature-Scaling)\n",
    "- [Introduction to Multiple Discriminant Analysis (MDA)](#MDA)\n",
    "- [Classification via LDA](#LDA)\n",
    "- [Stochastic Gradient Descent (SGD) as linear classifier](#SGD)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## About the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top]](#Sections)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the following tutorial, we will be working with the free \"Wine\" Dataset that is deposited on the UCI machine learning repository  \n",
    "(http://archive.ics.uci.edu/ml/datasets/Wine).\n",
    "\n",
    "<br>\n",
    "\n",
    "<font size=\"1\">\n",
    "**Reference:**\n",
    "Forina, M. et al, PARVUS - An Extendible Package for Data\n",
    "Exploration, Classification and Correlation. Institute of Pharmaceutical\n",
    "and Food Analysis and Technologies, Via Brigata Salerno, \n",
    "16147 Genoa, Italy.</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Wine dataset consists of 3 different classes where each row correspond to a particular wine sample.\n",
    "\n",
    "The class labels (1, 2, 3) are listed in the first column, and the columns 2-14 correspond to the following 13 attributes (features):\n",
    "\n",
    "1) Alcohol  \n",
    "2) Malic acid  \n",
    "3) Ash  \n",
    "4) Alcalinity of ash    \n",
    "5) Magnesium  \n",
    "6) Total phenols  \n",
    "7) Flavanoids  \n",
    "8) Nonflavanoid phenols  \n",
    "9) Proanthocyanins  \n",
    "10) Color intensity  \n",
    "11) Hue  \n",
    "12) OD280/OD315 of diluted wines  \n",
    "13) Proline     \n",
    "\n",
    "An excerpt from the wine_data.csv dataset:\n",
    "    \n",
    "<pre>1,14.23,1.71,2.43,15.6,127,2.8,3.06,.28,2.29,5.64,1.04,3.92,1065\n",
    "1,13.2,1.78,2.14,11.2,100,2.65,2.76,.26,1.28,4.38,1.05,3.4,1050\n",
    "[...]\n",
    "2,12.37,.94,1.36,10.6,88,1.98,.57,.28,.42,1.95,1.05,1.82,520\n",
    "2,12.33,1.1,2.28,16,101,2.05,1.09,.63,.41,3.27,1.25,1.67,680\n",
    "[...]\n",
    "3,12.86,1.35,2.32,18,122,1.51,1.25,.21,.94,4.1,.76,1.29,630\n",
    "3,12.88,2.99,2.4,20,104,1.3,1.22,.24,.83,5.4,.74,1.42,530</pre>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reading in a dataset from a CSV file"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top]](#Sections)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since it is quite typical to have the input data stored locally, as mentioned above, we will use the [`numpy.loadtxt`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.loadtxt.html) function  now to read in the data from the CSV file.  \n",
    "(alternatively [`np.genfromtxt()`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.genfromtxt.html) could be used in similar way, it provides some additional options)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "total number of samples (rows): 178\n",
      "total number of features (columns): 13\n",
      "\n",
      "1st sample (i.e., 1st row):\n",
      "Class label: 1\n",
      "[14.23 1.71 2.43 15.60 127.00 2.80 3.06 0.28 2.29 5.64 1.04 3.92 1065.00]\n",
      "\n",
      "Class label frequencies\n",
      "Class 1 samples: 33.15%\n",
      "Class 2 samples: 39.89%\n",
      "Class 3 samples: 26.97%\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# reading in all data into a NumPy array\n",
    "all_data = np.loadtxt(open(\"../../data/wine_data.csv\",\"r\"),\n",
    "        delimiter=\",\", \n",
    "        skiprows=0, \n",
    "        dtype=np.float64\n",
    "        )\n",
    "\n",
    "# load class labels from column 1\n",
    "y_wine = all_data[:,0]\n",
    "\n",
    "# conversion of the class labels to integer-type array\n",
    "y_wine = y_wine.astype(np.int64, copy=False)\n",
    "\n",
    "# load the 14 features\n",
    "X_wine = all_data[:,1:]\n",
    "\n",
    "# printing some general information about the data\n",
    "print('\\ntotal number of samples (rows):', X_wine.shape[0])\n",
    "print('total number of features (columns):', X_wine.shape[1])\n",
    "\n",
    "# printing the 1st wine sample\n",
    "float_formatter = lambda x: '{:.2f}'.format(x)\n",
    "np.set_printoptions(formatter={'float_kind':float_formatter})\n",
    "print('\\n1st sample (i.e., 1st row):\\nClass label: {:d}\\n{:}\\n'\n",
    "          .format(int(y_wine[0]), X_wine[0]))\n",
    "\n",
    "# printing the rel.frequency of the class labels\n",
    "print('Class label frequencies')\n",
    "print('Class 1 samples: {:.2%}'.format(list(y_wine).count(1)/y_wine.shape[0]))\n",
    "print('Class 2 samples: {:.2%}'.format(list(y_wine).count(2)/y_wine.shape[0]))\n",
    "print('Class 3 samples: {:.2%}'.format(list(y_wine).count(3)/y_wine.shape[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the Wine dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top]](#Sections)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are endless way to visualize datasets for get an initial idea of how the data looks like. The most common ones are probably histograms and scatter plots."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scatter plots are useful for visualizing features in more than just one dimension, for example to get a feeling for the correlation between particular features.  \n",
    "Unfortunately, we can't plot all 13 features here at once, since the visual cortex of us humans is limited to a maximum of three dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we will create an example 2D-Scatter plot from the features \"Alcohol content\" and \"Malic acid content\".  \n",
    "Additionally, we will use the [`scipy.stats.pearsonr`](http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html) function to calculate a Pearson correlation coefficient between these two features.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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I244dO4YbbrgBSUlJGDVqFLZt29bj8YsXL0ZmZiaysrJQWFjYvr+mpgZz5szBoEGDkJaW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\nQGL/D4Dmw0mQJl+RAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ad029b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from scipy.stats import pearsonr\n",
    "\n",
    "plt.figure(figsize=(10,8))\n",
    "\n",
    "for label,marker,color in zip(\n",
    "        range(1,4),('x', 'o', '^'),('blue', 'red', 'green')):\n",
    "\n",
    "    # Calculate Pearson correlation coefficient\n",
    "    R = pearsonr(X_wine[:,0][y_wine == label], X_wine[:,1][y_wine == label])\n",
    "    plt.scatter(x=X_wine[:,0][y_wine == label], # x-axis: feat. from col. 1\n",
    "                y=X_wine[:,1][y_wine == label], # y-axis: feat. from col. 2\n",
    "                marker=marker, # data point symbol for the scatter plot\n",
    "                color=color,\n",
    "                alpha=0.7, \n",
    "                label='class {:}, R={:.2f}'.format(label, R[0]) # label for the legend\n",
    "                )\n",
    "    \n",
    "plt.title('Wine Dataset')\n",
    "plt.xlabel('alcohol by volume in percent')\n",
    "plt.ylabel('malic acid in g/l')\n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to pack 3 different features into one scatter plot at once, we can also do the same thing in 3D:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lAprdUMGkxE2kvpWCIMDtdoNhGDgcjrQtrh1rwn6yoBNxMPF8H9EElOM4+Hy+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DNOPgbXOj60vnKYrh99wWHTBJ54ti5ff63kxRfVBARI1Ktn4bvvVIwcaSxgLHNy4PvvlYwebcTd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\nIiIiIiJPwf8DnH7AYGZn9eIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c6079b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "fig = plt.figure(figsize=(8,8))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "   \n",
    "for label,marker,color in zip(\n",
    "        range(1,4),('x', 'o', '^'),('blue','red','green')):\n",
    "    \n",
    "    ax.scatter(X_wine[:,0][y_wine == label], \n",
    "               X_wine[:,1][y_wine == label], \n",
    "               X_wine[:,2][y_wine == label],  \n",
    "               marker=marker, \n",
    "               color=color, \n",
    "               s=40, \n",
    "               alpha=0.7,\n",
    "               label='class {}'.format(label))\n",
    "\n",
    "ax.set_xlabel('alcohol by volume in percent')\n",
    "ax.set_ylabel('malic acid in g/l')\n",
    "ax.set_zlabel('ash content in g/l')\n",
    "plt.legend(loc='upper right')\n",
    "plt.title('Wine dataset')\n",
    "     \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting into training and test dataset "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top]](#Sections)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is a typical procedure for machine learning and pattern classification tasks to split one dataset into two: a training dataset and a test dataset.  \n",
    "The training dataset is henceforth used to train our algorithms or classifier, and the test dataset is a way to validate the outcome quite objectively before we apply it to \"new, real world data\".\n",
    "\n",
    "Here, we will split the dataset randomly so that 70% of the total dataset will become our training dataset, and 30% will become our test dataset, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "from sklearn import preprocessing\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X_wine, y_wine,\n",
    "     test_size=0.30, random_state=123)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that since this a random assignment, the original relative frequencies for each class label are not maintained."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class label frequencies\n",
      "\n",
      "Training Dataset:\n",
      "Class 1 samples: 36.29%\n",
      "Class 2 samples: 42.74%\n",
      "Class 3 samples: 20.97%\n",
      "\n",
      "Test Dataset:\n",
      "Class 1 samples: 25.93%\n",
      "Class 2 samples: 33.33%\n",
      "Class 3 samples: 40.74%\n"
     ]
    }
   ],
   "source": [
    "print('Class label frequencies')\n",
    "        \n",
    "print('\\nTraining Dataset:')    \n",
    "for l in range(1,4):\n",
    "    print('Class {:} samples: {:.2%}'.format(l, list(y_train).count(l)/y_train.shape[0]))\n",
    "    \n",
    "print('\\nTest Dataset:')     \n",
    "for l in range(1,4):\n",
    "    print('Class {:} samples: {:.2%}'.format(l, list(y_test).count(l)/y_test.shape[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Scaling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top]](#Sections)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another popular procedure is to standardize the data prior to fitting the model and other analyses so that the features will have the properties of a standard normal distribution with   \n",
    "\n",
    "$\\mu = 0$ and $\\sigma = 1$\n",
    "\n",
    "where $\\mu$ is the mean (average) and $\\sigma$ is the standard deviation from the mean, so that the standard scores of the samples are calculated as follows:\n",
    "\n",
    "\\begin{equation} z = \\frac{x - \\mu}{\\sigma}\\end{equation} "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "std_scale = preprocessing.StandardScaler().fit(X_train)\n",
    "X_train = std_scale.transform(X_train)\n",
    "X_test = std_scale.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zZw+8Xm+LQe2dd97BY489hrfffhuFhWZ/ztNOO60hgTzvvPOwaNEiAMBf//pX\nXH/99Th8+DDatWuH++67D/fddx/27NmDq6++Gr1798bEiRNbbVtdXR3nkBG51Lp96/DBlx+gQ0YH\n1NTVoPJEJeZsmtOkaO7Nl9yM2vrahscCQZu0Ng2P/b1jZ2SfAYU29JL1zuttqQ2pGr+YkFFSOHLi\nCDpldnK6GQCA/mf2xxnZZzR5rmNGx4afzzvtPJx32nnNvr+mrgbLS5bDq16UHiuFQrG3ci8+LfvU\n8qbmAwYMQJcuXVBUVIQZM2YgLS0NGzduPKXb/9ixY2jTpg06d+6M2tpaPPLIIzh69GjD6wsXLsSQ\nIUOQl5eHnJwciAg8Hg+Ki4uRl5eHwsJCZGdno02bNiED58GDB7Fq1SoMGzYM7dq1w/Lly/Hiiy/i\nxRdftPQ9iCi+cjJycNvXb2vy3Nk5Zzf83DatLW66+KYWz/HG9jdQ561r6DU76T2JN3e8aTkhS9n4\npaoJdzPNJjJ2Ht6pV867UksOl8T1c+38PTxy/IgerDrYcCurKlOv1xvWOfbu3asjRozQzp07a35+\nvk6aNElVVZ9//nm94oorVFW1vr5eb7nlFu3YsaOeeeaZ+thjj2mPHj105cqVqqo6btw4LSgo0A4d\nOuiFF16or732mqqqLl68WHv37q3Z2dl6xhln6OTJk7W+vv6UNhw8eFCvuuoqzc3N1ZycHL3ooot0\n7ty5zba5uX9T3/OOx55Y3Bi/yC3s+l08fvJ4k/h1sOqg1tTVhHWORIxfqtHFMFdV6reKla4p0LSV\n0/Dy1pcxss/IuO5Fl4hVrt2OlfqJ4ocxLPaSplI/UbhKykuwomQFenbuecrkUyIiokTBhIwS2pxN\nc+CBB+medHjgCblEm4iIyO2YkFHCKq0qxapdqwCYitAAsHLXyqTfyoOIiJIP55BRwlJVbD+0HfXa\nWD8mTdLQq3OvuGw+y/kXscc5ZETxwxgWe9HEMCZkRBFiMIs9JmRE8cMYFnuc1E9ERESUwFgYlihC\n3bt3j8vQaCrp3r27000gShmMYbEXTQzjkCVRjE1bOQ2rSlahILsApcdKMfjcwXGtj5aMOGRJFDk3\n7WSSqjhkSRRnXPlJRG5SUl6C4S8OZ43GBMAhS6IYys/KxwsjXjhl5Wd+Vr6DrSKiVDVn0xzsr9x/\nygbh5D4csiQi1+OQJVH4SspLMGrpKORl5aGsugxLrl+CHrk9nG5WSuKQJRERUYriTiaJhQkZERFR\nkuF81sSttyO4AAAgAElEQVTDIUsicj0OWRKFx+mdTKgpVuonoqTAhIyIEhnnkBERERElACZkRERE\nRA5jQkZERAntyIkjTjeBKGpMyIiIKGGxEj0lCyZkRESUsAIr0RMlMiZkRESUkErKS7CiZAV6du6J\n5SXL2UtGCY0JGRERJSQ3VaLnPDaKFhMyIiJKOG6qRO/EPDYmgMkn3ekGEBERhSs/Kx8vjHjhlEr0\n+Vn5cW9L4Dy2mYNn2v55JeUlmPjqRDw//HluFp5E2ENGREQJR0TQO683CvMLG26983rHfVsgJ+ax\ncSFDcmJCRkREFKF4z2PjQobkxYSMiIgoAk7MY3PTQgaKLW4uTkSux83FyY1UFdsPbT9lHluvzr1s\nGTotrSrFNYuvARTweDzwer2AAK+PeR0F7Qti/nkUO1ZimKsSMhHpCuAFAKcD8AKYo6p/CHEcAxpR\nCmFCRhT/BJBiJxETsjMAnKGqm0UkG8BGAMNV9dOg4xjQiFIIEzKKSkUFUFoKFBQAOTlOt4ZSkJUY\n1uocMhH5hog8JSIfishBEdkjIm+KyO0iEtPfbFX9UlU3+34+BuATAGfF8jOIiCiFrF4NDB0K3HST\nuV+zxukWEYXUYg+ZiPwdwBcAXgXwbwClADIB9ALwbQDXAPidqr4W84aJnAOgGMCFvuQs8DVeYRKl\nEPaQUUQqKkwSlpEBZGUB1dVATQ2wbBl7yiiurMSw1grDjlfVsqDnjgHY5Lv9VkTyomhjSL7hyqUA\nJgUnY34zZsxo+HnQoEEYNGhQrJtB1KIjJ46gU2Ynp5uRlIqLi1FcXOx0M2zD+BUnpaVAfb1JxgBz\nX1VlnmdCRjaKJIa5ag4ZAIhIOoA3APxdVZ9o5hheYZKjWCk7vthDRhFhDxm5RNRzyETkqIhUNneL\nbXMb/BnAx80lYwQTZHbsMPfRHEMRY6VsogSQkwPMnGmSsIMHzf3MmUzGyJUs9ZCJyG8AHACwAIAA\nuBFAF1W9P6aNEfkmgDUAtgBQ3226qr4VdFzqXmGuXg3cc4/phk9LM8HlyivDPyYF2DWkWFJeglFL\nRyEvKw9l1WVYcv0S9pLZjD1kFBWusiSHxazshYh8oKoXt/ZcvKRsQLPS/c4uegD2DilOWzkNq0pW\noSC7AKXHSjH43MFx2VA4lTEhI6JEFpOyFz5VInKjiKSJiEdEbgRQFX0TKSyhJqjW1ZnnwzkmBdg1\npOjEVilERJT8Wltl6TcWwBO+mwL4p+85iqeCAjMEWV3d2PuVnm6eD+eYJBe8+e5tl94Ws16y/Kx8\nvDDihVMqZedn5cfk/ERElJos9ZCp6ueqOlxV81Q1X1VHqOrnNreNglmZoMpJrLZuvisi6J3XG4X5\nhQ233nm9uW0JERFFxeocsl4AngZwuqpeKCIXAfiBqj5odwObaU9qz8GwMkE1RSexcvPd5MQ5ZESU\nyGI5qX81gLsBPKuq/XzPfaSqF8akpWFiQKPmcPPd5MSEjIgSWSwq9ftlqer6oP+h1UXcMiKb+IcU\nncQK/kREFC6rqyzLROQ8mAn9EJHrYeqSEVGAkvISDH9xOHaV74ro/UdOHIlxi4iIKBFYTchuB/As\ngPNFZD+AyQB+aluriBJUNOU2ok3miIgocVldZVmiqv8JIB/A+ar6La6yJGoquNxGuIlVcDLn9TZ9\nPfgxERElD0sJmYjUi8gjAKpV9ajvuU22towowURTbiM4mdt5aBemTgW2bDGvb9kCTJ3KpIyIKFlZ\nHbLc6jv2HyJymu+5pFjxRBQL0VbwD07m5m6egwkTgEceARYtMvcTJgAeq3+xRESUUKyusqxT1aki\nMgrAOyJyE3wT/IncxOttmrQEP7ZLNBX8m0vm7hhQiqFDC7B4MTBmDNCnjz1tJyIi51mtQ/Z+QP2x\nCwEsAtBNVR1Z2886PhSK12uG9SZMAPr2NcN88+cDs2a5u2cpVO000TQ8fHcvHCoT3HgjsHAhkJcH\nzJvn7u9iF9YhI6JEFss6ZLf6f1DVj0TkCgDDo2kcUax5PGgY5hs6FFi2DCgqcn8CE6p2mm+DASIi\nShEt9pCJyHdUdZWIXBvqdVX9X9ta1gJeYaa21gqvLlqEhmG+sWMjO4cbeL3Aiy82fpfRo92fXNqF\nPWRElMisxLDWwvtVvvtrQtyGRd1CojC1VqtryxbTMzZmjLn3r1IM5xxusXVr0++ydavTLSJyJxZU\npmTQYkKmqr/y3U8McbslPk0k8qmowJwVj2L/kb0hS0p4vWbOWFGR6RkrKjKPg0tFRFO8NV6sfhei\nVGf7BVZFBbBjh7knslFrQ5a/aOnNqvq7mLfIAnb5x49rhvZWr0bJg3dh1IWfIq+uDcp6nI4lE/+O\nHrk9mhzW2irLkvISjFo6CnlZeSirLsOS65eccg63cGrFqBtxyJKaM23lNLy89WWM7DMSMwfPjO3J\nV68G7rkHqK8H0tKAmTOBK6+M7WeEiXEhMcViyLKD7/YfMFslneW7/QTApbFoJLmXa4b2KiqAe+7B\nnG4H4UlPR7qkwbN3P+as+59TDg0OTMGPoyneGm+tfReiVBft7hgt8sUdZGSYJc4ZGcD06Y72lPlX\nkrNgdHJqbcjy16r6awBdAVyqqnep6l0Avg6gWzwaSM5xYmgv5HZBpaUoTTuBVadVAgDKMuoBKFaW\nrLBceBWIvngrEbmLrRdYpaWmZywryzzOygLq6szzDglcSc6C0cnHatmL0wHUBjyu9T1HSSr4yvO2\nS2+zfWiv2Tpi9xQgvz4DL3zSG/XtMoETJ4DaWqTd8SdLhVf9oineSkTu0tIFVkH7gug/oKDADFNW\nV5tkrLoaSE83zzuob19T1se/+rpvX0ebQzFkNSF7AcB6EXnF93gEgOdtaRG5Qqgrz5jPzwjSbB2x\n3Bxg5sPoPX06UHbCBMWZs4Ae/xHW+UPV+yKiFlRUmB6hggIgJ8fp1jRh+wVWTo6ZMzZ9OlBV5Ys7\nMx3/dwheSd63L5OyZGGpUj8AiMilAK7wPVyjqu/b1qrW28JJsTYqrSrFNYuvARTweDzw+qqUvj7m\n9dhcebai2TpiLv6fA9mLk/od4MIJ7Y5wUdxJ1N1IyFoMazUhE5E0AFtV9fxYNi4aCRPQElSorXzS\nJA29OveCiL3/T9yy5dQeMl79EROyOKuoMH+EGRmNw3U1NeaPkhdDjgpeVXm4+ghOy3LBSnhqUUy2\nTlLVehHZJiLdVHVP7JpHbuXU0F5g7S1/Nzyv/ogcEGpCe1WVeZ4JmaOCy/hMfHUinh/+vGvL95B1\nVv83lwtgq4isFJHX/Dc7G0apx+MxyZe/R6xvXyZjRI4InNAOuGZCOzWVCEWuyTpLc8hE5KpQz6vq\n6pi3yIKE6PInopjhkKUD1qwxE9rr6hontKfiHDKXSqQi1xSjOWRulDABjYhiggmZQ1w0oZ2amrZy\nGlaVrEJBdgFKj5Vi8LmDbV8JT5GLRaV+/4kuE5ENInJMRGpFpF5EKmPTTKLopeLmwiGL6BLFUk4O\n0LMnkzGXCVWD7R87/8Ei1wnO6uyc/wEwBsAOAO0A3ArgKbsaRcnHzoTJNVs8xRG3UCFKXf4abPNG\nzMPcH8zFA99+ACKCYzXHnG4aRcHydGlV/QxAmqrWq+o8AP9lX7MomdidMKXixFZuoUKUuvwr4Qvz\nC1GYX4ji3cUoP16O595/zummURSshu9qEWkLYLOIzBKRO8N4L6U4OxMmWzcXdrnALVSGDmW9NqJU\nlMoxMNlYTarGA0gD8DMAVQDOBnCdXY2i5GF3sLB1c2GXC95CxT98SUSpI5VjYLKxlJCp6m5VPa6q\nlar6a1X9hW8Ik6hFdgaLljYXTnaBRXTHjjX38+dzDhlRKknlGJiMWix7ISJbADR7gKpeZEejWpNQ\ny8bjzUXL1EPuiVlfj9e/+T8o6HZB1O1zcosnNwjeQiX4cTJh2QtKREdOHEGnTPu2NUr1GJhIoq5D\nJiLdfT/e7rtf4LsfB0BVtSjqVkaAAa0ZLtsM+JRgsWED0n7/BHodbQtJY6FJso4JGSUabmtEgWJW\nGFZE3lfVfkHPbVLVS6NsY0QY0EJw+2bAbm8fuRoTMko001ZOw8tbX8bIPiNZsJViVxjWnEu+GfDg\n8jDeS/EQajPgujrzvBu4vX1ERGFqrr4iVz5SJKwmVT8C8EcR+VxEdgP4I4BbYt0YEZkrIl+JyIex\nPnfSc/tmwG5vHxFRGFqqr8iVjxQJq6ssN6rqxQAuBnCRql6iqptsaM88AENsOG/yy8kxc7JqaoCD\nB839zJnuGQ50e/uIiMLQXH1FrnykSFmdQ5YBU3fsHADp/udV9YGYN8gsJHi9pRWcnIPRAhetsgwp\nDu2ze2UTxR/nkJGblJSXYNTSUcjLykNZdRmWXL+kYeI+Vz5SKFZiWHpLLwZ4FUAFgI0AaqJtGNko\nJ8ediZifze3jyiYislvwkOST65/E74b8DkDjtkZE4bKakHVVVVftXTljxoyGnwcNGoRBgwY51hZy\nj8BhBLtWNrEHzn7FxcUoLi52uhm2YfxKXMFDkifqT+C5Tc9hzIVj0P+s/g63jtwikhhmdcjyTwCe\nVFXbN2fhkCVFqqVhhFh+Bnvg4o9DluQWwUOSj7/3OP7vs//DjX1vxMP/+bAtn8mLwMQXy7IX3wKw\nUUS2iciHIrLFxpWQ4rsRhSUeK5vs3CidiNzPPyRZmF+IzPRMbP5yM/oU9MGKXStsKW/R0mpOSi5W\nE7KrAfQE8D0A1wAY5ruPKRFZBOBdAL1EZI+ITIz1Z1ALKiqAHTvMfYKJx8om1hYiokBuvAhsrjYa\nuZ+lIcuGg0UKAGT6H6vqHjsaZaEd7PKPNZdtuxSueKxsmrZyGlaVrEJBdgFKj5Vi8LmDWYE7Tjhk\nSW4Tcq9eAV4f8zoK2semvmK40zA4pcK9Yrl10g8A/BbAmQBKAXQH8Imq9olFQ8PFgBZj3NaoVfEI\nvtQ8JmTkNm68COR2Te4Vy7IXvwFwGYAVqtpPRL4Ns8E4JYNQ2xpVVZnnUygha27irNcL5Gfl44UR\nL6Be6+H1Ah6PCb75WfkOtJSInGZ3eYuWpmGEuggMnlJx26W3sZcswVhNyE6q6iER8YiIR1XfFpHf\n29oyip/AbY38PWQptq1Rc139Xi8wdSowYYKgb9/e2LIFmD8fmDXLJGVERHYIvAj0a+kiMNR8NvaS\nJRarCdkREckGsAbAQhEpBVBlX7MorvzbGk2fbnrG0tNTbluj5uqXeTzAhAnAI4+YUd1ly4CiIiZj\nRGSvcHrgwu1NI3eyOoesPYDjMKsybwSQA+AvqnrY3uY12x7OwYiBU4bo3L7tkk2sTJxdtAhYvBgY\nMwYYO9ahhqYwziGjWEnGml7crsn9YlmH7H5V9apqnarOV9U/APhl9E0kp4SsbZOTA/TsmVLJGND6\n0vUtW0zP2Jgx5n6L7eWRicgOyVrTK7A2mv/WO683k7EEYzUh+26I566OZUMovtxY4NSJ+jmt1S/z\nes2csaIi0zNWVGQee71xbyoRRcmNcY/Ir8UhSxH5KYD/B+A8AJ8FvNQBwD9V1ZGVluzyj048thiK\npE1O1M+x0tXvX1XpF/yY7MchS4qWXXEvGYdAKfZiMWS5CKYi/6u+e//t604lYxS9eFSXjqRNTly5\nWunqD06+mIwRJR474l6yDoGSM1r8X4uqVqjq5wDuBfClqu4G0APAOBHhJUECiscWQ+HilkREZCe7\n4h6HQCmWrK6y3AzgPwCcA+BNmB6zPqr6fVtb13x72OUfITeuxuGWRNQaDlkmCYdWctsR99w49YPc\nK5aV+r2qWici1wJ4UlWfFJH3o28ixZvd1aXDxfo5RCnCwf1y7Yh7LMRKsWa1h+xfAH4P4B4A16jq\nLhH5SFUvtLuBzbQnda8wk4wbe+zIfdhDluCSbL9c7m1L4YplD9lEAD8B8JAvGesBYEG0DSRyW48d\nEdkgHvvlxnE4NNxtjYissNRD5jYpeYWZYriUnAKxhyzB2d1D5uBwKJEVUZe9EJHXReQaEWkT4rVz\nReQBEbkl2oYSBeJScqIk498vt6YGOHjQ3Mdqv9yKCpOMZWQAeXnmfvp08zxRAmltyPI2AL8A8HsR\nOQzgIIBMmNWWOwH8j6q+amsLKeU0t9E3ESWwK680PWKxHlaMx3BokuOIhDu0VofsS1WdqqrnAbgB\nwG9gErQLVfW7TMYo1liTjCiJ2bFfbkGBGaasrjaPq6uB9HTzPLWKIxLuYbnmuKp+rqrrVHWzqlbb\n2ShKXW7cRYCIXMzO4dAUwOK27sFJ/W7mUBFFp3ApOTWHk/qpVSkWL2OBxW3jJ5ZlLyjeUnDVEJeS\nE1HEcnLimoglw7wrFrd1F/aQuVGSFVEkihZ7yMhNSspLMPHViXh++PMJ26PEEYn4irqHTES2AAgV\nOQSAqupFUbSPmsNVQ0RErpUMK8E5IuE+rQ1ZDotLK6ipwFVD/h4yrhpqkX/4wOsFPAFLVYIfExFF\nI3gl+G2X3paQvWTcJcV9Wit7sdt/A3ACQF/f7bjvObIDVw2Fxb9se+ehXZg6FdiyxTy/ZQswdapJ\nyiJ15MSR2DSSiJKCkyvBGY+Sm6W+AxEZCWA9TC2ykQD+JSLX29mwlOcvorhggbl3ekJ/RQWwY4cr\nq1/7hw/mbp6DCROARx4BFi0y9xMmRN5Dxvo8RBSotKoUq3atAgCUVZcBAFbuWonSqlLbP5vxKPlZ\nXWV5D4D+qloKACKSD2AFgKV2NYwQ91VDzXLxis9QwwdDh/bA4sXAmDFA376RnzsZ5okQUew4Oe+K\n8Sj5We078PiTMZ9DYbyXEpnL94kLHj6Y+dYcLFtmkrFlyxqHL8Pl9I4BHJogch//vKvC/MKGW++8\n3hCxdwGw0/GI4sNqUvWWiPyfiNwsIjcDWAbgTfuaRa4RasVnXZ153mHBwwcK4I1PVuK2yaUYOxYo\nKgLmz49sDpmT80Q4NEFEgbiDSWqwXIdMRK4D8E3fw3dU9RXbWtV6W1jHx27+qtcZGcDYsZZrosWz\nWKKqYvuh7U2GD0TTcH5+r4Yr1khWWTpdn2fayml4eevLGNlnJIcmfFiHjFKV0/GIYsNKDGNhWDpV\n8JyxUaOAl14yPWPp6Y1zyIK2KkmGYolA6EQvTdLQq3OvuAxNcCuTUzEho1TlZDyi2IlZQiYi1wJ4\nFEABTFFYf2HYjrFoaLgY0GzU3C4BixaZe/8+cSEm+k87+Xf27ERp2sppWFWyCgXZBSg9VorB5w7m\nvyWYkDmCe0MSxYyVGGZ1MGcWgB+oao6qdlTVDk4lY2Sz5uaM1dQAPXuawBxion/Jb36BFTv+z9Kk\nU05YD83JJfVETaxebS7MbrrJ3K9Z43SLiJKe1bIXX6nqJ7a2hNzByi4BIZK2OZ0+gacuv9VNamM9\nrJlMlfm5lQm5QuAFlz8GTJ/OvXSJbNbi/7pE5FrfcOW/ReQlERnjf873PCUbK7sEBCZtAEpPHsGq\n/KNAeptWe3YCa+lEy+tFzCvzO8mpJfVETbh4ZTVRMmtxDpmIzGvhvaqqt8S+Sa1LmDkYiay1+SNr\n1pir5ro6aHoatt/7U9R//dKGl0NNOg2esP7cNc/h4jMujqqZW7aYivxDh5oL+KKi6IrBkjtxDlkc\nNTePlD1kRBHjKkuyV5iTfgMnrO+p2IPy4+VYffPqqIcuFy1CQ2X+sWOjOhW5FBOyOAu44GqyspqI\nIhKzSf0i0lVEXhGRUt/tryLSNTbNPOWz/ktEPhWR7SLySzs+g2IkJ6dxon8rgiesH6w6iNKqUvz+\nvd9H1YQtWxCTyvxEFMBte+kSpQCrZS+WA1gEYIHvqXEAblTV78a0MSIeANsBDAbwBYANAEar6qdB\nx7n/CpOaCKyls7diL+76x13IbZeL4yeP4+UbXo6ol8w/h2zCBDNMuWWLqcw/a1biTuyn0NhDRkSJ\nLJZ1yDar6iWtPRctEbkMwK9U9Wrf4yKYuWqPBh3HgJbAYllrK5lWWVLzmJARUSKLZR2yQyIyTkTS\nfLdxMBuMx9pZAPYGPN7ne46SRKxrbQUnX0zGiIgoEVmtQ3YLgCcBPA5AAbwLYKJdjbJixowZDT8P\nGjQIgwYNcqwtruayatustUVWFBcXo7i42Olm2Ibxi5IFRylCiySGuWqVpW/Icoaq/pfvMYcsoxFi\neyNOznUPBjLrOGRJ5D6cx2tdLFdZzheRTgGPc0Xkz9E2MIQNAL4mIt1FpC2A0QBes+FzEk9FBbBj\nh7m3enzQ9kaYPt36+8lWyVbUlqhZ4cYuShgej0nGHnnElB965BHzmMlYZKz+s12kqg0bEKpqOYB+\nsW6MqtYD+BmAfwDYCuBFbtmEyPaVY7VtV2Mgo5TAPTGTXt++5j/t4sXmnoW5I2c1/HtEJNf/QERO\ng/X5Z2FR1bdUtbeq9lTVR+z4jIQSaU9X0PZGIfekJEcxkFFSi0UvPXvXXI+1IGPHakL2WwDrROQ3\nIvIgzKT+WfY1ixpE2tNlZU/KBBI8lJcMQ3sMZJSQgpOk5pKmaHvp2bvmel6vmTNWVGR2SSkqMo+T\nIT47wfKkfhEpBPAd38NVqvqxba1qvS2pMyk22n3lXLbKMhLJOHE08Dv16QNs3dr4nYDE/V524aR+\nlwheKDRyJLBkSeiFQ9HELu6nmTC4OMmaqAvD+oYmm6WqhyNsW1QSOqBFgvvKJeUm4v6ryOYSMwa1\nRkzIXCA4SaqsBN5/H+jXD+jYMXTSFGns2rHD9Izl5TU+d/Cg2cqpZ097vh+RjazEsNbmgW2EqTvm\nP4k/iojv53OjaiFZ68Hy7yuX4D1d0QicbzVmTOInY0BjwuWf3B+YbDIZI9cJHoL0eMxVRVqaeZyV\nBVRVmeP8MSrS2BU4B9bfQ8Y5sJTkWkzIVDX8DQbJunDqhOXkpGQi5hc836pv35aTskTqRo802Uyk\n70hJIDhJ8v/C1fuKPDeXNEUSu/xzYKdPN0mev3cthWMgJT/L4dtXe2yAiFzpv9nZsKTHOmGWhTtx\nNNFqfEUyuT/RviMlgeCFQvX1wEMPmXs7Fg75e9cWLDD3KTZNg1KP1c3FbwUwCUBXAJsBXAZgnap+\np8U32iRh52AE4hyJsITbG5Qoc87CWbAQ/J0/+MAc5/bvGAucQ+YiwdMskmDhEJHdop7UH3CiLQD6\nA3hPVS8RkfMBzFTVa2PT1PAkfEADQk+QPXYMeOUVoFs3p1uXFBYtahwGHDvW6dY0z0qy2Vzidskl\nwEsvuf87RosJGSWbIyeOoFNmp9YPtFGo2OPnf97/HKdDRCdmWycBOKGqJ3wnzVDVTwH0jraBKS2w\n+3/nTrNa6fhx839V1tuJml01vuyohxYc6EIFvlCV/QcOBN58s/E7fvABhyyJEkFJeQmGvzgcu8p3\nOdaGUNMe7r4bmDIFmDjRPN6yxfx8992MLfFgNSHb59vL8m8AlovIqwB229esFHHlleb/ru3amaXj\n553HuWQxYFexQqfnbQVO/h8yxCRlx46Z56+91nzXKVMYOIncbs6mOdhfuR9zNs1xrA2hLvJuvtkk\nYGVlwE9+Ym5lZeZ59pDZz3Jh2IY3iFwFIAfAW6paa0urWm9D8nT5p8pcsjjPM7E656y14wIfe70m\nCfPP23rjDWDatPjN2wqeF/fDHwLz5gFHfLvM5uQAjz6anPPIOGSZopJwflpJeQlGLR2FvKw8lFWX\nYcn1S9AjN7qCBtGsuA41tWPRImD2bPPzlCnJPR0iXmI5ZNlAVVer6mtOJWNJJxX2nHRgCxQrw4CB\nPV7+ZMvf4+W/Bb4+cSLwu98BV18NPPus+X9Fnz62f5WGtgb3+r33ngmix4+b27hxyZmMUYpK0q2T\n5myaAw88SPekwwNP1L1k0fTch5rasWULsHChGbhp1878zG3d4iPsHjI3SLorzGSuxB+jLVDC6ckK\n9bi55z/4wPQq+UeIH/FtZ+9f6bh1a2Ov1MKFZu2FP9B16mRei1cSFKrt06c39pDFuz3xxB6yFJOk\nWyeVVpXimsXXAAp4PB54vV5AgNfHvI6C9pFfhEeyqjzUQqHnnwdUgUOHTM8YYHrK8vKAxx7jsGU0\nYrbK0m2SMqAlYdc8gMYh2ZwcoLYWaNvWZBBhDMm2VhrCaumIllYqzplj8uHbbz81oPm79EeNMvfH\njgE//rF5vbn9J6Mt0mol4bz7bjO/IxUCJxOyFJOkUzlUFdsPbUe91jc8lyZp6NW5F0Si+/WOZFU5\nV1nGDxOyZGJnwhbpua28r6IC+Na3gD17GrOnbt2AtWvD+qzgmltTpwIXX9z4eqgrxD59Tg02gT1e\ny5aZyfD/+7/m8VNPmQ7K224zw3/+8z78MDBsmOkhUzWv+dvgT9qmTgXGjzdtCkwIgfATtXASzMDz\nJ3PgZEKWYpK0h8wuiVJ30U5u37nEljlk5AA751JEeu5w3+e/+ovgKtDrNRfGffuaK8C+fc3jwKu5\nwBWIQ4eaZCzUvIo+fRqPu/pqYN26xuDVqRPQvj3w4IPAX/9qzj97NtCmDTBypLlYz88HRo825/rR\nj8x5PR7gG98wz//lLyYwTphgPjeSuR3+1U8PP3zq+YKvYAMDTvBjooQVvCtArHcBSCJ2rSpPJE6v\ngI8V9pC5nZ1XipGeO5z3BQ5Z1tSY94QzZOnrhXt1XQEm3Z/TcAX4298C113XeFioK0Sg9ef8vVz+\nHqkLLjC9Zh99BDzwgBkGyM83qxn9/B19wSsuL7oI+Oc/zZDB6NHmOH+7rr4a+Pvfm++5C1UIdtgw\n8/7bbzefETwk6YbCkvHCHjKXs6sHP1mncsSY1wtU1jbGA7f1DsWD23sJ2UOWDEpLzV5xWVnmcVaW\nmexUWurcucN5n38V6cmTQHa2ube6itTXC6fjb8JF04biwe+twZ49pjbOunWNVz/NXSEG9ob5e82C\nj1uwwJxj1izzx5uebrbnO+MMs6KyosLM0fL3PgXOWfN4zHmffRbYt88Mq44ZY5KziRPNY/8m6L/6\nlcaDFQgAABbvSURBVEnKmuu5C76S27rVdCZ27mySz/Hjm9YDckNhSSIA9vbg5+SYC7cET8bsKCgd\n6PN9H2D4vO9h154PLH1+MgoeJXFTMmYVEzK3s7MsRmvnrqgwPVzBRWrDaVOkQw8Bm69Lfh46d81A\n/1em46bhFdiyxSQo/itAj6cxoQLMvX+FZOCS7q1bQx8XaqivpZFV/5BiUZGZd3byJLB3L1BVZc45\nbRpQXm56yR5+GHjmGTMv7e9/N20ILsY4YcKpPWbz55vXpk41vWIHDpjv4W+7GwpLEgX+nSIvj4Wt\nQ4hkOC2sBG71asy5fyj27/oQc+4bCm/xmrgM39mdZIYruITHB0G5qdPts4IJmdvFei5FYJIVfO6q\nKuD//T9zXPBV75tvNv++1tp05ZXmL2TBAnNvpaRHQC+cKrCvLAtnd6nDDVeVNvRshVoRFChUr1mw\nUEOFs2eb+WRTppj72bNP/WP21x9LTwd+9jPgb38DcnNNArZli+kMvOkm4LnnTI9eUVHzPXfBV3L+\nBBMwCwlOO81s4rB4sTl3SXkJVpSsQM/OPbG8ZDl7ycg5dvbgJwArSUmoivjBF2HB57CcUFVUoOTB\nu7CicyV6nuyA5XmV2P3gLzDx2grLnxcJt83ZCh4l8c/x9SdlTrfPKs4hSxSxmEuxerW5mq2vNz1c\n/npnFRVmnO3JJ03XkKpJzgoKTIDdvx/47DOgd29zBRz4PjtXfgbMU9Oqakht4zw1q6sVI1nhePfd\nZmgwsDZPcCmJwNWXgas6X3zRJE7f/KY5JnDuWN++oVd6hprrUFcH/PKXjWUtvF4zhJqXB7S5ehre\n3rUKBdkFKD1WisHnDsbMwTPD+ddNOJxD5lIpvBrS6mpov3DKUlieD7VjB6b9ZhBWnV6FgroMlKbX\nYPCXWZh5/2os2tAz7DIY4XDbnK1QdRoDV+Y73T7OIUsm0c6laG1o4emnzRLDvDyTlH3+uVleePKk\n+RkAOnRo+j4753cE9cJJbdNeOCtXe1aq9Yd6z2OPNR3WDE7G/Fdj06Y17X374APzhz9qlHk8YoQp\nkRG86qm1FVFer3n+ppsaFxMsWADMnQvcPaMUb3++CgBQVl0GAFi5ayVKq1KjR4JcJoVXQ4bT8xWq\nIn5LrM6HKs0WrMoz1arL0msBrxcr849izX4J6/Mi4bY5W8H/7hdf7K72WcEeslTRUqFFoOlrJ0+a\n5YIXXghkZgKbNpnf9gsvNElbBKskI+5Fc+kqq+Crsdpa4PLLTZJ23XXA0qUmQL/3nhnWDN4Ts7We\nu+auPu0sLOlm7CFzOZf+ncZDaz1f4fakAdZ7n1QV2/9vIeof/x1QXwekpUMm/QLPrboRN0+QVusY\nRlO3y209ZMHc1j4WhrUqmYJJc9+lpaEF4NTXSktN8lVXB3z8sflLbdPGDGeefba1wq7NDZEmKX8X\n+YhvV2Ddq6WY+MsC9P1W5L9PkVTeTlZMyChmYhjvrf5PP5zkJ5IELvg7WdnpI+zPiLaNceTG9jEh\nsyKZkobWvktLe2aGeu3ii4GdO82Sxn37wqu0b8PcErdUYm6pHcvvW42znroH+Z3rkX+69d8nt89/\ncBoTMoqJGMZ7O/+nH49YF20PklvicXPc1j4mZK1JpAmprV3VWf0uLZ0n1GuR7kUZ473o3HLF01I7\nPnmvAunDhyKnIANfHMlCz67V6NCm9d+n4HN+8IFZITR37qlbMbkp4MUTEzKKWhJfJEaKvfDxw0n9\nrUmUJdtWCi9a/S45OSbhKi09tVZQqEn6gYVd27e3Xtg1xvXTwl06bpfm2gEAr88tRdcz63HGuVn4\n2teAvWVZUAu/T8HnnDWrMRkDmtZLI6II2RDvI1k45BbhLjQg+yXQr48N7Cy6GitWCy9a/S4tJXeh\nCsFGuorKhtVXblnVE2oHAI8HmDq7AO07mP8GHTsCF3Svhlj8fQr+boEbpwOJFeiJXCkR4n2ccP9L\nd0rtIUug5XlVbhDO0F9r36WlLvvNm1ueWxHpRFgHJtDayes12yKVlQE33mgKt+blmfIUHg8i/n1y\nw3dzMw5ZpqhYL7hye7yPo0Qfbk00VmJYerwa41r+KvJuXWUZeFXnT6Kau6pr7buE6rKvqjIT9/29\ncP7PmD696dyKnJzI/m0ifV+QwCs6//6QrpxXFcHvU8J8N6J4smPBldvjfRwl8nBrsmIPmZOsXv3F\n6qquuR6yP/wBuP326Cfg+79PRoY5bxgB78iJI+iU2anFY9xyRef1NlbkHzPG7FkZTo2x5s7phu/m\nVuwhSzGJtOCKyAJO6nczKxP1/SLZC9Kvpb0r/fO6zjsv+rkV/u8zYoQpIDt8eOvfy6ekvATDXxze\n6p6MbrmiC7VpORDd/m5u+W5ErpAoC66IYog9ZE6I19VfS3tXBvfMRdML5/8+aWkmC1E12y/17Ws+\nu5XvNW3lNLy89WWM7DPS9XsytlZ+g3PB7MEeshTDHjJKMuwhc6t4XP21tDrTX94CaOw9i6YXzv99\n0tJMMta2rbn3eFr9XiXlJVhRsgI9O/fE8pLlrfaSOc3jMclX4F6XgXO93LISlCihObRH5pETR2w9\nP1FLmJA5IR7Lr1tL+kINmUa6Wbj/+9TXm56x2lpz7/W2+r3mbJoDDzxI96TDAw/mbJoT4ReOA9/w\nr+do05IjgcOLrO1DFCPRXCRGwOrUCSK7MCFzQjyu/lpK+qzWNgv3+9TXA2ec0fS+he9VWlWKVbtW\nAQDKqssAACt3rURplQvniViY88faPkQxFulFokWBPWJzNs3B/sr97r4opKTGOWROsntT8+bmhVmt\nbRZu+8JcZamq2H5oO+q1vuG5NElDr869IOKi6UJhzGfhakl7cA4ZxVpJeQkmvjoRzw9/HgrFqKWj\nkJeVh7LqMiy5fgl65PZwuomURFiHzO1iVKOrWc3V3PH3nlVWNm4YHjy0GEkNoDC/j4igd17vCL5Y\nnDVXv6209JTvy9WSRIkhsEdMoadMnXD7AiNKPq7534WIXC8iH4lIvYhc6nR7kkaoLv+cHGDkSOD9\n94ENG8z9qFGNx/iHNNPSgMxMcx/NkGai45YrREklcDHRmzvexN93/B1AAkydoKTmph6yLQB+COBZ\npxuS9CoqgCVLgH79Gifjv/SSGcbMyTE9P4cPAwcONPaQdekSskcoJfjnyE2fbnrG/MO/qfhvQRRP\nNk3rCFxMlJGWgUvOuASTLpvU8HqapCE/Kz9mn0dkhWsSMlXdBgDiqslDSco/BJeb2/jcwYONCVdG\nBrB7t5knJWJKWNTWmudTFbdcIYovO7ZOQujFRJu/2oy8rDwUtGevNznHNQkZRSmcK8nW9scsK2ss\n7go0JmVlZUC3bvZ+Dzeze84fERmBK8Gb21+3tfc3Ew/zs/LxwogXTllMxB4xclpcEzIRWQ7g9MCn\nACiAe1T19XDONWPGjIafBw0ahEGDBsWghQkq3CtJK0NwaWlNe8Tq6uxrP1GQ4uJiFBcXO90M2zB+\ntSKMhTSnaCUeJsxiIkpokcQw15W9EJG3AdylqptaOIbLxv2i2WKkuavIigrgkkuAvXsbnzv7bGDz\nZvYQkSNY9iLFRBrXuOUSuVQib52UFIE3LqLZhqmloovZ2eZc7dub++zs2LY7WoGbphNRcom0eDY3\nJacE5po5ZCIyAsCTAPIAvCEim1X1aoeb5X6tzQeLxM6d5hwDBpgaZW3bAkeOuGeVpU2TfYnIRSJZ\nSGNHPCSKE9cNWVrBLv8gzVXkj8Tq1cAvfwls3WqqmvbpA7Rr555ufw5JpCQOWZJlsYqHdu+kQinF\nSgxjQpYsYhE8ApOd48dNUlZXBxQWAr/9rTt6oaxu+xSMwTWhMSGjsET7985eeIqxRJ5DRuHyzwcD\nIp9bFTz/wr/vz8mTsWljLERSNd/CxuBElESi2ZQ8sORGXp65T+WdSihumJAlk2gTj8A9Lj/91DyX\nkWGCmtMByT+JHwhvsi+DKxGFgwsDyCFMyBJNc6sLY5F4+Fc2HTtmesVEgPPPBzp2dDYgBSeagJkz\ntmCBuW9pKIHBlYjCwb1rySFMyBJJSz1gsUo8rrwSeOUVoFcvoG9foHNnZwNSc4kmYG1IgsGViMIR\nackNoigxIUsUrfWAxTLx6NYNePxxk+A5HZCiTTQZXIkoXP6SG1Z64YlixDV1yKgVrW0lYmU7pHC4\nZTPtWNQVcst3IaLEwb1rKc5Y9iJRWK2/lYzlHWJZZ40SEsteEFEiYx2yZJPKiUkyJppkGRMyIkpk\nTMicYmfywMSEUhATMiJKZEzInMAKz0Qxx4SMiBIZE7J44z6LRLZgQkZEiYxbJ8Ubi5ASERFRBJiQ\nxRKLkBIREVEEmJDFEouQEhERUQQ4h8wOXAlJFFOcQ0ZEiYyT+okoKTAhI6JExkn9RERERAmACRkR\nERGRw5iQERERETmMCRkRERGRw5iQERERETmMCRkREf3/du49xo6yDuP49ym3AoUCElulaZEgYAWC\nrQiJCAKipZFLQCLiHyheIpiWGu9CABGUoIkCRoIIBMQKSYVAFQultBLAQildupa2NLaCgqAxGKhg\nLd2ff8y7dDg5ly17dt+Z3eeTTM47c+bynNndt7++M2fMLDMXZGZmZmaZuSAzMzMzy8wFmZmZmVlm\nLsjMzMzMMnNBZmZmZpaZCzIzMzOzzFyQmZmZmWXmgszMzMwsMxdkZmZmZpm5IDMzMzPLzAWZmZmZ\nWWYuyMzMzMwyc0FmZmZmlpkLMjMzM7PMKlOQSbpS0mpJPZJ+I2n33JkGa8mSJbkjDIhzdl9dstYl\npw2/Ov1u1CWrc3ZXXXIOVGUKMuA+4L0RcRiwDvh25jyDVpdfFufsvrpkrUtOG351+t2oS1bn7K66\n5ByoyhRkEXF/RPSl2aXApJx5zMzMzIZLZQqyBucAv88dwszMzGw4KCKG72DSQmBCeREQwAURMT+t\ncwEwLSJOb7Of4QttZpUQEcqdoRvcf5mNTp36sGEtyDqR9BngC8BxEbEpcxwzMzOzYbF97gD9JM0A\nvg4c7WLMzMzMRpPKjJBJWgfsCPwrLVoaEedljGRmZmY2LCpTkJmZmZmNVlX9lmVbki6V9KSkFZIW\nSJqYO1MrdXngraRPSPqTpC2SpuXO00jSDElrJD0t6Zu587Qi6QZJL0pamTtLO5ImSXpA0ipJvZJm\n587UjKSdJD2a/tZ7JV2cO1M31KUPc//VHe6/umuk9l+1HCGTNC4iNqb2LGBqRJybOVZTkj4CPBAR\nfZKuACIiKvfQW0kHAn3AdcDXIuKJzJHeIGkM8DRwPPA8sAw4MyLWZA3WhKSjgI3ALRFxaO48raQC\nYGJE9EgaBywHTqnoOd0lIl6VtB3wMDA7Ih7LnWsw6tKHuf8aPPdf3TdS+69ajpD1d2TJrhR/iJVU\nlwfeRsTaiFhH8SiSqvkAsC4inomIzcBtwCmZMzUVEQ8BL+XO0UlEvBARPam9EVgN7JM3VXMR8Wpq\n7kTxRaT6/S+yQV36MPdfXeH+q8tGav9Vy4IMQNJlkp4FzgIuyp1ngPzA27dmH+Cvpfm/UdE/vjqS\ntC9wGPBo3iTNSRojaQXwArAwIpblztQNNezD3H+9Ne6/htBI6r8qW5BJWihpZWnqTa8nAUTEhREx\nGfgVMKvKWdM6FwCbI2JulXPa6JKG++cB5zeM2lRGRPRFxPsoRmeOkDQ1d6aBqEsf5v7L6mqk9V+V\neQ5Zo4g4YYCrzgXuAS4ZujTtdcqq4oG3M4HjhiVQC9twTqvmOWByaX5SWmaDIGl7is7slxFxV+48\nnUTEy5IWAzOAp3Ln6aQufZj7ryHn/msIjMT+q7IjZO1I2r80eyrF9eNK0tYH3p5cowfeVu0+jGXA\n/pKmSNoROBO4O3OmdkT1zmEzNwJPRcRVuYO0ImlvSeNTe2fgBKByN+5uq7r0Ye6/usL919AYcf1X\nXb9lOQ84gOJG2GeAL0XE3/Omak41eeCtpFOBa4C9gX8DPRFxYt5UW6V/GK6i+E/EDRFxReZITUma\nC3wYeBvwInBxRNyUNVQTkj4IPAj0UtxkGsB3ImJB1mANJB0C3Ezxcx8D3B4Rl+dNNXh16cPcf3WH\n+6/uGqn9Vy0LMjMzM7ORpJaXLM3MzMxGEhdkZmZmZpm5IDMzMzPLzAWZmZmZWWYuyMzMzMwyc0Fm\nZmZmlpkLMjMzM7PMXJCZmZmZZeaCzMzMzCwzF2RmZmZmmbkgMzMzM8vMBZmZmZlZZi7IzMzMzDJz\nQWZmAyLpGEnzU/skSd8YouNMl/STFu9tkLRXi/cWSRrXZr/nSxrbxZwtswxw+66fT0mLJU1L7YWS\nxg92n2Y2PFyQmdm2CICImB8RVw7JASKWR8ScdsdvJGkm0BMRG9vseg6wy2DzdcrSiqRm/e1Qns9b\ngC93eZ9mNkRckJmNEpKmSFot6SZJayXdKul4SQ+l+fen9Q6X9Iik5em9dzfZ19mSrkntt0u6Q1KP\npBWSjmyy/s8kPSapV9LFpeWHS3o4bbtU0q4NI0d7Sbo3bXc9oBYf79PAXWmbXST9NmVZKekMSbOA\ndwKLJS3qkGmDpEvS539S0gGdski6U9Ky9N7nS8tfkfQjSSuAIyXNSD+Dx4HTGs7n1am9QtIT6fVV\nSR9Kn+mGdI6WSzo5rTtW0q8lrZJ0B1AeAZwPfKrF+TKzqokIT548jYIJmAL8D5ia5h8HfpHaJwN3\npvY4YExqHw/MS+1jgLtT+2zg6tS+DZid2gJ2a3LsPdLrGGAxcDCwA/BnYFr5uA3HuQq4MLVnAluA\nvZrs/y/Arql9GnBd6b3d0ut6YM92mdL8BuC81D4X+HmnLKV9jQV6+48D9AGnp/ZOwLPAfmn+9mbn\ns5Tv48AfgO2Ay4Gz0vLxwFpgZ+ArpZ/hIcDm/vOZlq0tf2ZPnjxVd/IImdnosiEinkrtVcCi1O6l\nKNgA9gDmSeoFfgxM7bDP44BrAaLwSpN1zpS0HFiR9jcVOBB4PiKeSNtujIi+hu2OBm5N798DvNQi\nw54R8Z/SZzlB0g8kHVXKI948wtYsU7870+tyYN8BZJkjqQdYCkwC+kcVXwfuSO2DgPURsT7N39ri\ns5BGJX8InBERW4CPAt9KI21LgB2ByQ2ZeoEnG3b1T4qRQTOruO1zBzCzYbWp1O4rzfextT/4HvBA\nRJwmaQrF6FE7be+lkrQv8FVgekS8LOkmtl5aa3UJsuXuWix//Y0wEevSje0zgcsk3R8Rl21DJth6\nXrbQup9U2tcxFEXpERGxSdLi0r7+GxHRuE076YsJtwOfi4h/lN46PSLWNazbNFPJWOC1Tsc0s/w8\nQmY2ugykABoPPJfanx3A+ouA86C4cV3S7g3v7w5sBF6RNAE4MS1fC0yUND1tO07Sdg3bPkhxfxiS\nTqQYvWtmraT90nrvAF6LiLkUo0zT0jovpyztMrXTKst44KVUjB0ElO+hK5/vNcAUSe9K863u77oR\nuDEiHiktuxeY/cZOpcOaZDoYOLRhXxMoLueaWcW5IDMbXaJFu+xK4Ip0OW8gfcQc4FhJKynuS3vP\nmw4YsRLoAVZTXF57KC3fDHwS+Gm63HcfxX1WZd8Fjk6XT0+luAermd8Bx6b2IcBj6fLeRUD/6Nj1\nwAJJi1pl6o/c4hitsiwAdpC0Cvg+8Mdm+4qITcAXgXvSTf0vNh5A0mSKe+DOKd3cPy19hh3SlxR6\ngUvTJtcC49KxL6E4//37mg4sbXIZ2MwqSG8eTTczqx9JE4GbI+JjubNUhYpnud0VEZ0uOZtZBXiE\nzMxqLyJeAK5XmwfDjkK9LsbM6sMjZGZmZmaZeYTMzMzMLDMXZGZmZmaZuSAzMzMzy8wFmZmZmVlm\nLsjMzMzMMvs/CW58UkE0SPQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fe1f748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(1, 2, sharex=True, sharey=True, figsize=(10,5))\n",
    "\n",
    "for a,x_dat, y_lab in zip(ax, (X_train, X_test), (y_train, y_test)):\n",
    "\n",
    "    for label,marker,color in zip(\n",
    "        range(1,4),('x', 'o', '^'),('blue','red','green')):\n",
    "\n",
    "        a.scatter(x=x_dat[:,0][y_lab == label], \n",
    "                y=x_dat[:,1][y_lab == label], \n",
    "                marker=marker, \n",
    "                color=color,   \n",
    "                alpha=0.7,   \n",
    "                label='class {}'.format(label)\n",
    "                )\n",
    "\n",
    "    a.legend(loc='upper right')\n",
    "\n",
    "ax[0].set_title('Training Dataset')\n",
    "ax[1].set_title('Test Dataset')\n",
    "f.text(0.5, 0.04, 'malic acid (standardized)', ha='center', va='center')\n",
    "f.text(0.08, 0.5, 'alcohol (standardized)', ha='center', va='center', rotation='vertical')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"PCA\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='MDA'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Transformation & Classification: Multiple Discriminant Analysis (MDA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top]](#Sections)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main purposes of a Multiple Discriminant Analysis is to analyze the data to identify patterns to project it onto a subspace that yields a better separation of the classes. Also, the dimensionality of the dataset shall be reduced with minimal loss of information.\n",
    "\n",
    "**The approach is very similar to a Principal Component Analysis (PCA), but in addition to finding the component axes that maximize the variance of our data, we are additionally interested in the axes that maximize the separation of our classes (e.g., in a supervised pattern classification problem)**\n",
    "\n",
    "Here, our desired outcome of the multiple discriminant analysis is to project a feature space (our dataset consisting of n d-dimensional samples) onto a smaller subspace that represents our data \"well\" and has a good class separation. A possible application would be a pattern classification task, where we want to reduce the computational costs and the error of parameter estimation by reducing the number of dimensions of our feature space by extracting a subspace that describes our data \"best\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Principal Component Analysis (PCA) Vs. Multiple Discriminant Analysis (MDA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both Multiple Discriminant Analysis (MDA) and Principal Component Analysis (PCA) are linear transformation methods and closely related to each other. In PCA, we are interested to find the directions (components) that maximize the variance in our dataset, where in MDA, we are additionally interested to find the directions that maximize the separation (or discrimination) between different classes (for example, in pattern classification problems where our dataset consists of multiple classes. In contrast two PCA, which ignores the class labels).\n",
    "\n",
    "**In other words, via PCA, we are projecting the entire set of data (without class labels) onto a different subspace, and in MDA, we are trying to determine a suitable subspace to distinguish between patterns that belong to different classes. Or, roughly speaking in PCA we are trying to find the axes with maximum variances where the data is most spread (within a class, since PCA treats the whole data set as one class), and in MDA we are additionally maximizing the spread between classes.**\n",
    "\n",
    "In typical pattern recognition problems, a PCA is often followed by an MDA."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](https://raw.githubusercontent.com/rasbt/pattern_classification/master/Images/mda_overview.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you are interested, you can find more information about the MDA in my IPython notebook   \n",
    "[Stepping through a Multiple Discriminant Analysis - using Python's NumPy and matplotlib](http://nbviewer.ipython.org/github/rasbt/pattern_classification/blob/master/dimensionality_reduction/projection/linear_discriminant_analysis.ipynb?create=1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Like we did in the PCA section above, we will use a `scikit-learn` funcion, [`sklearn.lda.LDA`](http://scikit-learn.org/stable/modules/generated/sklearn.lda.LDA.html) in order to transform our training data onto 2 dimensional subspace, where MDA is basically the more generalized form of an LDA (Linear Discriminant Analysis):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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CPbrsUa3euFofrP2gmrc279Yb9uu//lpNW5vU2tYqSVrStGS33rCnVz6tpU1L\nNaz/MN34/I1Z94atWLFCI0aMUFVV12HJ1VdfrbFjx2rgwIEaOHCgNmzYoHXr1kmS5s2bp8WLF+uA\nAw7QoYceqgceeECST7afPHmypk2bpn322UezZs3S9u3bO92Pmemwww7TihUr9NOf/jSrx5MpgjAA\nACpUohdM5nu8zGy33rB2165PDv+kDhx8oA4cfKA+MfwT2tq2dcftzjld9+x1qqmuUZ+efbSxdWPW\nvWHDhg3T8uXL1d6ePt9Mkh5//HFdddVVuueee9Tc3Kzm5mb1799fzjlJ0qhRozR//nytXbtWF1xw\ngU444QRt3bpV1dXVuvTSS/Xaa6/pqaee0oIFC3Tbbbdldoza2gqWE1ZdkK0CAICSt2nbJg3dY6j6\n1/Tfsaxvz75a/956Dek3RJJ0+sGn6/SDT0+7jZffeVmvrXlNfXv21brN63yS/0s3a+q4qRmXlpg4\ncaKGDh2qWbNmafbs2erRo4eef/753YYkN23apJ49e2rQoEHatm2brrzySm3cuHHH7XfccYcmT56s\n+vp61dXVycxUVVWlhoYG1dfXa+zYsaqtrVXPnj1T9rqtXbtWjzzyiI466ij16dNHDz30kO68807d\neeedGT2ObBGEAQBQoQb0HqAbj7oxp22M3nO0bjx61230qe6TVW2vqqoqLViwQGeddZaGDx+uqqoq\nTZ8+fbcgbPLkyZo8ebLGjBmj2tpazZw5U8OGDdtx+4MPPqjzzjtPW7du1YgRI3TXXXeppqZGb7/9\nts4880ytWrVKtbW1mjZtmmbMmLFbO8xMP/3pT/X1r39d7e3tGjFihK699lpNmTIly6OSGUt04YVk\nZlWS/iJppXPumBS3u1JoJwAAcWVm4rs0v9Id02h5l1FoqeSEnSPpr6EbAQAAUCzBgzAz20fSFyT9\nPHRbAAAAiiV4ECbph5K+LYk+UgAAUDGCJuab2RRJ7zjnXjKzSZLSjp/Onj17x/+TJk3SpEmTCt08\nAACALjU0NKihoSHr+wVNzDezOZK+LKlNUh9Je0i61zl3Sof1SMwHACAHJObnX66J+SVxdqQkmdkR\nkr7F2ZEAAOQfQVj+5RqEUScMAIAKMGLEiKxqd6FrI0aMyOn+JdMT1hl6wgAAlWb9e+s1oPeA0M1A\nN8StThgAAIg0Njfq2DuP1bLmZaGbggIiCAMAoMTc9MJNWrVhlW564abQTUEBEYQBAFBCGpsb9XDj\nwxo9aLSX3hukAAAgAElEQVQeanyI3rAyRhAGAEAJuemFm1SlKlVXVatKVfSGlTGCMAAASsSazWv0\nyLJHJEnrtqyTJP1p2Z+0ZvOakM1CgXB2JAAAJcI5pyVNS7Tdbd+xrIf10JhBYygvESOxK9baGYIw\nAAAQF5SoAAAAKGEEYQAAJFn/3vrQTUCFIAgDACBCkVQUE0EYAACRQhdJpZcNyQjCuqm9vfPrAIB4\nKXSRVHrZ0BFBWDe0t0sXXCAtWuSvL1rkrxOIAUB8FbpIKlMRoSOCsG6oqpJOPVW68kpp/nx/eeqp\nfnmpoKcOADJX6CKpTEWEVKpDNyCuxo+XpkyRfvlL6eST/fVSkeipO/VU365Fi6Rbb5Xmzi2tQBEA\nSsXgvoN12xdv261I6uC+g/Oy/VS9bHOOnJOXbSO+CMK6adEi6YEHfAD2wAM+2CmVQCy5p27KFN++\nWbMIwAAgHTPT/vX7F2TbnfWyDek3pCD7RDxQMb8b4tLTNH/+zp666dNDtwYAKhNTEVUepi0qsPb2\nXQOujtdDW7Ro956wUumpAwCgnGUahDEc2U0dA65SCsDa233PXCLwGj++NHvqAACoZPSElalS76kD\nAISx/r31GtB7QOhmlDUm8K5wpdxTBwAIg4KxpYWvZgAAKkQ+C8YyBVPuCMIAAKgA+SwYS49afhCE\nAQBQAfI5LRNTMOUHQVgnmPoHAFAO8jktE1Mw5Q8lKtKIS0FWAAC6ks9pmZiCKX8oUdEJCp4CALDT\nms1rdPQvj5acVFVVpfb2dsmkBScvYAqmJFTMzxOm/gEAwGMKpsxQMT8PSnmSbgAAiq2QE51XIrKb\n0kie+mf6dH95660k5wMA8o+aW5WJ4chOMPUPAKDQGpsbdfp9p+uWY2/RyIEjdyxneqH4YtqiPGDq\nHwBAoaWqudVZMVR6zcoHYQUAAAWQSbCUruZWumKoVKovLwRhAACkkEuPU6bBUqqaW50VQ6VSfXkh\nCENQzEoAoBTl2uOUSbCUror9j57+UcrphahUX34IwkpUJQQniVkJFi3y1xct8tfL8bECiJdcepwy\nDZYSVexv/uLNmnfMPN38xZv1w8k/1NMrn5a0+/RC+Zz7EaWBsyNLUCVNmcSsBABKTWNzo0665yTV\n963Xui3rdPcJd+9y1mJXLvzThXqk8RENqR2iNZvW6Mj9jsx4Wp+OxVA3tG7QwN4DNaD3AB1z5zFU\nqo8JirXGWFWVD8A6BiflFoBJPuCaMmXnrAQEYABCy2VuxM4mys4kWEouhtrY3KivP/B13XLsLRrS\nb0je5n5E6SAIK1FdBSflUsOsO7MSlMtjB1B6cg2i8j1RdmJIdM6Rc6hUX4YYjixRHYfpLrhAOugg\nf1t7u/Ttb0unnRbv4cruDLtW0lAtgOIrlbkRcx0SRVhM4B1jHQONl1+WvvIVad48H4gtWiRdfbX0\n/vvSUUfFO5eqO71a5JEBKHe55JUhPIKwmOsYjLz8su/tSQ48Fi3aOVw5fXq4toYwf37lPnYA5W3N\n5jU6+pdHk4QfYyTmx1zH3qCDDto1R0zKPpcqlHzncHUnjwwA4iKfeWUobfSExUTyENzvfif17Cmd\nf37p50XlO4eLnDAAQKljOLKMpAo8brlFuuqqnYFHKZ8hmO8cLs6OBACUMoKwMlNKgUd32kIOFwCg\nUmQahNF/EBMdg5yQAVi2Uw11zOFK3BcAKkEuE4GjvBGEISvJ1fznz/eXp57aeV2vW2/1Q5DTp/vL\nW29lfkgAlSHXicBR3hiORLdkM7xYSkOpAFBMF/7pQv3qtV9p6rip3arztf699RrQe0ABWoZCYjgS\nBdPZ8GLHHq5UARcBGIBK0NjcqIcbH9boQaP1UONDWfeG0YtW/vg6RFY6Di9ecMHO4cXEdErZ5IsB\nQLlKNRF4tvdPzB2J8kQQhqxUVfmaXOPH++Dq9tulGTP88tdek9atk773vczyxQCgXHU2EXgmcu1F\nQzxQMR9ZSwRVyUn66aZTopI9gEqUa9X7VL1ozB1ZfgjCkJPx4+M7nRIAFIqZaf/6/btcL1XifWe9\naKUydyQnDOQHZ0ciJ3GdTgkAQmtsbtTp952uW469RSMHjtyx3DmnJU1LdutFGzNojMy6POGu4NK1\nGzvF4uxIM9vHzB4xs9fMbJGZnR2yPchOxyT9Cy+U6uulceP87ePHE4ABQDrpEu8TvWhjB4/d8bd/\n/f4lEYBJnDCQT0F7wszsg5I+6Jx7ycxqJT0v6Vjn3N87rEdPWImiBhgAZK+xuVEn3XOS6vvWa92W\ndbr7hLtj0asU13YXWyx6wpxzbzvnXor+3yTpb5L2DtkmZI4ADAC6J9fyFaHEtd2lqmS+Ms1sX0kf\nlfRM2JYgE92ZQxIAkHv5ilDi2u5SVhJnR0ZDkfdIOifqEdvN7Nmzd/w/adIkTZo0qShtQ2rpylNk\n0hNGDxqASpZr+YpQ4truYmhoaFBDQ0PW9wt+dqSZVUv6naQ/OOeuTbMOOWElKps5JKWdPWinnsoZ\nlACA8hSLnLDILyT9NV0AhvxJNa9jLtLNIdnZfpJ70KiqDwCoZKFLVHxC0pckfcbMXjSzF8zs8yHb\nVK7yncPVsTzFrFn+eltb1/sZP17613/1PWhTpuycAglAeVn/3vrQTQBKWvDhyEwwHJmfPKrkwqqJ\nHK5cqtmna1NX+3n5ZWnaNN8DtmiRdNxx0p//zJAkUE4o6IlKFqfhSHQhX71YyVMMJXqgctExYEpc\n72w/iUm/r7jCP47x46VLLtk5CTiA8kBBT6BrfO3FQL7yqNLlcOVbZ/upqvI9Xscf7wO0J5+ULr5Y\nOuigwrQFQPE1Njfq4caHNXrQaD3U+JCWNS8L3SSgJBGExUSuvVjpcrjynYuVyX4SQ5aJQO0Pfyhc\nQAig+CjoCWSGnLCYyEc+V7Hqc3W1H8pUAOVrzeY1OvqXR0tOqqqqUnt7u2TSgpMXaEi/IaGbBxRF\npjlhBGFFkGvwU45BCwVbgfLknNOSpiW7FfQcM2hMyUxADRQaQViJyFcAle+gJXH/dJcAAKB7ODuy\nROQrqT7dmYjdkQgMX37ZX/7617teL1bNrsR+0l0CAFDOCMKKIN+lIXKVCAznzpXq66Vvfctfzp1b\nvOr1pRIIAkAhUbAWnSEIK4JilYbIRiIwfPLJXS+LFSCWQiAIAIXU2NyoY+88lhIdSIuvugIrVmmI\nbCUCw098YtfLYgaIoQNBACgkCtaiKwRhBZYoTpoILMaPD39WYyIwvOACad066Zpr/OUFFxQ3QMw0\nEMz3xOMAUGgUrEUmODuyQoU+OzKREzZjhp/G6OMf9/NHJq4nAtVyLM8BoPxd+KcL9UjjIxpSO0Rr\nNq3RkfsdqTlHzgndLBQJJSpQ8jINBPM98TgAFBIFa0EQhrIyf74/u/Tkk31uHQCUKgrWItMgrLoY\njQEylaoo7Wuv7Xp26fjx9IQBlW79e+s1oPeA0M1Iycy0f/3+oZuBGCCrBiUjkf+VSMxftEj69rel\nW24pvbNLAYRD6QeUC4YjUVJS5X+NGxdmnslSmfAcwK4u/NOF+tVrv9LUcVNJdkdJYtoilKSuyk2k\nml0gn1M2ZSpVr1whKvkXaz9AuaD0A8oJQRiKJpOAI9PZBQpdOyxfc36Wyn6AcnHTCzepSlWqrqpW\nlaoohIpY46MeRdNVwJHp7ALF6j0q1pyfpTa3KFCq1mxeo0eWPSJJWrdlnSTpT8v+pDWb1xR0v8z/\niEIhJwxF11m5iUzzo4pRO6xY9cmogwZkJkTph8bmRp1+3+m65dhbNHLgyILsA+WHnDCUpK6GGzPN\n/yp071Gx5vws1blFgVKUKP0wdvDYHX/71+9f0NpbzP+IQqInDEWTzymI0vUe5fNMQ86OBCpbY3Oj\nTrrnJNX3rde6Let09wl3x7Y3rJTrqpUjesJQcvI1mXly79G0aTt7j9rafF2xfOWKFeuszBBnfwLo\nWrmcBEBdtdLFxz2KKh8BRyKYGzfOB1mSv/63v0nr1knf+x5nGgLITaiTAAqBIdXSxXAkYi3VsOSi\nRcwzCSA35TL/YzkNqcYJw5GoCB0T9KXM6oyFUuj6ZkC+FKIsQ5xKPYQ4CaAQymVItVwRhKHkZBOo\nJJ9t+bvfSVdfXbpnGlIdH3FRiBwi8pKKr5yGVMsVw5EoKdmcQZlq3Vtuka66atcCsKWUE0ZNMMRB\nIeZmZL7H4iuXIdU4ynQ4kiAsxuJW2qAQhVizOQalcrw6K1YLhFaIHKJKyUuiDAQSyAkrc3Eb2sqm\nvdkUYs30bMtSOV6Zzo0JhFKIHKJKyEtiuBXdQRAWU3Gb+Dmb9hYiUCmF40V1fJS6QuQQVUpeEmUg\n0B0MR8Zc3Ia2umpvPqvqd2f/hVYqQ6JAKoXIIaqEvKRKGW5F5jIdjqwuRmNQGB17jMaPL+0k70za\nmyjEmghMultVv7v7LzSq46OUJcoylPo2OypULlam20013MrJB8gEXwExFbehrWzaW4hAJW7HC0Bm\nCpWLlel2K2W4FYXBcGSMxW1oK3R7Q+8fQP4VqvRFptuthOFWZI8SFQCAslaoXCxyvJArSlQAAMpa\noUpfVEJJDZQGgjAAQOwUKheLHC8UE8ORRUROEoBSFbdq74XKxSLHC/lATliJKXT9KwDorsbmRp1+\n3+m65dhbyH0C8oCcsBJTChXbET8dS2hQUgOFQLV3IAxCgCLKZk5EoFTmu0R5a2xu1MOND2v0oNF6\nqPEh5j4EioggrIiYvBnZoPcUxcCZgEA4fJwXCRXb0R30nqKQOBMQCIvE/CLi7Ehka9Ei3wM2ZYrv\nPZ01i0AM+cOZgEBhcHYkEHOcUQsA8UQQBpSY7vSE0nsKAPFDiQqghHT3TMeOARcBGACUD3rCUHZK\ntfeI/C4AqAz0hCG2cilQWsq1tTjTEQCQjCAMJSXXIKqUa2tRJw4AkKw6dAOAZMlBVPKwXTZBVHKP\n08knl0aPU3KduPHj/R9nOgJAZSMnDCVp/vydQdT06dndt1Rzr0o1Vw0AkF/khCG2chm2K+WZCTjT\nEQCQLHhPmJl9XtKP5APCec6576dYh56wCpGPAqX0OAEAQopFsVYzq5K0RNKRkt6S9Jykac65v3dY\njyCsghBEAQDiLC7DkRMlLXXOvemce1/SnZKODdwmBMawHQCgEoT+ettb0oqk6yujZQAAAGUtNiUq\nZs+eveP/SZMmadKkScHags4xnAgAqCQNDQ1qaGjI+n6hc8I+Jmm2c+7z0fVZklzH5HxywuIjH4n1\nxUKwCAAohLjkhD0n6UNmNsLMekmaJun+wG1CDkq5Yn2yUp7eCABQGYIORzrntpvZf0j6o3aWqPhb\nyDYhd6VYsb6jfFTmBwAgF8FzwpxzD0raP3Q7kD8di60mpukpNXEIFgEA5Yvf/cirUq5Y3xETagMA\nQgpeMT8TJObHSxwS3uN0AgEAIF5iUTE/UwRhkPIf3MUhWARy1tIirVkjDRki1dWFbg1QEeJydiSQ\nkUKczUhlfpS9hQt94uMpp/jLxx4L3SIASegJQ2wsWrT72YyZJNPT44WK1NLi3yw1NVLfvtKWLVJr\nq3/z0CMGFBQ9YSg7yWczTpmSeQBGPTBUpDVrpO3bfQAm+cu2Nr8cQEkgCENsdOdsxrgUjwXybsgQ\nqUcP3wMm+cvqar8cQEngqwixkEvpi+70oAGxV1cnzZnjhyDXrvWXc+YwFAmUEHLCEBvdze3qbi4Z\nUBY4OxIoupxzwsxsvJk9bWYrzOxnZjYw6bZn89VQIFPdOZsxTsVjgYy1tEhLl/rLrtTVSaNHE4AB\nJShtT5iZPSHpCklPS/qqpNMlHeOce8PMXnTOHVy0RtIThhxwdmSJoWcmNwsXShdf7JPue/TwQ4yH\nHx66VQCS5Fys1cxeds4dlHT905J+JmmGpJ845w7JV2O7QhAGlAkCiNxQdgKIhbyUqDCzHe9q59yj\nko6XdLukETm3EEBlaWnxAVhNjVRf7y8vuiizITV4lJ0AykpnQdj3JR2YvMA594qkIyXdW8hGAShD\nBBDZSZX3RdkJoKykDcKcc/Odc0+nWL7cOfe1wjYLQNmp1AAimyT6hHTTDVF2AigrlKgAUDyPPeaH\nINvafABW7jlh3cmByyTvi5MbgJKWc2J+KSEIA8pIpQQQ3U2iX7rU94DV1+9ctnatdPvtvtQEgJKX\nr8T8HmY2M3/NAlDxKqVuVXdz4Cp12BaoQJ0GYc657ZJOLlJbAKB8dDeYIu8LqBhdDkea2Q8l9ZR0\nl6TNieXOuRcK27Rd2sBwJID4ySUHrlKGbYEylLecMDN7NMVi55z7THcbly2CMACxRTAFVBwS8wEA\nAALIS2J+tKE6M/uBmf0l+rsmuZI+gBjrTg0rAEBeZDKN8S8kbZQ0NfrbIOnmQjYKQBGkKwgKACiK\nTHLCXnLOfbSrZYXEcCSQZ0wEDQAFk7fhSElbzeyTSRv+hKStuTQOQGDM4wgAwVVnsM6Zkm5LygNr\nlnRq4ZoEoOCSa1glesIoCAoARZVJT9gG59xBkj4i6SPOuYPlc8QAxFUhC4Jmm+zPyQEAKlQmOWEv\nOOcO6bDseefcPxW0Zbvuj5wwoBDyXcMq2wmruzPBNXJH7TKgoHKuE2ZmB0gaJ2mupG8n3dRf0red\nc+Py0dBMEIQBMZBtsn/cTw6IayBD4AsUXD4S8/eXdJSkAZKOTvo7RNLX8tFIAGUk22T/OJ8cENfy\nHi0tPgCrqZHq6/3lRRcxFAwEkjYx3zl3n6T7zOzjzrk/F7FNAELJpXcn22T/uJ4ckBzIJNp90UXx\n6MFLFfhu3uyXl3rbgTKUSWL+mWY2IHHFzAaa2S8K2CagsoVKVM+1dyfbZP9CnhxQSHHuwUsOfKX4\nBL5AmcokMf/F6IzITpcVEjlhqBih8nXymZ+VbW9a3HKr4p7L9thjvueurc0HYOSEAXmXtwm8zexl\nSZOcc83R9T0lLXTOjc9LSzNAEIaKEPLLfelS3wNWX79z2dq10u23S6NHF3bfcRT3QCZugS8QM5kG\nYZkUa71G0p/N7FfR9RMlfTeXxgFIIWS+Tlzzs0I5/HAfHMc1kKmri1+bgTLUZU6Yc+42ScdJeif6\nO845d3uhGwZUnJD5OnHNzwqprs73EnKMAHRTl8ORkhTNHTnaOXezmQ2WVOucW1bw1u3cP8ORqAyh\nh7kYpgKAnOUzJ+wySf8saX/n3Bgz20vSr5xzn8hPU7tGEIaKQiAEALGWz5yw/yfpYEkvSJJz7i0z\n2yPH9gFIh3wdAKgImdQJ2xZ1QzlJMrN+hW0SAABA+cskCLvbzG6UNMDMvibpYUk3FbZZAAAA5S3T\nxPzPSfoXSSbp/5xzDxW6YR32T04YAACIhXwm5p8n6S7n3Kp8NS5bBGEAACAuMg3CMhmO3EPSH83s\ncTP7DzP7QO7NA1DWQs1/CQAxktFwpCSZ2UcknSTpeEkrnXOfLWTDOuybnjCUp3IsR7FwofSf/ym9\n957Uu7c0d252tc7K8ZgAqCh5G45M2uAH5acsmiZpD+fcR3JrYuYIwlCWQk3WXUgtLdInPymtWCGZ\nSc5Jw4ZJTzyRWUBVjscEQMXJZ07YNyRNlTRY0q8k3e2c+2teWpkhgjCUnZCTdRfSCy9IRxzhH1eP\nHj6Yam31wdUhh3R+33I9JgAqTj6LtQ6TdK5z7qXcmwVAUtjJuksVxwRAhclkAu8LCcCAPAs5WXe2\nskmyHzVK2ndf6f33pW3b/OW++/rlXYnTMQGAPMjk7EgA+VZX5/OdWlultWv95Zw5pdfjs3ChHyI8\n5RR/+dhjna9fVyddf7104IHSiBH+8vrrM3tccTkmAJAnGSfmh0ROGMpWKZ8JmEuOVi6Pq5SPCQBk\nIJ85YQAKpZQn684lRyuXx1XMY0LAByAghiMBeB1zv8o9RyvboVYAyLNgQZiZzTWzv5nZS2b2azPr\nH6otQMVLFZCUc45WS4uvR1ZTI9XX+8uLLqLCP4CiCpYTZmaflfSIc67dzK6U5JxzF6ZZl5wwoFC6\nyv0qxyG7pUt9wFlfv3PZ2rXS7bdLo0eHaxeAspDPuSMLwjn3sHOuPbr6tKR9QrUFqGipcr/a2vxy\nyQdeo0eXTwAmlf9QK4BYKJWcsDMk/SF0I4CKVIkBSTkPtQKIjYKeHWlmD0n6QPIiSU7Sxc65BdE6\nF0t63zk3v7NtzZ49e8f/kyZN0qRJk/LdXKAyJQKSiy7yZz9WV1dGQHL44X7ItdyGWgEUXUNDgxoa\nGrK+X9A6YWZ2mqSvSfqMc661k/XICQMKLU65X3FqK4CKk7cJvAvFzD4v6RpJhzvnmrpYlyAMCClV\n0JPPQCibbS1c6M9s3L7dD6POmeN7tfK1fQDIURyCsKWSeklKBGBPO+e+kWZdgjAglFRBj3PZB0LZ\nbD/dtrpTxb87QVuq/RLEAchQyQdh2SAIAwJJFfRs3uxv69cv++mMMtl+Z9vKtrRELlMvJeQjiANQ\nUUq+RAVQMTpWoo9TW1KVr3jvPf+XrqRFNroqj9FRtmdyZrv9jijqCqCACMKAQiqlqXG605ZUQU/v\n3v4vHyUtsg2qsi0tkWv5jVyDOADoBMORQKHkYyisFNry2GO+96etbWf5Cmn3ZZkM0aXKrUq1/Xwm\n2ndn+8n7KeRzSK4ZUJbICQNCK6WpcXJtSz7Ojuwst6rQwUgu288liOsMuWZA2SIIA0Irl56wcth/\nrvIdJMb9eADoFIn5QGilNDVO6LbEPbcq3/Nnxv14AMiLgk5bBFS8TKfGKUZuUMhpepIT5BM9P+U+\nP2Vnz2klHg8Au6EnDCi0rnpRinkGZb57dLLZb6n0ChZDV89pd45HKZU6AZAX5IQBxdSxd6TScoMK\n0eNXamcYZvOcZtp2kviBWMk0J4zhSKBYUn2RDh26e27Q5s3+i7kUAop8q6vL7+MqxeAkVb5Xuuc0\nk+ORXDA2EdRddFH5BupABWE4EiiGdJXXa2pyKyYaR/kaVivVava5FojtiCR+oGwRhAHFkO6LNJEL\nFOdcqWyCqnzmv6U7pm+8ETZ3Kt/5b/kO6gCUDHLCgGLoKk+o1PKaMpXNcGC+899SbW/NGj+xuFnm\nw5OFOvb53G6hCsYCKAiKtQKlpty+SLMNqgoxg0DyMZV87tWQIZkHeaWYU5ZOXAN1oAKRmA+UmpB1\nugohmwR0qTC1sZKP6caN0je/mXl74pbwnu+TGgAER04YUEyh6nQVQra5SoWqFZY4pqNGZdceEt4B\nBMZwJIDu684QayGH1bJpT6XVaANQNOSEASiOUstVyqY95ZanB6AkEIQBQCZKLYgEEHsEYQAAAAFk\nGoSRmA8gM4WYQJpJqQFUMIIwAF3LZ6X7Qm4TAGKE4UgAnSvEWYScmQigjDEcCSA/ClFPixpdAEAQ\nBiCNRL5WTU3+J5BmUmoAIAgDkEJyvtb06dJJJ+W30n2hqucDQIyQEwZgV+nytebP95f5rKdFjS4A\nZYgJvAF0zxtvSJs2SbW1/npiIuzWVj9HYz4xKTWACsZwJICdFi6UvvENH4g9/bTU1ES+VgI1zQDk\nGUEYAK+lRbr4YqlfP2n8eMk5adEi3wsWKl+rVAIfapoBKABywgB4S5f6IKO+3l9//33p7belX/xC\nOuSQ4rdn4UIfFG7f7s+kDDW5NjXNAGSJOmEAstOxbMT77/u8sFGjCrvfVL1diV65mhofFNbUSBdd\nFKZHjJpmAAqEIAyAF6JsRLphvkwCn2INVVLTDECBMBwJYFfFKhvR2TCf1PkQYLGHKh97zPfEtbX5\nACzd/ii5AUCZD0cShAEIo2MOmuR74G6/3ZfCSBf4hMrR6irAKpUcNgDBUScMQGlLHuZLBFPJw3yH\nH+4Dq46BT6qhys2b/fJCBmGd1TRLzmFLPJaLLiJ5H0CnyAkDEEYmOWh1db5XLHlZKeZokbwPoBsY\njgQQVnfyqDLN0SoWylgASEJOGIDyVmpJ8KUWGAIIhiAMAIqt1AJDAEEQhAEAAARAxXwA5atU5pQE\ngBwQhAGIFybTBlAmGI4EEB+chQggBhiOBFB+Otbj6tlT2rRJeuONsO0CgG4gCAMQH8mFWpuapD//\n2Qdg3/gGw5IAYocgDEB8JKrsb94sLVokmUnjx0v9+vkaXXFN1OdEA6AiEYQBiJfDD5d+8hNp1Cjp\nYx+TBg2K9zRBnGgAVCyCMKAU0BOSnVGjpNpa6f33/fVSmD+yO5In/q6v95dx7tEDkBWCMCA0ekKy\nl8nk33HAxN9ARaNEBRASJRdyE/dpgnj+gbJEiQogDugJyU1dnTR6dHwDlnLp0QPQLdWhGwBUtOSS\nC4mekDjmNqH7Dj/c93zFuUcPQLfQEwaERE8IpPj36AHoFnLCgFIQ99wmAMAOsckJM7NvmVm7me0Z\nui1AMPSEAEDFCRqEmdk+kj4n6c2Q7QAAACi20D1hP5T07cBtAAAAKLpgQZiZHSNphXNuUag2AAAA\nhFLQEhVm9pCkDyQvkuQkXSLpIvmhyOTb0po9e/aO/ydNmqRJkyblq5kAAADd1tDQoIaGhqzvF+Ts\nSDP7sKSHJW2RD772kbRK0kTn3G5VKjk7EgAAxEWmZ0eWRIkKM1sm6RDnXHOa2wnCAABALMSmREXE\nqYvhSAAAgHJSEj1hXaEnDAAAxEXcesIAlKOWFmnpUn8JANgFQRiAwli4UJoyRTrlFH/52GOhWwQA\nJYXhSAD519LiA6+aGqlvX2nLFj85+QMPMDUTgLLHcCSAcNaskbZv9wGY5C/b2vxyAIAkgjAAhTBk\niNSjh+8Bk/xldbVfDgCQRBAGoBDq6qQ5c/wQ5Nq1/nLOHIYiASAJOWEACqelxQ9BDhlCAAagYsSq\nYn5XCMIAAEBckJgPAABQwgjCAAAAAiAIAwAACIAgDAAAIACCMAAAgAAIwgAAAAIgCAMAAAiAIAwA\nACAAgjAAAIAACMIAAAACIAgDAAAIgCAMAAAgAIIwAACAAAjCAAAAAiAIAwAACIAgDAAAIACCMAAA\ngGeUngUAAAquSURBVAAIwgAAAAIgCAMAAAiAIAwAACAAgjAAAIAACMIAAAACIAgDAAAIgCAMAAAg\nAIIwAACAAAjCAAAAAiAIAwAACIAgDAAAIACCMAAAgAAIwgAAAAIgCAMAAAiAIAwAACAAgjAAAIAA\nCMIAAAACIAgDAAAIgCAMAAAgAIIwAMXT0iItXeovAaDCEYQBKI6FC6UpU6RTTvGXjz0WukUAEJQ5\n50K3oUtm5uLQTgBptLT4wKumRurbV9qyRWptlR54QKqrC906AMgrM5Nzzrpaj54wAIW3Zo20fbsP\nwCR/2dbmlwNAhSIIA1B4Q4ZIPXr4HjDJX1ZX++UAUKEIwgAUXl2dNGeOH4Jcu9ZfzpnDUCSAikZO\nGIDiaWnxQ5BDhhCAAShbmeaEEYQBAADkEYn5AAAAJYwgDAAAIACCMAAAgACCBmFmdpaZ/c3MFpnZ\nlSHbAgAAUEzVoXZsZpMkHS1pvHOuzczqQ7UFAACg2EL2hH1d0pXOuTZJcs6tC9gWAACAogoZhI2R\ndLiZPW1mj5rZPwdsCwAAQFEVdDjSzB6S9IHkRZKcpEuifQ90zn3MzCZIulvSfum2NXv27B3/T5o0\nSZMmTSpAiwEAALLT0NCghoaGrO8XrFirmf1e0vedcwuj669LOtQ515RiXYq1AgCAWIhDsdbfSvqM\nJJnZGEk9UwVgAAAA5SjY2ZGSbpb0CzNbJKlV0ikB2wIAAFBUzB0JAACQR3EYjgQAAKhYBGEAAAAB\nEIQBAAAEQBAGAAAQAEEYAABAAARhAAAAARCEAQAABEAQBgAAEABBGAAAQAAEYQAAAAEQhAEAAARA\nEAYAABAAQRgAAEAABGEAAAABEIQBAAAEQBAGAAAQAEEYAABAAARhAAAAARCEAQAABEAQBgAAEABB\nGAAAQAAEYQAAAAEQhAEAAARAEAYAABAAQRgAAEAABGEAAAABEIQBAAAEQBAGAAAQAEEYAABAAARh\nAAAAARCEAQAABEAQBgAAEABBGAAAQAAEYQAAAAEQhAEAAARAEAYAABAAQRgAAEAABGEAAAABEIQB\nAAAEQBAGAAAQAEEYAABAAARhAAAAARCEAQAABEAQBgAAEABBGAAAQAAEYQAAAAEQhAEAAARAEAYA\nABAAQRgAAEAABGEAAAABEIQBAAAEQBAGAAAQAEEYAABAAARhAAAAARCEAQAABBAsCDOzg8zsz2b2\nopk9a2b/HKot5a6hoSF0E2KLY5cbjl9uOH654fh1H8euOEL2hM2VdJlz7mBJl0m6KmBbyhpvpu7j\n2OWG45cbjl9uOH7dx7ErjpBBWLukuuj/AZJWBWwLAABAUVUH3PdMSf9nZtdIMkmHBWwLAABAUZlz\nrnAbN3tI0geSF0lyki6W9FlJjzrnfmtmJ0j6d+fc59Jsp3CNBAAAyDPnnHW1TkGDsE53bLbeOTcg\n6XqLc66us/sAAACUi5A5YavM7AhJMrMjJS0J2BYAAICiCpkT9jVJ/2NmPSS9J+nfArYFAACgqIIN\nRwIAAFSyWFXMN7OzzOxvZrbIzK4M3Z64MbNvmVm7me0Zui1xYmZzo9fdS2b2azPrH7pNcWBmnzez\nv5vZEjP7z9DtiQsz28fMHjGz16LPurNDtymOzKzKzF4ws/tDtyVuzKzOzH4Vfe69ZmaHhm5TXJjZ\nTDN71cxeMbM7zKxXZ+vHJggzs0mSjpY03jk3XtLVYVsUL2a2j6TPSXozdFti6I+SxjnnPippqaQL\nA7en5JlZlaQfS5osaZykk83sgLCtio02Sec558ZJ+rikb3LsuuUcSX8N3YiYulbS751zB0o6SNLf\nArcnFsxsL0lnSTrEOfcR+ZSvaZ3dJzZBmKSvS7rSOdcmSc65dYHbEzc/lPTt0I2II+fcw8659ujq\n05L2CdmemJgoaalz7k3n3PuS7pR0bOA2xYJz7m3n3EvR/5vkvwD3DtuqeIl+dH5B0s9DtyVuop7+\nTznnbpYk51ybc25D4GbFSQ9J/cysWlJfSW91tnKcgrAxkg43s6fN7FHmmsycmR0jaYVzblHotpSB\nMyT9IXQjYmBvSSuSrq8UgUTWzGxfSR+V9EzYlsRO4kcnSc/ZGylpnZndHA3n/szM+oRuVBw4596S\ndI2k5fKzAK13zj3c2X1Cnh25m06Ku14i39aBzrmPmdkESXdL2q/4rSxNXRy7i+SHIpNvQ5LOCgs7\n5xZE61ws6X3n3PwATUSFMbNaSfdIOifqEUMGzGyKpHeccy9FaSx83mWnWtIhkr7pnPuLmf1I0iz5\nOZ7RCTMbIN/jP0JSi6R7zGx6Z98ZJRWEpauYL0lmdqake6P1nosSzAc555qK1sAS1slsAx+WtK+k\nl83M5IfSnjezic65NUVsYknr7LUnSWZ2mvzwxmeK0qD4WyVpeNL1fcT8sBmLhjLukXS7c+6+0O2J\nmU9IOsbMviCpj6Q9zOw259wpgdsVFyvlR07+El2/RxIn1mTms5IanXPvSpKZ3Ss/JWPaIOz/t3c/\nIVaVcRjHv08xUYhagTW0KJSsqEW0kcR2YrSyoAyhf+jSsiRazWZwEUItKoKgJMNFkFoRtikEQ5CM\nqRzFcOmiPwuhHMmCJPPX4p6pQbK5o6PHM/f72Vzumfc983thztyH973vOV1ajvyE5gMwyR3AkAFs\nelX1XVUNV9WSqlpM7wK7zwDWvyQP0VvaWF1Vp9uupyO+Bm5PcluzO2gt4C61/m0DjlbVG20X0jVV\nNVJVt1bVEnp/d3sNYP2rquPAD83nLMBK3ODQr++B+5Nc20x6rGSaTQ1X1EzYNN4DtiU5ApwGvKgu\nTOH0/Ey9CVwD7OldV3xVVRvaLenKVlV/JXmO3s7Sq4B3q8odVn1IsgJ4AjiSZJzeNTtSVZ+1W5kG\nyPPA+0mGgGPAupbr6YSqGkvyITAO/Nm8vvN/fbxZqyRJUgu6tBwpSZI0ZxjCJEmSWmAIkyRJaoEh\nTJIkqQWGMEmSpBYYwiRJklpgCJM0UJI8nOSuizzHnUm+TPJHkhdnqzZJg8UQJmnQPALcM5MOSa4+\n59AvwEbg1dkqStLgMYRJ6oQkW5JsmPJ+dHIWKslLScaSHEoyOqXN00kOJxlPsj3JcmA18EqSg0kW\nJ7k3yYGm70dJFjZ9v0jyWpIxencQ/0dV/VxV3wJnLsfYJc1NXXpskaTBtgN4HXiref848GCSVcDS\nqlrWPK9td5IHgBPACLC8qiaSXF9VJ5PsBj6tqo8BkhwGnq2q/Uk2A6PA5BLjUFUtu3xDlDRIDGGS\nOqGqDiVZlGQYuAk4UVU/JdkErEpykN5zUecBS5vXXVU10fQ/ee45kywAFlbV/ubQdmDnlCY7Lt2I\nJA06Q5ikLtkFrAGG+TcgBdhSVVunNmweIH6xfp+Fc0jSf/I7YZK6ZCewFniUXiAD+BxYn2QeQJJb\nkiwC9gJrktzYHL+haX8KWABQVb8CE0lWND97Ctg3w5pygWORNOCcCZPUGVV1NMl84MeqOt4c29Pc\ncuJA7ythnAKebNq+DOxLcgYYB9YDHwBbk2wEHgOeAd5Och1wDFg3+evOV0eSm4FvgPnA2SQvAHdX\n1W+zP2pJc1Wqzvt/RpIkSZeIy5GSJEktMIRJkiS1wBAmSZLUAkOYJElSCwxhkiRJLTCESZIktcAQ\nJkmS1IK/AZjA0DHBAPVbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fe69860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "sklearn_lda = LDA(n_components=2)\n",
    "sklearn_transf = sklearn_lda.fit_transform(X_train, y_train)\n",
    "\n",
    "plt.figure(figsize=(10,8))\n",
    "\n",
    "for label,marker,color in zip(\n",
    "        range(1,4),('x', 'o', '^'),('blue', 'red', 'green')):\n",
    "\n",
    "\n",
    "    plt.scatter(x=sklearn_transf[:,0][y_train == label],\n",
    "                y=sklearn_transf[:,1][y_train == label], \n",
    "                marker=marker, \n",
    "                color=color,\n",
    "                alpha=0.7, \n",
    "                label='class {}'.format(label)\n",
    "                )\n",
    "\n",
    "plt.xlabel('vector 1')\n",
    "plt.ylabel('vector 2')\n",
    "\n",
    "plt.legend()\n",
    "plt.title('Most significant singular vectors after linear transformation via LDA')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classification via LDA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top]](#Sections)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The LDA that we've just used in the section above can also be used as a simple linear classifier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1st sample from test dataset classified as: [3]\n",
      "actual class label: 3\n"
     ]
    }
   ],
   "source": [
    "# fit model\n",
    "lda_clf = LDA()\n",
    "lda_clf.fit(X_train, y_train)\n",
    "LDA(n_components=None, priors=None)\n",
    "\n",
    "# prediction\n",
    "print('1st sample from test dataset classified as:', lda_clf.predict(X_test[0,:].reshape(1, -1)))\n",
    "print('actual class label:', y_test[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another handy subpackage of sklearn is `metrics`. The [`metrics.accuracy_score`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.accuracy_score.html), for example, is quite useful to evaluate how many samples can be classified correctly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction accuracy for the training dataset\n",
      "100.00%\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "pred_train = lda_clf.predict(X_train)\n",
    "\n",
    "print('Prediction accuracy for the training dataset')\n",
    "print('{:.2%}'.format(metrics.accuracy_score(y_train, pred_train)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify that over model was not overfitted to the training dataset, let us evaluate the classifier's accuracy on the test dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction accuracy for the test dataset\n",
      "98.15%\n"
     ]
    }
   ],
   "source": [
    "pred_test = lda_clf.predict(X_test)\n",
    "\n",
    "print('Prediction accuracy for the test dataset')\n",
    "print('{:.2%}'.format(metrics.accuracy_score(y_test, pred_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Confusion Matrix**  \n",
    "As we can see above, there was a very low misclassification rate when we'd apply the classifier on the test data set. A confusion matrix can tell us in more detail which particular classes could not classified correctly.\n",
    "\n",
    "<table cellspacing=\"0\" border=\"0\">\n",
    "\t<colgroup width=\"60\"></colgroup>\n",
    "\t<colgroup span=\"4\" width=\"82\"></colgroup>\n",
    "\t<tr>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" colspan=2 rowspan=2 height=\"44\" align=\"center\" bgcolor=\"#FFFFFF\"><b><font face=\"Helvetica\" size=4><br></font></b></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" colspan=3 align=\"center\" bgcolor=\"#FFFFFF\"><b><font face=\"Helvetica\" size=4>predicted class</font></b></td>\n",
    "\t\t</tr>\n",
    "\t<tr>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#EEEEEE\"><font face=\"Helvetica\" size=4>class 1</font></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#EEEEEE\"><font face=\"Helvetica\" size=4>class 2</font></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#EEEEEE\"><font face=\"Helvetica\" size=4>class 3</font></td>\n",
    "\t</tr>\n",
    "\t<tr>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" rowspan=3 height=\"116\" align=\"center\" bgcolor=\"#F6F6F6\"><b><font face=\"Helvetica\" size=4>actual class</font></b></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#EEEEEE\"><font face=\"Helvetica\" size=4>class 1</font></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#99FFCC\"><font face=\"Helvetica\" size=4>True positives</font></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#F6F6F6\"><font face=\"Helvetica\" size=4><br></font></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#F6F6F6\"><font face=\"Helvetica\" size=4><br></font></td>\n",
    "\t</tr>\n",
    "\t<tr>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#EEEEEE\"><font face=\"Helvetica\" size=4>class 2</font></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#FFFFFF\"><font face=\"Helvetica\" size=4><br></font></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#99FFCC\"><font face=\"Helvetica\" size=4>True positives</font></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#FFFFFF\"><font face=\"Helvetica\" size=4><br></font></td>\n",
    "\t</tr>\n",
    "\t<tr>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#EEEEEE\"><font face=\"Helvetica\" size=4>class 3</font></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#F6F6F6\"><font face=\"Helvetica\" size=4><br></font></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#F6F6F6\"><font face=\"Helvetica\" size=4><br></font></td>\n",
    "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#99FFCC\"><font face=\"Helvetica\" size=4>True positives</font></td>\n",
    "\t</tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confusion Matrix of the LDA-classifier\n",
      "[[14  0  0]\n",
      " [ 1 17  0]\n",
      " [ 0  0 22]]\n"
     ]
    }
   ],
   "source": [
    "print('Confusion Matrix of the LDA-classifier')\n",
    "print(metrics.confusion_matrix(y_test, lda_clf.predict(X_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, one sample from class 2 was incorrectly labeled as class 1, from the perspective of class 1, this would be 1 \"False Negative\" or a \"False Postive\" from the perspective of class 2, respectively"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='SGD'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stochastic Gradient Descent (SGD) as linear classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top]](#Sections)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now compare the classification accuracy of the LDA classifier with a simple classification (we also use the probably not ideal default settings here) via stochastic gradient descent, an algorithm that minimizes a linear objective function.  \n",
    "More information about the `sklearn.linear_model.SGDClassifier` can be found [here](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.SGDClassifier.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Prediction accuracy for the training dataset\n",
      "100.00%\n",
      "\n",
      "Prediction accuracy for the test dataset\n",
      "96.30%\n",
      "\n",
      "Confusion Matrix of the SGD-classifier\n",
      "[[14  0  0]\n",
      " [ 1 17  0]\n",
      " [ 0  1 21]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDClassifier\n",
    "\n",
    "sgd_clf = SGDClassifier()\n",
    "sgd_clf.fit(X_train, y_train)\n",
    "\n",
    "pred_train = sgd_clf.predict(X_train)\n",
    "pred_test = sgd_clf.predict(X_test)\n",
    "\n",
    "print('\\nPrediction accuracy for the training dataset')\n",
    "print('{:.2%}\\n'.format(metrics.accuracy_score(y_train, pred_train)))\n",
    "\n",
    "print('Prediction accuracy for the test dataset')\n",
    "print('{:.2%}\\n'.format(metrics.accuracy_score(y_test, pred_test)))\n",
    "\n",
    "print('Confusion Matrix of the SGD-classifier')\n",
    "print(metrics.confusion_matrix(y_test, sgd_clf.predict(X_test)))"
   ]
  }
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