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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[Sebastian Raschka](http://sebastianraschka.com)  \n",
      "\n",
      "- [Open in IPython nbviewer](http://nbviewer.ipython.org/github/rasbt/python_reference/blob/master/tutorials/python_data_entry_point.ipynb?create=1) \n",
      "\n",
      "- [Link to this IPython notebook on Github](https://github.com/rasbt/python_reference/blob/master/tutorials/python_data_entry_point.ipynb)  \n",
      "\n",
      "- [Link to the GitHub Repository pattern_classification](http://nbviewer.ipython.org/github/rasbt/pattern_classification/blob/master/python_howtos/)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext watermark"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%watermark -a 'Sebastian Raschka' -v -d -p numpy,scipy,matplotlib,scikit-learn"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Sebastian Raschka 10/07/2014 \n",
        "\n",
        "CPython 3.4.1\n",
        "IPython 2.1.0\n",
        "\n",
        "numpy 1.8.1\n",
        "scipy 0.14.0\n",
        "matplotlib 1.3.1\n",
        "scikit-learn 0.15.0b1\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<font size=\"1.5em\">[More information](http://nbviewer.ipython.org/github/rasbt/python_reference/blob/master/ipython_magic/watermark.ipynb) about the `watermark` magic command extension.</font>"
     ]
    },
    {
     "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": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Entry point: Data  "
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "- Using Python's sci-packages to prepare data for Machine Learning tasks and other data analyses"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this short tutorial I want to provide a short overview of some of my favorite Python tools for common procedures as entry points for general pattern classification and machine learning tasks, and various other data analyses.  "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Sections"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- [Installing Python packages](#Installing-Python-packages)\n",
      "\n",
      "- [About the dataset](#About-the-dataset)\n",
      "\n",
      "- [Downloading and saving CSV data files from the web](#Downloading-and-savin-CSV-data-files-from-the-web)\n",
      "\n",
      "- [Reading in a dataset from a CSV file](#Reading-in-a-dataset-from-a-CSV-file)\n",
      "\n",
      "- [Visualizating of a dataset](#Visualizating-of-a-data)\n",
      "\n",
      "    - [Histograms](#Histograms)\n",
      "\n",
      "    - [Scatterplots](#Scatterplots)\n",
      "\n",
      "- [Splitting into training and test dataset](#Splitting-into-training-and-test-dataset)\n",
      "\n",
      "- [Feature Scaling](#Feature-Scaling)\n",
      "\n",
      "    - [Standardization](#Standardization)\n",
      "    \n",
      "    - [Min-Max scaling (Normalization)](#Min-Max-scaling-Normalization)\n",
      "\n",
      "- [Linear Transformation: Principal Component Analysis (PCA)](#PCA)\n",
      "\n",
      "- [Linear Transformation: Linear Discrciminant Analysis (LDA)](#MDA)\n",
      "\n",
      "- [Simple Supervised Classification](#Simple-Supervised-Classification)\n",
      "\n",
      "    - [Linear Discriminant Analysis as simple linear classifier](#Linear-Discriminant-Analysis-as-simple-linear-classifier)\n",
      "    \n",
      "    - [Classification Stochastic Gradient Descent (SGD)](#SGD)\n",
      "\n",
      "- [Saving the processed datasets](#Saving-the-processed-datasets)\n",
      "\n",
      "    - [Pickle](#Pickle)\n",
      "\n",
      "    - [Comma Separated Values (CSV)](#Comma-Separated-Values)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Installing Python packages"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "**In this section want to recommend a way for installing the required Python-packages packages if you have not done so, yet. Otherwise you can skip this part.**\n",
      "\n",
      "The packages we will be using in this tutorial are:\n",
      "\n",
      "- [NumPy](http://www.numpy.org)\n",
      "- [SciPy](http://www.scipy.org)\n",
      "- [matplotlib](http://matplotlib.org)\n",
      "- [scikit-learn](http://scikit-learn.org/stable/)\n",
      "\n",
      "Although they can be installed step-by-step \"manually\", but I highly recommend you to take a look at the [Anaconda](https://store.continuum.io/cshop/anaconda/) Python distribution for scientific computing.\n",
      "\n",
      "Anaconda is distributed by Continuum Analytics, but it is completely free and includes more than 195+ packages for science and data analysis as of today.\n",
      "The installation procedure is nicely summarized here: http://docs.continuum.io/anaconda/install.html\n",
      "\n",
      "If this is too much, the [Miniconda](http://conda.pydata.org/miniconda.html) might be right for you. Miniconda is basically just a Python distribution with the Conda package manager, which let's us install a list of Python packages into a specified `conda` environment from the Shell terminal, e.g.,\n",
      "\n",
      "<pre>$[bash]> conda create -n myenv python=3\n",
      "$[bash]> source activate myenv\n",
      "$[bash]> conda install -n myenv numpy scipy matplotlib scikit-learn</pre>\n",
      "\n",
      "When we start \"python\" in your current shell session now, it will use the Python distribution in the virtual environment \"myenv\" that we have just created. To un-attach the virtual environment, you can just use\n",
      "<pre>$[bash]> source deactivate myenv</pre>\n",
      "\n",
      "**Note:** environments will be created in ROOT_DIR/envs by default, you can use the `-p` instead of the `-n` flag in the conda commands above in order to specify a custom path.\n",
      "\n",
      "**I find this procedure very convenient, especially if you are working with different distributions and versions of Python with different modules and packages installed and it is extremely useful for testing your own modules.**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "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.\n",
      "\n",
      "Bache, K. & Lichman, M. (2013). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.\n",
      "\n",
      "</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": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Downloading and saving CSV data files from the web"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Usually, we have our data stored locally on our disk in as a common text (or CSV) file with comma-, tab-, or whitespace-separated rows. Below is just an example for how you can CSV datafile from a HTML website directly into Python and optionally save it locally."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import csv\n",
      "import urllib\n",
      "\n",
      "url = 'https://raw.githubusercontent.com/rasbt/pattern_classification/master/data/wine_data.csv'\n",
      "csv_cont = urllib.request.urlopen(url)\n",
      "csv_cont = csv_cont.read() #.decode('utf-8')\n",
      "\n",
      "# Optional: saving the data to your local drive\n",
      "with open('./wine_data.csv', 'wb') as out:\n",
      "    out.write(csv_cont)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Note:** If you'd rather like to work with the data directly in `str`ing format, you could just apply the `.decode('utf-8')` method to the data that was read in byte-format by default.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "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",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "# reading in all data into a NumPy array\n",
      "all_data = np.loadtxt(open(\"./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]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "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"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Visualizating of a 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": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Histograms"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Histograms are a useful data to explore the distribution of each feature across the different classes. This could provide us with intuitive insights which features have a good and not-so-good inter-class separation. Below, we will plot a sample histogram for the \"Alcohol content\" feature for the three wine classes."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import pyplot as plt\n",
      "from math import floor, ceil # for rounding up and down\n",
      "\n",
      "plt.figure(figsize=(10,8))\n",
      "\n",
      "# bin width of the histogram in steps of 0.15\n",
      "bins = np.arange(floor(min(X_wine[:,0])), ceil(max(X_wine[:,0])), 0.15)\n",
      "\n",
      "# get the max count for a particular bin for all classes combined\n",
      "max_bin = max(np.histogram(X_wine[:,0], bins=bins)[0])\n",
      "\n",
      "# the order of the colors for each histogram\n",
      "colors = ('blue', 'red', 'green')\n",
      "\n",
      "for label,color in zip(\n",
      "        range(1,4), colors):\n",
      "\n",
      "    mean = np.mean(X_wine[:,0][y_wine == label]) # class sample mean\n",
      "    stdev = np.std(X_wine[:,0][y_wine == label]) # class standard deviation\n",
      "    plt.hist(X_wine[:,0][y_wine == label], \n",
      "             bins=bins, \n",
      "             alpha=0.3, # opacity level\n",
      "             label='class {} ($\\mu={:.2f}$, $\\sigma={:.2f}$)'.format(label, mean, stdev), \n",
      "             color=color)\n",
      "\n",
      "plt.ylim([0, max_bin*1.3])\n",
      "plt.title('Wine data set - Distribution of alocohol contents')\n",
      "plt.xlabel('alcohol by volume', fontsize=14)\n",
      "plt.ylabel('count', fontsize=14)\n",
      "plt.legend(loc='upper right')\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rdu3alXCd/v3789RTT/HII4/QokUL2rRpw8033wzApk2bku7n7bffzowZM1ix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\nrA8xusMnb/cPHAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105662d30>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Scatterplots"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "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()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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i4nUKWlIXzSVohQM7gAtq2UdBS0REvE5BS+qiIYOWN+867AqkAvOA7cCbQLAX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\nRERERERERERERERERERERKSW+H/CqQ+gYvnblgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10584d198>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "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",
      "\n",
      "plt.title('Wine dataset')\n",
      "     \n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FrigKgsEgAKRs1g3oPwFm4741ymRWKZRbpJIx0m9GBZTneVU4y9lEO5WFyVyy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\nZFLfDZEkSZKkxkKFnA6RpEbn/wFnNYMMVynu2gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106f1beb8>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "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",
     "collapsed": false,
     "input": [
      "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)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "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]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "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"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Feature Scaling"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Standardization"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another important 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; standard scores (also called ***z*** scores) of the samples are calculated as follows:\n",
      "\n",
      "\\begin{equation} z = \\frac{x - \\mu}{\\sigma}\\end{equation} \n",
      "\n",
      "Standardizing the features so that they are centered around 0 with a standard deviation of 1 is especially important if we are comparing measurements that have different units, e.g., in our \"wine data\" example, where the alcohol content is measured in volume percent, and the malic acid content in g/l. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "std_scale = preprocessing.StandardScaler().fit(X_train)\n",
      "X_train = std_scale.transform(X_train)\n",
      "X_test = std_scale.transform(X_test)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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 left')\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()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wV5BXlgeAXdlZ+stSlwsyyV9CiIaoutS3vrmKK4pVVklWjcVmtzVqH0ePHlW3\n3HKLatu2rYqPj1dJSUlKKaVmzpypBg4cqJRSym63q5EjR6ro6GjVsWNH9eabb6oePXqoNWvWKKWU\nGj58uEpISFCRkZGqT58+aunSpUoppebNm6fOP/98FRERodq3b6+SkpKU3W6vFUNWVpa6/PLLVWxs\nrIqJiVG/+93vTu3jdJ76Lt2tsLxQXTb9MnXxBxerH478YHQ4wkOA1jTDZ72f0ROsdmut/FViKWnU\nPnwtfynlOzlM+AdcyGG+OvO18/PVJDMzu4+vfJfTt03ng80fEBoUSsfIjsy/Y760krVCMlO/aCz5\nPoU38dWZ+oVwSVFFETO2zyAuLI6YkBgO5R1iY9pGo8MSQgghGk0KMuGzvj34LYXlhRRbiskty8Xi\nsDBn5xyjwxJCCCEazVe7AKTJ38N84bssqigirTCtxrrY0FjOijrLoIiEp0iXpWgs+T6FN3Elh/lq\ngpOE5mHyXTZPWkEas3fO5vnLnq/8RRTNIAWZaCz5PoU3kTFkQhjk460f8+mOT0lOl1nEhRBCnJkU\nZEK42ZH8I6z4dQVtwtowcdNEOUsXQghxRq1qYti4uDjpHnKTuLg4o0PwWdO2TcNkMtEmrA0pOSkk\npyfTv3N/o8MSXk7yl3tJDquilJL/Wz7AV/+F6hyDIYTRjhYcZcjcIYQGhmI2mSmyFHFx+4uZc9sc\nSYjN4A9jyITwhIV7FnIw7yCjLxttdCh+zZUc1qpayITwBnf3uRuHcpx6HhMSI8WYEKLFlVhKeH/z\n+5RaShl+0XA6R3c2OiTRAF/9KyFnmEL4EWkhE6Lx5uycw3ub3sOMmRvOvYGxg8YaHZLfkqsshRBC\nCD9UYinh460fExsaS9vwtixPXc6xwmNGhyUaIAWZEEII0cosS1lGRlEGeWV5ZJZkkl+ez6zts4wO\nSzTAV7sApMlfCD8iXZZCNM7+7P3szdpbY12XmC70O6ufQRH5N7+bqV8I0TpJQSaE8GUyhkwIIYQQ\nwgdIQSaEEEIIYTApyIQQQvgspRT55flGhyFEs0lBJoQQwmdtSt/EHQvvkKJM+DwpyIQQQvgkpRST\nNk0irTCNhXsWGh2OEM0iBZkQQgiftCl9Eym5KXSP7c6nOz6loLzA6JCEaDIpyIQQQvicytaxkIAQ\nggOCsdgtLNizwOiwhGgyKciEEEL4nN2Zu9mXvQ+7w05OaQ4O5WD+7vnYHLYWj2Vz+mayS7Nb7HhW\nu7XFjiWT7gmwAAAgAElEQVRajq9OtCgTKwrhR2RiWHE6q91KSk4KiqrvMjQwlHPizqn8/9IiiiqK\nuOGzG7jq7Kta5ObduWW53L/kft677j3Ojjvb48cT7iETwwohhGiVggKC6J3Qmz4JfU4tPdv0bNFi\nDGDR3kWUWEtYnrqctII0jx9v3q557M3ay8dbPvb4sUTLkoJMCCGEaIKiiiKmb59OfHg8JkxM3zbd\no8fLLcvls12fcXbc2aw5tIaDeQc9ejzRsqQgE0IIIZpg0d5FlFhKCDAHEBMaw7KUZR5tJZu3ax5W\nh5XQwFBMmKSVrJWRgkwIIYRogp2ZO4kKiaLUWkqFvYKo4Cj2Zu31yLFKLCXM2z0Pu8NOVkkWDuVg\n5YGVpBeme+R4ouX56iBZGRQrhB+RQf3C39kddjalb6pxhaXJZCKxUyKhgaEGRiZc4UoO88YE1wX4\nFEgAFPARMPG0bSShCeFHpCATQvgyXy3IOjiX7UAksAW4BdhXbRtJaEL4ESnIRJPt2QNvvw3Z2TBo\nEDzxBISEGB2V8DOu5LDAM+wjAbgT+BPQHd1idQRYD3wOZDY3yDpkOBeAYnQhdhY1CzIhhBCiYenp\n8Oij4HBAWBh89hmUlsKLLxodmRC1NDSofxqwEN1KNRW4H3gA+BCIcr72iYfj6w70BTZ5+DhCCCFa\nm61bobwc2rTRBVlCAnz9tdFRCVGnhlrIJgI76li/D/gOeB24yBNBOUUCi4AkdEtZDS+//PKpx4MG\nDWLQoEEeDEWImvLL83nt+9d49YpXiQiOMDqcVmfdunWsW7fO6DA8RvJXCwkJgerdw1arLsyE8LCm\n5DBvHZMRBPwX+AZ4t47XZQyGMNSHP3/IhI0TeGXQK9x70b1Gh9PqyRgy0SRlZfDAA5CSAmZnh9DY\nsXDjjcbGJfxOcwf172rgNYXnWsdMwCwgB3iyvuP7bULbvRumT9eJ5pZb4Jpr4PRbhZSX6+2Ugj59\n5IzQzfLL8xk8dzCB5kBMmFg+bLm0knmYFGSiyUpKYNkyyM+Hfv30IkQLa+6g/spTiMedP2c7d+bp\n5oA/AsOBncA257rngRUePq73S0mBhx7SjwMDYfNm3QQ/ZEjVNgUF8PDDcPiwft6tG3z0EcTGtni4\nRrLarWw+vpkBXQa4fd8Ldi/AYrfQJqwNGcUZLPllibSSCeGtIiLg7ruNjkKIM2poUP9h53IN8Cy6\nxWwn8JxznadscMZ1MXpAf1+kGNNWrgSLBeLjdYEVEQHz59fcZvp0OHBAD15NSICDB+Fj/7u9xsoD\nKxn19ShSc1Ldut/CikJmbJ+B1W4loziDClsFH235iDJrmVuPI4QQwr+cadoL0K1il6ELJdAtWK2l\n68C3BATU7J5USq+r7uhRCK02a3NoqF7nR6x2K+8nv4/FYeGjLR8x4ZoJbt3//b+9H6ujarbs0MBQ\nFNIFJYQQoulcKchGAjOAGOfzfPT0F6KlDR6sW8QyMnQhZrfDyJE1t7nkEvj+e4hx/nOVlcGll7Z8\nrAZaeWAl2aXZdI3pyrrD60jNSeXctue6Zd/RIdE89rvH3LIvIYQQolJjWrpinNvneyiWxvDfQbGH\nDumirKxMF2j9+9d83WaD8ePhv//VLWiDB+tJEIOCjIm3hVntVm6adxNltjIigiPILsnmT93+5PZW\nMtGyZFC/EMKXuevWSR2A8UAn4DqgF/AH9MSxRpGEdiYlJfpnhH9d/ZeSk8Jfv/orFbaKU+vahrfl\ny6FfEhIot0vxVVKQCSF8mbsKshXoLst/oqe6CEJf/dinmfE1hyQ0IfyIFGRCCF/mSg5r6CrLSvHA\nAsDufG4FbM2KTIhWKr0wnSX7lhgdhhBCCB/jSkFWDLSt9vz3QIFnwhHCt03ZPIVXvn+F9ML0Rr83\ntyyXV79/FZtDzneEEMLfuFKQPQ0sA84GNqIniP27J4MSwhcdyjvEtwe/JcAcwMztMxv9/jk75zBn\n5xzWHFzj/uCEEEJ4NVcKsi3An9Dzjz0C9Kbum44L4dc+2foJJky0i2jH0v1LG9VKlluWy7zd82gX\n0Y5JyZMot9RsJbNJo5kQQrRqrhRkB4GHgN3o2fot6Bt/CyGcDuUdYnnqckKDQim3lVNmLWtUK9mc\nnXOwO+y0CWvDyZKTjBy3hu++06/t3w+jRkFFRcP7EEII4btcmRjWCgwCEoFHgQr0FBhCCKfs0mx+\n2/63OJQDgM5RnbHYLS69N7csl9k7ZqNQZJdmU2Gr4GS3ScyY9WdSUgLZsAGSkiA42JOfQAghhJFc\nuYx8G/p+ks8CtwN3AUuc64wil42LWlJTITISOnbUz5OT4aKLat5JyhtllmTyydZPatyOqbQgghNf\n/p2czGAuvxw6d4bo6Jr3kfcnMu2FEMKXuWsessqCDOAq4H2gDdCuOcE1kyQ0Ucu338K8efpGBbt3\nw9y58O9/Q4cORkfWeHv3wvDhcO65kJ4ObdvCrFn6nvL+SAoyIYQvcyWHudJlOaba49XANcD9TQ9L\nCM+4+mp9e8+HH9bPp071zWIM4MsvYcoUXVyGhUGnTvqnEEKI1qmhQf0XOH8eBy6ptrQFlns4LiHq\npJTiaMHRel8PCKh6bK7nf/eB3APM3z3fzZG51wsvwMGDuquyf3+IjwdTa2kfEkIIUUtDBdlTzp9v\n17G85eG4hKjT9ozt3PPFPRzOP1zrtTVrdDfl1KnwxBPwz3/CyZO19/HOT+/w+obXmzR5a0tJSYGN\nG3WX6yuvQFQULFtmdFRCeB+L3cLm9M2eO4DdDg6H5/YvhJOvnnPLGAx/s2sXas0a/mr5nB+CT3DX\nhcMY9+dxNTbZv18P6u/kvAb4p5/gt7+t2dW3J3MPI5aMAOCW39zCP//0zxb6AI1nsVRdWWm3g1IQ\n6Mogg1ZIxpCJ+izZt4TxG8bzxV1f0DWmq/t2bLHAm2/CV1/p5vaHH4YHHpCmatEkzb2X5e3AbQ0s\nopVLK0hzeeoGj9q0Cf76V7Z/9RE7j2+j56FCVu1fXquV7Pzzq4oxgN//vva4qw9+/oBAcyDxEfGN\nnry1pVWf5iIgwH+LMSHqY7FbmPLzFMqsZXyy9RP37nz6dFi8WI8XiI2F99/XVw4ZKD9fp8NK+/fD\n4cOGhSPcrKGC7Ebn8iAwDbjXuXwCjPR8aMJIpdZSHvzqQRbuWWh0KPDBB6jgICb3KiYoMIQAixVT\nfgGfbGlcAt6TuYfvj3xPYEAgJZYSSiwlTbrFkRDCO3yd8jV5ZXl0jenKil9XNDi+tNE2bNBzzQQE\nQFCQXpKT3bf/Jigs1HXh+vW6GHvtNcjJMTQk4UYNFWQjgAeAYKAXusXsdvStk2SKylZu6S9LySjO\n4JOtn1BiKWmRY06erOcSA8jNhddf170GlJVxJNLG7rAi7CbICrahHHbWHllLQbnr97kvs5Xxp65/\n4sKEC+mT0IfLu19OeFC4Zz6MEMKjKlvHokKiCDDrq3nc2krWsSOUlVU9t1oNv2y7a1ddhE2YAP/4\nB/zf/8GllxoaknAjVzpBugAZ1Z6fBNzYUS+8Tam1lI+2fERCRAIFFQV8+cuXDL9ouMeP+7vfwauv\n6tsEzZgBV1zh7La79Va6TXiTJTsvwGGzgs0Ob79F0AV9iAmNcXn//c7qR7+z+nnuAwghWkxKTgpF\nFUVU2CvIL88HIDk9GZvDRqDZDf37o0bB9u1VVwadcw4MHdr8/TZTeXnV49JS4+IQ7ufK6MTJwHnA\nXOf2Q4FUYJQH4zoTGRTrQfN2zeM/P/2HDpEdKLeVY7VbWT5sORHBER4/9ooVukl+wAB4/nnnSocD\nPv8clizRg8Iee0xXb8JvyKB+A2Rnww8/6Md//CMkJBgbjxFyc2HbNt1d+bvfGT4Z4IEDMHasbhlr\n1w5eegkefVTnS+Hd3DVTP+hB/AOdj9cDXzY9LLfwjYTmo4Z+PpRfc38lKCAIAKvdyutXvc7V51zt\n0ePm5uqpKiIjISMDxozRM9ULIQVZC0tPhxEj9C8l6EHtM2boPjNhmJISOHQI+vTRz48c0b0IlbeL\nE97LHQVZILAb+I2bYnIX709oPqywopAya1mNdfHh8afGaXjKP/+pp6m46y59JdFHH8EHH8hNtYUU\nZC3uX//SLdLt2+vnJ0/CDTfAyy8bGpaoaU/mHjalb2JkX7nOztu549ZJNmA/0A044p6whLeLDokm\nOiS6xY87erSeABX07PS9ekkxJoQhcnN1N12l4GDIyzMuHlGLUooJGyewI2MH15xzDZ2jOxsdkmim\nhq6yrNQG2AN8ByxzLl95MijhnyqLsfqeCyFayBVX6NHjZWX6Z2kpXHml0VGJarae2MqerD0EBQQx\nbes0o8MRbuBKF8Cgetavc18Yjeb9Tf5CCLeRLssWphTMmwczZ+rH992nF5ml3isopXhg6QOk5qYS\nExJDdmk2i4cullYyL+bOQf3exvsTmhDCbaQgE6LKluNb+MuSvxAToqf9ySvP485ed/LqFa8aHJmo\nT3NvnVTpD8BmoBiwAg6gsLnBCeEuJ4tP4m9/4BwOPWdb5W1TDh3Sz+UeyEK0fmaTmVvOv4VB3Qcx\nqPsg+nXsxzep32Bz2IwOTTSDKwXZZGAYeu6xUPStlKZ4MijRumzP2I5DeaZSyC3L5e4v7uZ/af/z\nyP69ldmsh/SMGQNr1+q5ia68Uq8XQrRufTv2Zfyfx/OvP/+LcVeOo9RaSom1hNUHVhsdmmgGV9N3\nKhAA2IEZwHUei0i0Kvuz9/Pwsof5Me1Hj+x/7q65HC86zqRNkzxW9Hmryy6Da66B//xH/7zsMqMj\nEkK0tB+O/MDRgqMkRCQwefNkaSXzYa4UZCVACLADeBN4itYzlkN42NSfp1JsKWZSsvsLptyyXObu\nmkv32O4czDvIxrSNbt2/tzt0CFat0oXYqlVV3ZdCCP/gUA4mbppIWFAYUSFRnCw5Ka1kPsyVguwv\nzu3+BpQCndE3GReiQfuz97Ph6AZ6xPXgQO4Bt7eSzd01F5vDRnBAMKFBoX7VSuZwwDvvwMMPw3PP\n6Z//+Y+MIRPCnySnJ5OSm4LFbiGrJAuLzcIn29x4g3XRony1pUuuUvIBT654kp/SfyI+PJ788nw6\nRXVi7u1zMZuaP9DJ5rBxzexrKKooOnUjYYvdwoxbZnBR+4uavX9fUFEBISH1P29N5CpL4WvKrGWE\nBXn23pf55fnsPLmzxrqo4Cj6duzr0eOKxmvutBe7GnhNAUb+1ZOEVpeyMti/HwID4Te/0T8NUlhR\nyI3zbqTEUnJqXXBAEHMvHkd3YvVNKqObdzeA9MJ0ym3lp56bTCa6xXTz+C2eRMuTgkz4khNFJ7h/\nyf18dONHdI/tbnQ4wgs0tyDr7vz5uPPnbOf29zqfP9eM2JpLEtrpsrJ0v9WJE7rfqm9feO89CA01\nLCSL3YLdYddPHA5M48cT+s23ulCMjISpU+GccwyLT/gOKciEL3l9w+t8vPVj7ul9D+P+PM7ocIQX\naO48ZIedyzXAs+gWs53oQuwadwQo3Oi99yA9Hdq1g4QE+PlnWLTI0JCCA4IJCwrTy4+bCV2+UscW\nHw/FxXKjYiFEq3Oi6ARLfllCzzY9WXVwFYfzDxsdkvARrgzmMQHVL6j/I63nTLX1OHQIIiL0Y5NJ\n3xj4iBfdDz4jQ9+CpXKirJgYOHrU2JiEEKKJfs39lc92flZr/awds3AoB8EBwZgw8ckWGWQvXONK\nQTYSPRHsEecyxbnOU6YDJ2l4DJs43cUXQ2GhLnrsdrBaoU8fo6Oq0rOnLsasVh1jbi5ceKHRUQkh\nRJP858f/MGHjBI4VHju1Lr88n6X7l6KUIrs0G4Vi5YGVZBRnGBip8BWNaemKcf4s8EQg1QxE36bp\nU6C+v9gyBuN0JSV6/oNNm/Tz22+HZ5/1rqnbZ86EDz7Qj3v2hHff1V2sQpyBjCET3mR35m5GLBmB\nyWTixvNuZMzlYwCwO+xsz9heY3JWs8lM3459T10NLvyTu24uHoqed6w7UPk/SgGevItpd2AZUpA1\njlKQl6cHzTfzCkaPKSnRV4O2aeORYjG9MJ2l+5fy+O8eP/PGwmdIQSa8yePLH2fbiW3EhcWRU5rD\nF0O/oHN0Z6PDEl7MXTcXXwrchL6xeLFzKWnwHcIYJpMudLy1GAM9zi0+3mMtdx9t+YjJyZPZddJz\nPd7+MvmsEKK23Zm7+eHIDwSYAyiyFJFVmsX7ye8bHZZoBVxpQ+0EXOvpQBrr5WpX6A0aNIhBgwYZ\nFovwDkcLjvLNr98QGRzJBz9/wJTBU9x+jP3Z+3nxuxeZdesswoPC3b5/oa1bt45169YZHYbHSP7y\nXRW2Cq7scSUKRYWtgl9zfmV/zn6PHjO/PJ/Y0FiPHkO4V1NymCtdAB8Bk9FTXrSU7kiXpWiksWvH\nsuLXFbSLaMfJkpNMv2k6F7Z374UDSSuS+Drla1654hWGXTjMrfsW9ZMuS+GNpv48lQ9//pDQoFCW\n3bOM+PB4tx8jOT2ZF9a8wKK7FklR5sPc1WU5ENgCpKCvfKycj0wIr3G04ChL9y/FbDaTX55PqbWU\nKZvd20K2L2sfG49upGtsVz7e8jGl1lK37l8I4Tvyy/OZvWM2CZEJ2B125uyc4/ZjKKWYtGkSRwuO\nMm/3PLfvX3gXVwqy64Fz0ZPB3uhcbvJgTPOAjcB5QBrwgAePJSo5HHD4MKSm6qkpfEyFrYKrz7ma\nAV0G0L9zf67reR3dYru59RhTt0wlwBxAeFA4xdZilvyyxK37F0L4jvm751NhryDQHEhsaCzzd88n\nuzTbrcfYfHwzv2T/Qo+4HszeMZv88vwGty8oL6hxhafwLY3pAkhAX3FZychZPaXJ352sVnjhBfj+\nez3YvkcPmDIF4uKMjsxrHMg9wG0LbiM4MBgzZsrt5bQLb8eK4SvkcvYWIF2Wwts8uPRB9mTtOfU8\nwBzAa1e8xpU9rnTL/pVS/OXLv3Ao/xBxYXFkFGcwsu9IHuv3WJ3bO5SD4YuHc0X3K3jo0ofcEoNw\nH3dNe3ET8DZwFpAJdAP2Ab2bGV9zSEJzp4UL4Y03oEMHfaXmyZMweLDf3drIarcSFBBU52vFlmJ+\nTPsRRdX/u5CAEAZ2G4jZ5EVzvbVSUpAJf7Mncw/3fXkfIQEhmEwmLHYL0SHRrBy+ss489cORH/j7\nN38nIjiCr+/9mugQL77a3g+5ksNcObUfB/wB+BboC1wB3Nfc4IQXOXBAz11WORVFZCTs9+xVQ97m\nYN5BklYk8ektnxIXVtUyaLfrryUyOJKrz7kaux0CAgwMVAjhF86PP5/Zt86udRJYV4u8QzmYuGki\nUSFRlNnKWLB7gbSS+SBXTu2tQLZz2wBgLdDPk0GJFnbeeWCz6XFkSukbf/fqZXRULeqjLR+xN2tv\nrYGzn3wC8+bpryUrC/72N92AKIQQnhRoDqR3Qm/6JPQ5tZzb9tzKlpYaNhzdwOH8w0SHRBMXGses\nHbMorCg0IGrRHK4UZHlAFPAD8BkwET05rGgtbr4ZrrtOVxxZWboYGzXK6KhazMG8g3x36DvOjjub\nOTvnkFeWd+q1oUNh40aYOFEPs7vuOmjf3sBghRDiNHN3zcXqsJJblkuxpZiiiiJWHVhldFiikVwZ\nkxEBlKOLt3uBaHRhluPBuM5ExmA0k1KKjOIMOkZ1rFwBJ07oAf6dO/tVv9zo1aNZd3gd7SLakVGc\nwQMXP1Dj1kupqfDUUxAeDvPn62F2omXJGDLhDtml2USHRBMcEGx0KG6VUZxR6wrMLtFdiAiOMCgi\ncTp3zUM2BrCjuy5nolvInm1mbMJgPx77kbu/uLvqMm2TCc46C7p186ti7FjhMVYdWIXdYSerJAu7\nw868XfNOzTGWlQVvvgl33qnvg17ZfSmE8C12h51H//soM7fPNDoUt+sQ2YHfxP+mxiLFmO9x5Yxz\nG3owf3W7qH8W/ZYgZ5jN4FAOhn0xjG0Z23j00kd58g9PGh0SuzN3E2QO4vz481v0uOW2cpLTk6n+\n/ykoIIj+nfoTYA5g2jR9682bb4b8fBg3Dp55RrotW5q0kInmWn1gNc98+wwRwREsH7acmNAYo0MS\nfqS50148BjwOnAMcqLY+CvgfuvvSKJLQmmFj2kb+/s3fiQ+Pp6C8gGXDPHPLD1fZHXZuW3AboYGh\nzLtjnldNI6FUzS7K05+LliEFmWgOu8PO7QtvJ688j1JrKQ9d8hAPX/pws/drc9jIKsmqGvohRD2a\n22U5Fz0r/1fAEKpm6b8EY4sx0QyVl0eHBYURFBCEXdmZvWO2oTGtPbSW40XHOZh3kI1pGw2N5XSn\nF19SjAnhe9YeWkt6YTrRIdG0CWvDpzs+paC8oNn7/WLvF4xYOoIya5kbohT+rqGCrAA4DLwInHQ+\n7gEMB+QOpz5qb9Zefs39FavdSnZpNkoplu5fisVuMSQeu8POpORJhAeHExoUyqRNk3AohyGxCCFa\np4V7F2JTNrJLsymsKKTYUszqg6ubtc8yaxlTt0zleOFxlqUsc1Okwp+5cr6/HT3vWHfga2Apepb+\nGzwX1hlJk38TOZSDowU173oVHBDMWVFnGRJP5biOdhHtAMgqyWLSDZO4rOtlhsQjvJN0WbYCJSXw\nyy8QFKSn1glsuVuO5ZTmUGQpqrGuQ2QHQgND63nHmS3YvYC3fnyLmJAYlFL8d9h/CQsKa26oopVy\n10z9CrABtwGTnMu25gYnjGE2meke293oME7Zn7Of9pFVI+TbR7YnJSdFCjIhWpOTJ+GhhyAzU09A\nffHFenK/0KYXRI3RNrwtbcPbum1/la1jMSExhAWFkVGUwbKUZdzV+y63HUP4H1fOODcB7wEvoMeQ\nHQJ2A308GNeZ+OcZphB+SlrIfNzo0fDdd/ry5Mo5D59+GoYNMzqyJllzcA3PfPsMIQEhAFgcFs6O\nPZvP7/rc4MiEt3JXC9lI4BFgPLoY6wEYOwpcCCGE7zhyBCKc82KZTLq78ujRht/TGAUFMHUq/Por\n9O4NDz+sZ3L2kMu7X87Su5fWWCfzfonmcqUg2wP8vdrzQ8AbnglH+DuL3cLo1aN5ZsAzcim5EK1F\n376wYIEuyhwOfe/cC900laXVCk88ocenRUTA1q26MJs4EcyemUIn0BxIl5guHtm38F8N/W9dDtwJ\n1HWaEQ4MRQ/yF8JtVvy6gmX7l7XK2bSF8FtPPAEDBuixZFlZuqvy+uvds+8DB/T9zTp0gOho6NgR\nkpP1sYTwIQ0VZA+gZ+P/GT0z/yrgW+fjLcAFwP2eDlD4D4vdwvub3+es6LNYsn8JJ4pOGB2SEMId\nIiJ0i9W338LatXr8mLtar8zmmvczq3zsodax1qbYUswb/3sDq91qdCh+r6H/sZno+1j2Aq4GXkLP\nSXY1uhh7GcjycHzCj6z4dQW5pblEh0SjlJJWMiFaE5MJYmMhMtK9+z3nHLjkEn2hQE4OZGTAlVdC\nQoJ7j9NKLd63mGlbp7HywEqjQ/F7vnrVkv9dpdTK2Rw2bvjsBtKL0gkLDMOu7KBgxfAVNabFEP5J\nrrIUDSorg7lzdddlnz4wdKie70w0qNhSzODPBmN1WIkNjWXp3UsJCpDvzRPcdZWlMIJSsGuXPuPr\n2RO6tO4BpEophl04jHJb+al1AaYASQ5CiDMLC4MHHzQ6Cp+zeN9iSm2ldIjsQEZRBisPrGTIeUOM\nDstv+eoZZ+s+w1QKXn8dFi+GgAC97o034PLLjY1LCINIC5nwFla7lf9b8X8888dnvGqS7cYqthRz\n3ZzrKLeVExIYQqm1lA4RHfjqnq/kRNgDpIXMV+3erYuxhAQ9MLW0FMaM0YNhZaCqEEIYZuWBlaw6\nsIq40DjG/Xmc0eE0WbmtnEHdB9W4j3F4UDgWu0UKMoM0VK3tauA1BVzk5lgao3WfYX7/PTz3HLTT\n93dEKT1Qdf16j052KIS3khYy4Q2sdis3zbuJUlspZdYyFt650KdbyUTLaW4L2Y1ujUa4rmdPfUVS\nSYkuwLKy4NxzpRirR0ZxBmkFafQI+R2hoVUXcR09Cp07N71R0WK3EBwQ7L5AhRA+beWBlWSXZtMh\nqgPl1nI+2fKJT7eSCe/S0J+qw9WWMvScZH2AUuc64SmdOsGECXpG64wMOPtsePtto6PyWu/+9C5P\nr3qar1eXMGYMFBfr6yGefx6OHWvaPostxdyx8A52Z+52b7BCCJ9kd9h5P/l9iq3FpBemU2GvYOn+\npRwtcOMtoM4gozijxY4lWp4rY8juAiYA3zufTwaeAeQuqp502WX6ZrwVFfoKIqMoBZ9/Dl98AaGh\n8MgjesZtL3Ew7yDfHfoOu8MOlyymV/F93HOPvhbitdega9em7XfR3kXsy97HlM1TmDJ4inuDFkL4\nHJPJxF8v+WuNK8FNJhMRQS1zD8s9mXt45L+PMOe2OdJN2kq5MiZjJ3AVeqJYgHbAGmQMmX/4/HN9\nxWd0tL7/nMUCH38MFxn5z19l9OrRrD20lujQaCw2C2/89mvGj9UJct68ps1BWVRRxOC5gwkJDCG/\nLJ/pN0/nwvZuuu+eC2wOG6Dvlyc0GUMm/N3fvv4bKw+sZGivodJN6oNcyWGujK4xUXNG/pwz7VS0\nIkuWQFSUrmxiY3U36rffGh0VoFvHvj3wLTGhMQSYAsgsKOTJjxYzfjzcfDOnui8b64t9X1BuKyc0\nMJTAgEA++PkD9wffgHHrx/HWxrda9JhCCO+1J3MPm45tomebnqw6uIrD+YeNDkl4gCsF2QpgJTAC\nfX/Lr4FvPBiT8Cbh4bplrJLD0eDFBS155v9L1i/EhcVhc9iw2C2Em+PodfkeLrpIzxH5+99DefmZ\n91Od1W5l9o7Z2Bw2skuycSgHG9M2kpKT4pkPcZqjBUf5OvVrvvzlS7mXpxACgA9+/oBAcyCB5kBM\nJhOfbPnE6JCEB7jS0mUCbgMuQ0938QPwpSeDcoE0+XvSjz/Czz9DfLy+Q8A//qGLMqUgLg5mz4aO\nHSjvd3QAACAASURBVGu9bXfmbt758R0+vPFDn+1ucygHW45vocJeUWP9pR0vJSzI82P5xqwdw4pf\nVwBw629u5fmBz3v8mL5AuiyFvzpWeIzbF9yOyWTChAmHcmA2m1k+bDltwtoYHZ5wkSs5zFcTnCQ0\nT/n8c31XAJMJ7Hb4zW/gmWfgf//Tg/oHD9bFWEoKzJypp+YYMgSuuorHv36C1QdXM/G6iVx37nVG\nfxKfc7TgKHcsvIP48HgUityyXJYMXULHqNrFr7+Rgkz4K6UURwqO4FCOU+sCzYF0ie5S+XshfIC7\nZuq/HXgdaF9tZwqIbk5wwgspBZMmQZs2EBKi16WmQn4+/O1vVdsdPgwjR4LVqm/g+7//sSvvFzYX\nbOasqLOYvHkyV51zVb2tZEopSSR1WLhnISXWEgLK9e2yii3FLNq7iFH9RxkcmfA7SsGWLXremC5d\n4NJLjY7Ib5lMJrmq0k+4UpC9CQwB9nk4FmE0pfQ0G9UvTTSZ9LrqVq3St3Pq1Ek/Lyrig/+9R+BF\n7YgKiSKjOIPVB1bX2Uq2/sh65u+ez/s3vC9F2Wnu6n0Xf+zyxxrrusS07pvKCy/1/vswa1bV84ce\ngocfNi4eIfyAK4P6M5BizD+YzXDDDXDypC64srP1AP6+fWtuZzLpxWlfWAnfR2RhtVvJKM6g1FrK\nlJ+n1Brgb3fYeefHd/jhyA8kpyc3O9yNG6GoSD92OGDNGv3TV3WN6cofuvyhxtI5urPRYQl/c+IE\nfPqpHkPaoYP+OW2azgdCCI9pqIXsdufPn4EFwBKg8i6kCljswbiEUUaP1nOOrV+vb9f01FPQvn3N\nba69Vg/sP3kSAgNJUFbG90mCSy45tUl4UHitFrD1R9ZzrPAY0aHRTE6eTGKnxGa1kqWmwoIFegLY\nTz+FtDT44x/1UDchRBMVFuqTs0Dnn4fAQH0CVlioizMhhEc09NdwJrrwqtzu9FGoD3giIBfJoFij\nHTwIc+boQf3XXw+DBjW4ud1h546Fd5BbnktUcBTpRenc0+cenv3js00OQSl9XcHixXqYy9tvG3tT\nA+E5Mqi/BZWVwW23QUGBnnswLw/attV366gcWyqEaJTmDuof4c5gRCtz9tl65lUXbUzbyC85vxAZ\nHEmZtYwTRSd4fcPr3HbBbfRs07NJISil60HQF4RWny5NCNFEYWEwZQq8+CL8+iucdx6MGyfFmBAe\n5soZZxdgInoeMoD1QBLQxNs2u+Q64F0gAPgEeOO01737DFPUcqLoBFtObAH0rYle+f4VlFLcdP5N\nTLhmQpP2+cEH+oLPl1/WXZfbtum7PEkrWesjLWRCCF/mrnnIVgOfAXOcz+91Llc3J7gGBAD70ffP\nTAc2A/dQ88ICSWg+bOKmiczZOYd2Ee3ILMlk3u3zmtRKtmOHPnkPC9OtZcnJkJhY43oD0UpIQSaE\n8GXuupdlO2AGYHUuM4GEZsbWkETgV+Cw83jzgZs9eDzRgnLLcpmzcw6hgaGU28qx2W18+POHTdrX\nb39b1RpmMkH//lKMCSGE8E2uzEOWw/+3d97hUdTbG3/TQxJCJwgooIhIFSxw8QooFgQbdhQVRRQF\nRRFFBTEXBPwpAopYL8qjVDsgFpQqFpqUG7ooCqQQEtLLJtn9/fHuOJuYskl2M7vJ+3mefTKzZebs\nZPfs+Z4K3AVgMWjd3Q7Am/XPrQAcddk/BqCXF88napD4zHi0a9gOhXYmfDUMa4jsgmyLpRJCCCGs\nxR2D7D4AcwHMcu7/BO9WWLrly4+Njf17u3///uhfQZVfnSQ9HYiPB5o185ly9S7Nu2DZLcusFkP4\nOOvXr8f69eutFsNrSH+J2kJRERDE4SJwONgL0tivy1RFh/ligKc3gFgwsR8AngFgR/HEfuVgVMSW\nLRwKXlDAb8nTTwM33GC1VMLJTz8BZ5wBtG7Nf8+qVcCAASpIKAvlkAnhexw/ztHHsbFAo0ZsT1lU\nBNxrZVMsH8VTOWQfAGjost8IwHtVF6tCtgE4G0BbAKEAbgOwwovn832OHWPPr8WL2Yy1Imw24Kmn\nuExp2pSNXmfMoLdM+AS5uewqcOwYm6CvWUNFJkStYutW4Lrr2LH5qafM0RqiVtCqFf+1EycCr70G\nbNsG3HRTxa8TpeNOyLIbgDSX/VMAepbxXE9QCGAMgG/Bisv5qMujm377jYO8s7K4P38+Z8y1Lmek\nzqlT/MVv7qy9CAtj5+2EBKBlS+/LLCpkwAD+feghesXee6/4CFEh/J6//gLGjgVCQrgoNFYdr7xi\ntWTCg9x6K/0Fx44Br7/Of7WoGu54yAIANHbZbwwaSt7kawDnAGgPYIaXz+XbzJ/P4d6tWvGWkQEs\nWlT+axo1AiIj+VwAyMvjX2MYuLAchwP44w9u2+1AWlr5zxfC74iLY7fm6GiOX2rRAvjhB3743eHk\nSaZa3HwzY2L6kvgcDgfDlO3aAddfzz6QqalWS+W/uGOQvQLgZwBTAbzg3K5aJ09ReTIygNBQcz84\n2DS0yiI0FJg1i16x5GS2s3/+eSpEPyQ1lU4/g7/+8v+u/IsWAXv2AEuW0Es2aZJmNws/IDsb+Phj\n4N13gZ07gQMHaDD16sXEIde0iKgo/mIbBlhuLo0zd3rT2GzAqFHA2rVUAF9+SW+b4vo+RXw8sHs3\nBzncfz8n6K1cabVU/ou7SbKdAVwGVkCuBbDXaxK5R91Jil2xAvjPfzhTzuGgMfbSS8Bll1X82pwc\nIDHRzCPzU776ivp42jS+nWnTaF+efbbVklWdI0f4bwkPp928bx9w7rn0lgW7k0hQx1BSvw+QkwMM\nH840ioAA09iKiAAaNKDh1KoV8NFHzF8tLAQefZQFRgEBvM2YYcbry2P/fp6rWTPuOxxcXH76afnp\nGqLGsdupw8raF6S6syxdw5QJYB8ygEZZYwByTHoCQzGXtWq89loqwkWL+CkfO9Y9YwygojzzTM/I\naSGDBtEOvftu7sfG+rcxBgBt2/LvkiX0jI0ezS4lzz0HjBtXK/5toraxcSPw++9m6kNiInDoEHDJ\nJdxv1oyJRMnJ9MYHBzPTe8MGfrg7dwbOOce9c4WG8pfd+HU3+im4RguET1DS+JIxVnXKM8h+Rfk9\nwdp5WJa6hd1Ot/8HH3B76FBgzJh/fpoDAoDbb+etDtO9u5k6546x4nAUt3FL7vsKN9xAB+i0aXT/\n9+snY0z4KEYuqkG9egwhGo2obDZ+yVyrU4KD3fOIlaRtW34Z1q41vW1DhpgeMyFqIT74E+UW/uny\nd2X5cv4SN2tGJXbiBMvC67jhVRr79tFgefxxLsg3buR+o0alP7+wkDlZDz0EtGnD3OLPPqP3yReN\nsoQE4IEHuL18uXsrTIeD7zMkhPs2G7d98f15AoUsfYC//uLCMSCAsfaUFCAmhi5e44P32GPAnXd6\n5nyFhUxIOnwY6NiRrnK5X4Sf4qnh4gB7j50NINzlvo1VE8sj+KdCc+Wpp4AffwQaOyPDaWlAt27A\nvHnWyuWDbN/Ov+efz78rVnCIeHk1Chs3Av/9L+3bRYuACRN4eX2NU6fYw+eii5g206oVw5cV/e6s\nW0fnwaRJdLDGxtLb9q9/1YjYNY4MMh9h9262rUhNZQb3mDFM7k9MZKmdL37JhPABqptDZjASwKMA\nTgewA+yk/zOY5C+qSkwM21kY5OebfcNEMQxDzOC66yp+Td++9Iy9+Sbw4IO++zuxdi1lvf12FqHN\nmAH8+Sd/21zJzATeeYdev4gIoEkT5lZPnEhHwtlns9BNCK/SrRv7ILqiD16VyLZlIzI00lIZXFM5\njG1/Sfeojbjj/x0L4CIARwBcCqAHgHQvylQ3uOceungSExmzCg2lmyRbg7Y9QVwcHZBXXsmirz//\ntFqi0rnxRjNKXa8eo9gljTGAbeUiIlhdumULx5WMHcuuA4cPAyNGKJojhL+wI2EHbvroJqTnWfdT\n+t13wFtv0cNeUMDWFV9/zT7kRveSRYvofff3NkP+gjsqPA9ArnM7HMB+sGmrqA5Nm3IUUmwsvWU5\nOfw1vu02jTiqJoWFwBtvMEz5yCPsj/PGG+73oyyP5GRz26jErw4lV55lrUQDA+npy8kBpk7le3r2\nWX50+vUDJk9mD829VjekEUKUi8PhwOtbXsfhU4exbM8yy+S4+GIWzb7+OjB9OnNQBwxgDcWgQSyQ\nnT+f6c2uwRzhPdxxRH4O4D7QUzYAHJ0UDGCQF+WqCP/NwSjJRx/R3XHaaWZy/yWXADNnWi2ZX1NQ\nYCa8l7ZfWRwOHmP0aOCWW6i4Fi6kh2ratJpx6cfFMaQZHc2Uw7w8nn/CBH5cgoKYA3366d6XpaZR\nDlkdJTOTRQPNm9NNXAvYkbADI1eORON6jZFTkINVd6xCg/AGlsiSng4MG8btzz9nUazdDlxwAQeH\n9+tHo6x+fUvEq1V4arj4ENAIiwXwHID/ArihmrIJg6NH+Utq/KJHRvpufK2qHD8ObNoEHDxYY6cs\naXyVZYzl5rq3/9lnNMCefpqjQrp1Y/7XM8/UjDFm9AOeMIF1H337MoH/zjtZH+Jw1F5jTNRR1q8H\nBg4E7rgDuPpqxur9HMM7FhoUirDgMNiKbNX2kuXn04gyKKnDyqKgAJgzB+jRA+jQgV2Y7Hb2RmzQ\ngPVme/ZoHnxNUtmsk/UAVgCweV6UOkrXruzjU1jIX9X0dKCnN2e31zDr1nG0yvjxXIq99ZbVEv1N\nXh6LxD79lMbV55/TA/Xll3TlJyUBDz/Mav/LL6chNnEi7eXAQPbsramVY3Q0MHcuDUEjfHnnncC2\nbXw8OxvYvLlmZBHC66SmMiYfHs70jqAg4MknGbP3Yw6kHMCvib/C4XDgZM5J2B12LPnfEtiKqv6T\nungxdYPdzmyX0aO5Bq6INWuAsDCmO0ydSp33zTfA+++zy8gvv7Be4+67ZZTVFP4aAqg9Ln+7nd+m\nhQu536sXQ5i1wT1vs3GqQHg4M9YLC9m7aMkS4Kyz3D5MQgK9UEabi3372Dw1LIz7H37IFV6vXtTX\nr75Kg6Vx4+LHOXAAOOMMigIAu3bRuJk8maOMWrYEbr2VxQDTp/N3YN06KqjWrRkm3LSJyumrr+ix\nGjqUhQOexnX8iN1uTp5xffzuuyn3kiX04L37LqtKjcbptQmFLOsYcXHAyJH8EhokJwNLl5pjLvwQ\nW5ENcSfi4Pr/DwsOQ+dmnY3PeKXJywOmTOG6PimJC7Urrqj4dcbwg6Ag7hcWMmS5YwfQvj0Xm3Y7\nDbPevVU0VF082YfM16h9Ci07mz7kBg1qT41xSgpw1VX0oWdk0BKKjmbMrRKl8mvWcBU4bRpXfrNn\nc0VnVCP+9hvrIe67j4bSmWfSICupQN5+m6vA2FhWE337LXOvXn2V0ZHsbOr/9983fwfsdlZBZmUx\ngT4tjX9796bS+/Zb5pRt2WI2JD9yhI7O7t2rdtl272Zq4aRJLL6dO5cG59VXF3/ewYNsit6yJZXr\nr79yHmZERNXO68vIIKtjnDxJF3RUFBd0OTmMzX37be1YrHqY339n1TXgfnNpUbN4KodM1ASRkRwg\nXpox5nCw0+miRXTReEqZOxw85pVX8rZwoXvHTk1lR+7+/bkcKys3rGFDdj49coQKNSGBmqOS/dbq\n1aOhMXIk2z706FF8pF379oxmzJrFRfSDD1J3p7pMWz1xgrOKW7emF+yLL2jgff89Q5L9+jEUeegQ\njTOAnrC77mJeVvfu9MzNmUMH5uLFfDv33cffjilTaEQdOUKPW2YmV6zz59MWBfi8BQsqvsRdutAg\nnDKFBmNSEnDppf98XocONMYAfmzOP792GmOiDtK0Kb/sWVn84uTl0W0tY+wfxMdzgfrAA8yAMcKX\ndYnUVC6ki4q4HxfH8Ku/IYPM13E4gJdf5sTpV16hITR7tmeOvWoVrRhjiO/s2byvInnGjWNcLzyc\nFsioUTS8SpKVRQUaFcVvSmgo444pKZUSs0ULhg5TU1kDsX8/HW0GOTlm2LKwENi6lbenn6Yuj49n\nMnxcnGnAhIXRVb9rFzB4MI+7dCmNv/HjmSA/ejSnBDz3HI236dOBH36gE3PECE4C+OMP/luGDuVY\n0kceoeH4739zlRoSQk/XH38w/yw6umIHaGAg21p8/DH/HRMm8PVPPKE2daIOMXAgEzrnz+ffvn2t\nlsgn2bSJdQ/XXsvFYFYW21vWJaKiqCNnz2aE4cUX2bjA35BB5uskJACffEKvUqtW/Lt0Kd0m1WXN\nGlogrrc1a8p/TXo6S29iYmhtNG5Mi6g0L1lwMC2fnj0Z4+vdm4kJwe4MiADf+9q1yP9xG0KC7AgN\npQ2Yn188t3f+fIYpX36Z4cg33gA6d2aI79576TG74w56wlav5kqqWzd+aSdMoHNwxgzq+3fe4Vub\nMYNvc+ZMOvoCA5kON2wYbddrrwUuvBB49FGmtFxxhWloJSTQoLPb6WGLieH5+/Th/E3DHrXb+byS\nTRftduanORymF+6GG/jvMRwEqbmpmP7DdBTa1bFRWExmJj34mza5X+LnLk2aAJ06lT24VuDWW4G2\nPQ8hrzAP4eFc+BkLz7pCaCgXvj/9xPf/xBNVTxmxEhlkvk52Nq0BI/MyKIj7nnCVNG7MxHsDm61i\nxVevHs9fUMB9w7tWWighMpIJVidO0JBLTKRy7dy5Ytl+/ZWvffZZtH3pIUw49TQa1LejVSsONHAN\nWY4YYeaMtW9Pg6xJk+Jpaj168L5p0xgNGT2aBlhwMN9SkyZ8XqdOXFn9/jsfu/DCf4q2aRO/8Js3\n863Pn88E+3HjGJJcvZres1deYQh08WJeru3bgWPHqDBOnmT4c/Nm081uEBfH+774grKuXk2j7oUX\nzOcs3L0QC3YuwPo/1ld8LYXwFklJdA8/+SS/AHfdxe+6+BuHg4tBg/x8z6ynDTJ/Xo8HZvwLS4d2\nBZ55Bns2Z+HLL83Hv/iC6Ra1nYMHqbODguhXKKlX/QEZZL7OGWfQK5acTIPpxAlaDK1bV//Yw4cz\nhhYfz1t0NF1KgGkxPPsswwVG4lNYGN1CqanMsE9MZIJTp06ln2P8eMb8Bg5kj4l589zr0Boby29W\ns2ZID4tBq4NrsXj0j5g5kwn0rh3yIyKKJ7FGRvLtTJxIUe+7j2+jUyczWT8wkKFKV1EcDtNYGjWK\nx330UdP2NDA6XB88SEOpb1+muGzYwEs4ZAiPf/iwmZ63dSubLe7ezct1770sRnjuObNa1KBbN+aE\nBAXxfbRoQaNx1y4+npKTgiVxS9AsshnmbpmLIrsfah5RO3jzTeqk5s35ZThyxKwYFwCoq559ljog\nP5+5oeVlhqSmMn3OaDWxaRMXfaVy5Ag+mTkCqcjFe2ekIHPN12j74RQsXw6sWMGWPl9/7fkxyTk5\n1GUGx46512rDWyQlMeIxcSJzeU+doh42Qrf79plRB1/GX6uW6laV0vHjLCM8dIgNYiZPrlqA/PBh\nGllJSbQiHnjA7OVw8CCwcyctiauvBpYt46c5JITPb9aMnq0HH6Traft2ytO8OTPiDQ+ep+jdmx68\noCCG9JISEfz8JOD66/8Wp7xKov/9j+Ib5d8rV/LSnX122a9xOGgzXn01cM01VKBz5tDrVdKGPHSI\nDgGAHrC0NNZH/Pgj8xmMBq5HjlCGJ56gvPHxvLTr1tE4fOWVf7bnABiqvOYavnbECPNcS5cC8+Ne\nw8LdCxETFYPEzETMGDADl591uZsX1j9RlaWPMnIk+8k0cHaaT0nhimPaNGvlqgGys5lCYai+jIzi\nua2uHDjAkFpeHlMfxo4tW385HNQ5u3ZxHbt4cdkzbjOXf4TBa0YgLDgM6UGFeDjpDAw/UA8nVvyC\nEffz67JggRkB8BRHjnAxOWYMM2kmTeLC16o0P4eD+t74WbTZ2Apo9Wo6befPpw7u0cMa+QC1vRCu\nJCcz2SAvj+6W9HROtp44kUudkSMZBwwKogFot9OlFB9P6yMggK4bm40Nr7p18668Y8YwnhcTQ5kz\nMpi5f453x6jm5pp9ykrbB7hyfe455ig4HLx8U6eyf8/LLzPqGxHBItQbb+RvU8OGwOOPc25cYiJf\nv3IlB/zOmmVGfB0OXt6+fbnqvOACKuRLL+WlP71DKq768CogAAgJDEGWLQttG7bF57d9jqBADxvF\nPoQMMh/lvfe48oiJ4Yf3xAl+uG+o/cNc3n2XC7Fx41ihHRtLL4zRL9GV/Hzmn+bl8fJcdFH5x3Y4\nqJKTkqg/ylK37y95Cm9unoeYgCjkBRQh31GIVft7YvX9a7FoEZ8zfDhw3XXVeael47oofewxs+2P\nLzFrFhe/Dz/8z7ZBNY3aXgiT7dtZftO0KX/9Y2Lo07bbuYyw22k11K/PZV9aGl+XmMjAfGAgH7fb\naUV4mylTgPPO4/nz87lE9LIxBvzT+Cq5D9CZ2KMHFd2991LM0aOpOGfPZpL/tm1UUKGhtHkNZXDF\nFWaY8uabaXe6tqoICGCU+qWXGJWeNImXvWNHGoAFRQW4psM1GHjWQAxoNwDXn3M9Lj79YhQ5FLYU\nFnDXXVx1JCfTO3bPPd759fdB7rmHKnXMGH6nR40q2xibMoVFPS+/zKHdW7eWf+wff+QCrEcP2rxl\ndcr/OvB3FEXWQ5IjC+n2XOSgAEsvH4zVq2kwvvUWF37emOLhqhujojx//Oqybx9Tkf/1L1as+0Pl\nqb+uOGvPCrOmWLuWcTRDY+Tn0/2zcSNXuAsWmP7e5GS6Z1q2ZDZqRgYfa9KEfvrRo7nkqIjMTCZ8\n2e3Mjm/YsPJy5+czXujjnQ7nz2deiNGc1uhWUlVFtWwZU3H69+cqtLb0Cq4q8pD5OAUF/JC6W0Ft\nJca198CXav9+1jOEhPBHv7TMjbQ06oahQ6nGDhygWi2rm35qKsNrkydzcbdgAVWw0fjVlbzCPBTk\nZgM/bgIyMoFO5yL07J7IyQn4uz4rNZXr7JJpF2lppko2pva5q6KPH+dC8667uICcMoUtfyry/NUU\nNhsN5YceolH71VdsWTR9unW6VCFLd0hJ4bclN5dxonPP9cxxrcDoahoayuSDmBjzsdxcLul++41K\ns6iImuT22/ntuvtufkMNpTp5MvDzzyz527iRvnaAGmfmTOaflUdKCt1HxrKkSRMu9arRHMbhML9M\nrts1TclzG/u7dgFTn87GVQUrcf+NqQi48MLSyzQrIC2NnrGMDP4rpk3zz546nkQGmag2NhtXSStX\n0kU9ZgwruauIMfVjxAiud6OiuHjyRDptXh4DFQD1S36+ue8JbDYaK/feyyKlJUvY5sfd1L/0dGDv\nXnqfAP70BAZWaiKe13G9hqXt1zQyyCri5Ema+ElJ/EUNCaE/2VfM/Mqwezd95vn5/AY3acJOpa6/\n5JmZzHQ8eZLv0XXoYXw8Q5g2G2NtRmuKw4eZD1JUROugUSOeY82a8rtmz57N5CfDI5eURCNxypQq\nvb3vv2ci6YgRFGXmTCa9d+lSpcNVmaIi2qr3388k2wMHqMzGjgWmPJOLET+NQOSx/WjaPBD1o0DL\nqoJ8GqM8OyiI/7rx49l1f+hQTor5/HM6Mf3B+eAtZJCJajN3Lt1NzZuz+d+pU9T3ffpU6XCffkr1\n2qcP1ea8eRxc4umKRm9hTBWJjKTueeGFqgUxhHu4o8PqsIoHPWNJSSwTAeiaeP11GjK+xIkTnNdz\n8CDzqJ5+uvjQXYDl54DZETAhgRpjzBjzOfXr00tmTKt2pWVLGnQlSUvj0s/1fCdOmF34yyIpqbiP\nPDycr6sivXvT7fz222Zj1Y4dq3y4KhMUBAwaxLL0O+5gWPHxx6nnBzf6CZ1DDyG3RyscPAR0bpGL\nkDlzKjTIVqzgCtPoxJ+Rwby0gADasBdcULeNMSE8woYNrAYNDjbzYrdsqbJBdtNN5nZoKPWAP9Gm\nDX9OfvmFql/GmPX4dmKOt8nJKZ6bFBLie7NpbDbma/3wA8OOGzYwh6tkc6ycnOIGUGAgjSZXsrOZ\nR9arF1tVrFhR8fnPOovu/bQ0um+Sk2nAljQIS9KnDz1pBQVcjWZnc55QFYmK4mpu1SoqkAkTrDNS\n+vRhbte8ecD119ObNXo0MODf+QgIDEBEBNCtKxASEcr/WQXekMGD+e97/nngmWf+GTmv6FILIdyg\nWbPikwQKCz3fD8JPcDjo2U9IYIX4smXsfiSspW4bZJdcQpdHejp/EdPTORPHl/jrLybYx8SwrKVF\nC9ZYHztW/HnXXEMDzHCxOBz/zBqdOZOxv+bNaWRNncreYwCV0+7drMZ0NUobNqTXsFEj5oO1b083\nf0WJEtdcw7rt9HSGBoYNYwyuihQW0gDq2pWhQneGdHuDdetoGK5Zw35C06fTSAwNBQJ69qAnMCUF\ngfm5vF6DBlWY7BYaSkfmrl38d99xh5L4hfA448ZR7yUmmrqsDrTnKI2CAl6CF16gN37KFKYLC2vx\nV7XvuRyMn3+mwZGTw3Lte+7xrYq+Y8dYVm50QrXb6aVavrx4fpjdzmXOJ5/QUzZqFN04rlx5Jf8a\nreHj45n8dOutbElvNIZt3pw1065FAcY5KnttHA7eqnlNv/qKfb4mTGBy5uTJrEM477xqHbbSZGXR\ng3XppbRR//qLkdtZs5xG1L597PaanEyD/5FH/tmKvwQZGaxYOu88DjmPiGD40tO9dv0Z5ZDVQRwO\nhhTj4xlf69mz+sdMSuKiMyyMGemuPWeE8CJK6q8NOBzswbVihWmQGQ1dK+tGGTaMmZyNGpmTq//z\nH3qxZs2igRcQwFyvyy7jhO2qkJnJRC/Dq+cBjJGZRpiyoMC9CUzeIDWVdjvAGgmgerJ89RUv17Bh\nfF8vvcTirxpou+Y3yCCrg8yaxbgaQH310EOs6hHCD5FB5stkZbFr34ED/OUdNarsplVG89bff2dO\n1xVXVM3jFBdHpWaz8ZjdunES96xZnEBrlAdlZTE0aihDd3A42JTnm284Qyg4mKvPOXMq7Oq/7LuQ\ntwAAFKBJREFU8uBKNI9ojl6te5X7PF+gsJD1Fbm5vLVrxxS/wEBe1h9+oC0bEMBi1iNHmJRfHiXb\nIlnZ0sNXkUFWxzh6lFnzTZvSVVxYyJXQN9/g7wZbQvgRqrL0VYqKGCrctYvxrh07aMy8/XbpcarA\nQJbbVZbVq2lw5eXRq3b//Zy8uns3PVe9ezOBqWtXhjqLiniuzEzmPrmL0QV18WKzz1nXrjzeuHGc\nbluGCykzPxP/t+n/0LheY3x222cIDvTtj+S6dfwbG0tvVmws/33nn88ahuXLGWUePJgDhQcPrtgg\nK2l8yRgTdZ7MTOoRQx8GB/OLkZkpg0zUWnwoWaoOcfQovVUtWnAabYsWnIZ99KjnzrF1Ky2C9HSu\nLt9+mz0aTjsNuOoqJkLl5LDPWL9+TLhPTmaORZ8+7nXiN9i1i22qIyNpeAUF0cCsX58JUqmpZb70\n470fI78wHwlZCVj3xzoPvHHvcvnlZoVnvXpspHj++Xysfn0myX77LRsuDhrEKkwhRCVp04ZfqJMn\nubBLTqae9GKH5PS8dK8dWwh3kEFmBYGB/ywR9EDiezE2bODxoqJoOURH091v8M03tBiGDWNl6aWX\n0v3z3XfAq6+W32OsJMnJPJeRIBsQwPhdZibPXcaKNjM/E+/vfB+N6jVCREgE5m6Zi0J7YTXetPcp\nOR2mZOsNIxoM0BZWZEqIKhAZyd6K7dpxQdexI4uvvJQ4mp6Xjls+vgWbj3lh6KMQbiKDzApat2aF\nT0ICs7kTEuiVat3ac+eIjjZbwAOMpzVowO2kJCbzR0aaTa7Gj2f4smHDysfMjHkZDge38/KoOO12\nZqiHhpb6so/3foyUnBTkFOSgyF6Ew6cOY+3vayv5RmuIwkKGgJcsoUewFNLS6JS8/Xam0W3fXrk0\nPCGEC2eeyTSIX35hnxtP6kcAdocddgdXT8v2LMOf6X/itc2vQfl9wip8O2GnthIYyJyrJUsY2uvY\n0Zw86yluvJEzd44fp4EVHs7upQDvA8zBXvXrs7IyJaVqIYEzz6SBN3Uqz3XZZcBjj7FMvZz2z/WC\n6+Gqs64qdl+ALyZQFRby/fzyC43MoCCORCoRj4yO5ohPI2fshRfMSy2E8C3+b9P/ITI0Evd0vwcf\n7PoAbRq0wcGUg9hyfItfFBiJ2ocP/vq5haqU3CE1lWHI/Hx64Nq25f0JCcCQIbQgwsJYVelwMPnJ\n6Jl15AhnvyUlMd/svvsqbo1fWMhjNWhQuzLTN29m59aYGL6v/Hy+z02bfKtnXS1GVZbCkxzPOI4h\ny4YgKDAIt3S6BUvjliImKganck+hTYM2WHjjQt9cHAq/RVWWdZ3GjYsPXDNo1gzo3p0eusBAjkJ6\n/33TGDt5kv1+MjJ43969jMc99VT55wsOrp0D0bKzeZ0MBR0aymSxwsIyw7FCCN9lwc4FAIAiexHe\n3PomosOjkZKTAgcc2HtyL+JOxKFrTFdrhRR1Dl8zyG4BEAugI4ALAfxqqTS1lQ8+ALZtY2wtN5c5\nX66zMbdtYwv6kyfpOatXj1MAnnyydnm+3KVzZxqmp04x7y4lxWwZIoTwK45nHMfyA8vRJKIJHHYH\nCooKMOeqOWhUzyw+6tCkg4USirqKr8Vb/gdgCICNVgtSq1mzhuFKI6k/JIQdTQ3i43kzwipZWXU7\nGSomhv3cWremZ2zAAA6xFEJ4lz17WPl94IDHDrk0bikybZk4lXMKaXlpyCvKw97kvejSvMvft9Ag\nLbZEzeNrHrL9VgtQJ2jcmF3/jckARUW8zyAqivfl5dEjZrfTgKvLdOkCLF1qtRRC1B3efRd45x1z\nZNyTT3LubkUUFjLFokGDUttkXHvOtTivRfEhuO0atfOU1EJUGV8zyERlcTiAtWu5imzQgH3FTj+9\n/NeMGQOMHMnkfgBo2RK4+Wbz8bQ0s6+YMRzcZqub4UohRM0TH0+DrGlT5qbabMArr7CptdG+pzT2\n7gUef5zpBRERwIsvMr3AhQ5NOigkKXwSKwyy7wC0KOX+ZwGsdPcgsbGxf2/3798f/fv3r65c/smK\nFWw3ERrKleF337F3T4vSLrGTc85hQv+WLVR2ffsWV3ItWrAVxqlT3A8OZiGAhiyKGmL9+vVYv369\n1WJ4DemvCjh1iu1ljMru0FAuEg3PV2nYbBxJl5fHNIOsLHrVli8vHgEQogaoig7z1V/XdQCeQNlJ\n/SobN7j+enbENzrrHz/OJq933FH1Y/7yC3DllWbPLZuNA8I3q4u1sAa1vahjZGZStxUU0ABLTeXf\n5cvLLqY5doye/mbNzPtSUoC33qL+EsJC3NFhvpbU70ptUb7epaTXKiCg+vN6UlMZxgwL4/GaNqX3\nzVd+RAoKOAs0Lo7GohCidlG/PkclNWjA1IoWLbhfXmVzo0b0ouXmct9mYy6sMY1ECB/H13LIhgB4\nDUBTAKsA7ABwtaUS+Tp33snxRPn5NFSiooDqhD9sNmDfPnrHevY0e275iuGTnc2JA/v2cb99e868\nq+tFB0LUNjp1Ar78krrHnRYzkZFAbCzw/PMMV9rtwLhxXFxWFbtdzZ9FjeGvXii5/A0cDiqtb7+l\nUTJihDlbsrLk5QEPPQTs3g388QcVYdu2HLE0YQJwyy0eFb1KvPEGMH++OeIpMZHDI8ePt1Yu4VUU\nshRuEx8PHD1Kr1qbNlU7xrZtwHPPsRdj9+7AjBnFQ6FCVBJ3dJi/KjgpNG+wYgVnUp52Gl39+/cz\nbDlnDjBwoNXSkfHjgZ9/NpN009KYHzJvXtmvKSxk9VVREeeG1qtXM7IKjyGDTNQYCQnMRQsJYcTh\nxAnqjQ8+sFoy4cdodFJdIykJ2LqVlUkXX8w8jMqQlsa/AQGcZZmSwu0XX2RT1C5dPC5ypenShW0+\n7Hbu5+SUn7Cbk8M2H3v2cL91a/Y2atLE+7IKIfyPAweK92Zs3pwLupwcttIQwkvIIPMncnOB5GQa\nE0ZVpcHvvzNcaQwKb90aWLCgcrMlu3dnvkRiIt3+gOktmziRFU5WsGMHsGEDDcxBg6gwv/+ej116\nKTB8eNmvXbIE2LWL7yMggCOh5s0DJk+uEdGFEH5Gw4bUeUb+WF4e0zbCw62WTNRyZJD5C9u3A088\nQeUQHAxMmwb062c+PncuDTaj/9jRo8BHHwEPPOD+Obp3Z1LsM89QIZ12GnDmmTRkjFFKNd2HbN06\nc6h5URHwySfAhx+yv5DdTuO0PJn+/JMJwcZzIiKYHyeEEKXRrRtTNL75hnojIIC9HpXcL7yMDDJ/\nIDeXxhjAxNKcHODZZ4GVK023enJy8RVccDBDjpVl8GAaYXffzWMHBTGHonNna5rCvvEGjSijivL4\ncWD1avf7rHXrBqxaRWMuMJAexB49vCevEMK/CQxkLu0111CHdujAam4hvIxMfn8gOZltLYycMGOk\nkRFWBNjqIiODrS/y8pjI3qdP1c537rmsqkxPZ17aGWdYN0w7P7/4PLqAgMq14BgyBLjxRl7DpCRO\nJRg50vNyCiFqD4GBQK9eTJGQMSZqCH+tWqpbVUrZ2ZzhFhZGYywvj56eFSvMUuzCQuC114DPPqMB\nM2oUB/FWx6uVm8tzN25snbv+vfeY8xUdTUPMbmfIsrJKMjOTXrIGDTT+yQ9RlaUQwp9R24vaxIYN\nDFMaw74nTWJ4sbZjtwMLFwJff80S9NGjgfPOs1oqUcPIIBNC+DMyyGobqakMU8bEqEmhqFPIIBNC\n+DMyyKxg0yY2ECwqAoYOBS6/3GqJhPB7ZJAJIfwZGWQ1zdatwMMPm0O5c3OBl19mrywhRJWRQSaE\n8Gfc0WGqsvQkX3zBdhONGrG5YHg4k+yFEEIIIcpBBpknCQ9nqNKgqIjeMiGEEEKIcpBB5kluv51d\n4RMSOH4IYINVIYQQQohy8NecDN/NwfjtN858LCwErruOTVaFENVCOWRCCH9GSf1CiFqBDDIhhD+j\npH4hhBBCCD9ABpkQQgghhMXIIBNCCCGEsBgZZEIIIYQQFiODTAghhBDCYmSQCSGEEEJYjAwyIYQQ\nQgiLkUEmhBBCCGExMsiEEEIIISxGBpkQQgghhMXIIBNCCCGEsBgZZEIIIYQQFiODTAghhBDCYmSQ\nCSGEEEJYjAwyIYQQQgiLkUEmhBBCCGExMsiEEEIIISxGBpkQQgghhMXIIBNCCCGEsBgZZEIIIYQQ\nFiODTAghhBDCYnzNIHsZwD4AuwB8BqCBteJUj/Xr11stgltITs/jL7L6i5yi5vGnz4a/yCo5PYu/\nyOkuvmaQrQbQGUB3AAcBPGOtONXDXz4sktPz+Ius/iKnqHn86bPhL7JKTs/iL3K6i68ZZN8BsDu3\nNwNobaEsQgghhBA1gq8ZZK7cB+Arq4UQQgghhPA2ARac8zsALUq5/1kAK53bEwH0BHBTGcf4DcBZ\nnhdNCOGjHAbQ3mohPIT0lxB1D7/UYcMB/Agg3GI5hBBCCCHqJAMB7AHQ1GpBhBBCCCFqCitCluVx\nCEAogFTn/s8AHrZOHCGEEEIIIYQQQgghfJSpYPPYnQDWADjdWnHKxV+a3d4ChouLwIIKX2MggP2g\nF3WCxbKUx3sAkgD8z2pBKuB0AOvA/3kcgEetFadMwsEWODsB7AUww1pxPIa/6DDpL88g/eVZpL98\niPou248A+K9VgrjBFTDbi7zovPkiHQF0AD/kvqbQgsDKtLYAQsAP97lWClQOlwDoAd9XaC0AnOfc\njgJwAL57TSOcf4MB/ALg3xbK4in8RYdJf1Uf6S/PUyv1ly/3ISuPTJftKAAnrRLEDfyl2e1+cDqC\nL3IRqNCOACgAsBTA9VYKVA4/ADhltRBukAj+MABAFugFaWmdOOWS4/wbCv64pZbzXH/BX3SY9Ff1\nkf7yPLVSf/mrQQYA0wD8BeAe+O6qrSRqdls1WgE46rJ/zHmf8AxtwVXxZovlKItAUPkmgR6QvdaK\n4zH8TYdJf1UN6S/v0ha1RH/5skH2Heg2LXm71vn4RABnAFgAYLYF8rlSkawA5bUBWFzj0pm4I6cv\n4rBagFpMFIBPAIwFV5q+iB0MT7QG0BdAf0ulcR9/0WHSX95F+st71Cr9FVxDAlWFK9x83mJYv2qr\nSNbhAAYBGOB9UcrF3WvqaxxH8aTn08FVpqgeIQA+BbAQwBcWy+IO6QBWAbgAwHprRXELf9Fh0l/e\nRfrLO0h/+Qhnu2w/AuBDqwRxA39rdrsOwPlWC1GCYHDsRFswDu/LSbEA5fT1pNgAAB/Aeu9yRTQF\n0NC5XQ/ARlhvGHgCf9Fh0l/VR/rL80h/+RCfgB+YnaCF3NxaccrlEIA/Aexw3t6wVpwyGQLmOeSC\nCZNfWyvOP7garKT5DcAzFstSHksAxAPIB6/nvdaKUyb/Bl3pO2F+NgdaKlHpdAXwKyjnbgBPWiuO\nx/AXHSb95RmkvzyL9JcQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEII\nIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCFEnaA/gJXO7WsBTPDSec4H\n8GoZjx0B0LiMx74HUL+c4z4GoF7VxaqULO4wHMBc5/aDAO6qpjyAKVMYgI0AAj1wTCGElwm2WgAh\nhN+yEqZx5mm2O2+l4Sjj/ssAHACQWc5xxwL4EEBu1UVzS5ayCARgL+Oxt6spi4EhUz6AHwDcAOAz\nDx1bCOEltHISom7RFsB+AO+DxssiAFcC+BHAQQAXOp93EYCfAPzqfKxDKccaDtO7EwPgcwA7nbd/\nlfL8NwBsBRAHINbl/gud59gJYDOAKBT3xDUBsNr5uncBBJTx3u4AsNy5HQlglfOY/wNwK4BHALQE\nsA7AGufz3ixDpiPO/e0AdgM4xw1ZPgewzfnYSJf7swDMhHld7gWv/WYAfVyeFwvgCQCnAdjhcisE\ncDqAZgA+AbDFeTNeW55MKwAMhRBCCCF8irYACgB0Bn+4twGY73zsOtCoABj2C3JuXw4aAkBxQ2k4\nTINsGYBHnduBAKJLOXcj598g0CjqCiAUwGEwRAnQGAsqcZ7XAExybg8CPUylhQn3udx/E4B3XB4z\nwph/lHhtSZm6uDxvtHP7IdDQqUgW41j1QCPQ2LcDuNm5fRqAP0EjKgTAJucxAeB50CBzZTSApc7t\nxQAudm6fAWCvGzKFATgOIYTPo5ClEHWPPwDscW7vAfOuAHpY2jq3GwL4AEB7MAQWUsExLwUwzLlt\nB5BRynNuAz1HwaBh0sl5fwLM8GRWKa+7BMAQ5/ZXAE6VIUNLAKnO7d2gV+pFAF+Chk9plCZTnPMx\nI8z3K4Ab3ZBlLBgeBOjROhv0ZBUB+NR5fy/Q8Etx7i9D6d5HgMbX/TCNsMsBnOvyeH3QE1ieTPmg\ngRwOIK+M8wghfAAZZELUPfJdtu0AbC7bhk6YCob1hgBoA2C9G8ctK5QIAO1A788FANLBkGk43M/B\nKu/YpXEIQA8AgwG8AL6XqW7KZGBcpyIU15WlydIfwAAAvUHDZ53LsfJgvk9HideX9b5OA/BfsHAi\nx+W5vWD+v1wp7/oEoPK5bkKIGkY5ZEKI0ogGEO/cvteN568BQ3sAw38lQ5bRALJBz1kMgKtBI+EA\naHxc4Hyea6jUYCOYHwbn6xqhdOJhhupOAw2hRaCnrIfz/kwX2UqTqSLKkiUa9EzlAegIGmalsQVA\nP6ecIQBugWksGUZVMICPATwF4DeX166GGRYGgO4VyAQwZFmE4ka4EMIHkUEmRN2jpLfEUcr2SwBm\ngOG6oDKe43DZHguGLXeDeWmuoTUA2AUmqO8HjSQjhFgAhg3ngknv38L0nBnH/g+AvmAocQiYg1Ua\nm2AWJXQFk+Z3AJgMeskA5pV9AxqQZclUEndk+QY0pPaC1+3nEq83SACT9392nm9Piec5wGT98wFM\ngZnY3wI0xi5wyr0HbJNRnkwADVFXWYQQQgghvEp/sGpSmEyHmV8mhBBCCFEjVNQYti5hNIatbP6d\nEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQtQQ/w9tumyoeHsVsgAAAABJRU5E\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107ad14a8>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a id='Min-Max-scaling-Normalization'></a>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Min-Max scaling (Normalization)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "An alternative approach to standardization is the so-called Min-Max scaling (sometimes also referred to as \"normalization\").  \n",
      "In this approach, the data is scaled to a fixed range - usually 0 to 1.  \n",
      "The cost of having this bounded range - in contrast to standardization - is that we will end up with small standard deviations, for example in the case where outliers are present.\n",
      "\n",
      "The equation to calculate the \"normalized\" score is:\n",
      "\n",
      "\\begin{equation} X' = \\frac{X - X_{min}}{X_{max}-X_{min}} \\end{equation}"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "minmax_scale = preprocessing.MinMaxScaler(feature_range=(0, 1)).fit(X_train)\n",
      "X_train_minmax = minmax_scale.transform(X_train)\n",
      "X_test_minmax = minmax_scale.transform(X_test)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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_minmax, X_test_minmax), (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 left')\n",
      "\n",
      "ax[0].set_title('Training Dataset')\n",
      "ax[1].set_title('Test Dataset')\n",
      "f.text(0.5, 0.04, 'malic acid (normalized)', ha='center', va='center')\n",
      "f.text(0.08, 0.5, 'alcohol (normalized)', ha='center', va='center', rotation='vertical')\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HFpRh7trT0vZ5azMYDNI3wUHkuxSuxNYp3F3Lq7qk/GoF8n0KV9KSMqzNN3EKIYQQQrgb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       "text": [
        "<matplotlib.figure.Figure at 0x107acb198>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a id=\"PCA\"></a>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Linear Transformation: Principal Component Analysis (PCA)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The main purposes of a principal component analysis are the analysis of data to identify patterns and finding patterns to reduce the dimensions of the dataset with minimal loss of information.\n",
      "\n",
      "Here, our desired outcome of the principal component analysis is to project a feature space (our dataset consisting of n x d-dimensional samples) onto a smaller subspace that represents our data \"well\". 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\".\n",
      "\n",
      "If you are interested in the Principal Component Analysis in more detail, I have outlined the procedure in a separate article  \n",
      "[\"Implementing a Principal Component Analysis (PCA) in Python step by step](http://sebastianraschka.com/Articles/2014_pca_step_by_step.html)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here, we will use the [`sklearn.decomposition.PCA`](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) to transform our training data onto 2 dimensional subspace:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.decomposition import PCA\n",
      "sklearn_pca = PCA(n_components=2) # number of components to keep\n",
      "sklearn_transf = sklearn_pca.fit_transform(X_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",
      "    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 PCA')\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bfbr0CSiG008/nZ49e3Lbbbdx991343Q6+e677w5qbiwqKiIyMpKUlBTKy8t5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\nSIDt28Mb0/9v787D4yzLxY9/k7SBpFu6ktKCFBD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Pnw9//St0777muZlM9AOrrc0nh3Pm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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106fe0780>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "PCA for feature extraction"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As mentioned in the short introduction above (and in more detail in my separate [PCA article](http://sebastianraschka.com/Articles/2014_pca_step_by_step.html)), PCA is commonly used in the field of pattern classification for feature selection (or dimensionality reduction).  \n",
      "By default, the transformed data will be ordered by the components with the maximum variance (in descending order).  \n",
      "\n",
      "In the example above, I only kept the top 2 components (the 2 components with the maximum variance along the axes): The sample space of projected onto a 2-dimensional subspace, which was basically sufficient for plotting the data onto a 2D scatter plot.\n",
      "\n",
      "However, if we want to use PCA for feature selection, we probably don't want to reduce the dimensionality that drastically. By default, the `PCA` function (`PCA(n_components=None)`) keeps all the components in ranked order. So we could basically either set the number `n_components` to a smaller size then the input dataset, or we could extract the top **n** components later from the returned NumPy array.\n",
      "\n",
      "To get an idea about how well each components (relatively) \"explains\" the variance, we can use `explained_variance_ratio_` instant method, which also confirms that the components are ordered from most explanatory to least explanatory (the ratios sum up to 1.0)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sklearn_pca = PCA(n_components=None)\n",
      "sklearn_transf = sklearn_pca.fit_transform(X_train)\n",
      "sklearn_pca.explained_variance_ratio_"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "array([0.36, 0.21, 0.10, 0.08, 0.06, 0.05, 0.04, 0.03, 0.02, 0.02, 0.01,\n",
        "       0.01, 0.01])"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a id='MDA'></a>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Linear Transformation: Linear Discriminant Analysis (MDA)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The main purposes of a Linear Discriminant Analysis (LDA) 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 Linear 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": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Principal Component Analysis (PCA) Vs. Linear Discriminant Analysis (LDA)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Both Linear Discriminant Analysis and Principal Component Analysis 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 LDA, 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 LDA, 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 LDA we are additionally maximizing the spread between classes.**\n",
      "\n",
      "In typical pattern recognition problems, a PCA is often followed by an LDA."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![](../Images/lda_overview.png)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If you are interested, you can find more information about the LDA in my IPython notebook   \n",
      "[Stepping through a Linear Discriminant Analysis - using Python's NumPy and matplotlib](http://nbviewer.ipython.org/github/rasbt/pattern_classification/blob/master/dimensionality_reduction/projection/minear_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:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.lda import LDA\n",
      "sklearn_lda = LDA(n_components=2)\n",
      "transf_lda = 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=transf_lda[:,0][y_train == label],\n",
      "                y=transf_lda[:,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()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DAoph4MCBdO3albvvvpsHH3yQiIgIvvnmm8OaOQsKCoiKiiIlJYWysjIeffRR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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107d32e80>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "LDA for feature extraction"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we want to use LDA for projecting our data onto a smaller subspace (i.e., for dimensionality reduction), we can directly set the number of components to keep via `LDA(n_components=...)`; this is analogous to the [PCA function](#PCA-for-feature-extraction), which we have seen above.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Simple Supervised Classification"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Linear Discriminant Analysis as simple linear classifier"
     ]
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "# 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,:]))\n",
      "print('actual class label:', y_test[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1st sample from test dataset classified as: [3]\n",
        "actual class label: 3\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "from sklearn import metrics\n",
      "pred_train_lda = 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_lda)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Prediction accuracy for the training dataset\n",
        "100.00%\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "pred_test_lda = 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_lda)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Prediction accuracy for the test dataset\n",
        "98.15%\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "print('Confusion Matrix of the LDA-classifier')\n",
      "print(metrics.confusion_matrix(y_test, lda_clf.predict(X_test)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Confusion Matrix of the LDA-classifier\n",
        "[[14  0  0]\n",
        " [ 1 17  0]\n",
        " [ 0  0 22]]\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "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": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Classification Stochastic Gradient Descent (SGD)"
     ]
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "from sklearn.linear_model import SGDClassifier\n",
      "\n",
      "sgd_clf = SGDClassifier()\n",
      "sgd_clf.fit(X_train, y_train)\n",
      "\n",
      "pred_train_sgd = sgd_clf.predict(X_train)\n",
      "pred_test_sgd = 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_sgd)))\n",
      "\n",
      "print('Prediction accuracy for the test dataset')\n",
      "print('{:.2%}\\n'.format(metrics.accuracy_score(y_test, pred_test_sgd)))\n",
      "\n",
      "print('Confusion Matrix of the SGD-classifier')\n",
      "print(metrics.confusion_matrix(y_test, sgd_clf.predict(X_test)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Prediction accuracy for the training dataset\n",
        "99.19%\n",
        "\n",
        "Prediction accuracy for the test dataset\n",
        "100.00%\n",
        "\n",
        "Confusion Matrix of the SGD-classifier\n",
        "[[14  0  0]\n",
        " [ 0 18  0]\n",
        " [ 0  0 22]]\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Quite impressively, we achieved a 100% prediction accuracy on the test dataset without any additional efforts of tweaking any parameters and settings."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Decision Regions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sgd_clf2 = SGDClassifier()\n",
      "sgd_clf2.fit(X_train[:, :2], y_train)\n",
      "\n",
      "x_min = X_test[:, 0].min()  \n",
      "x_max = X_test[:, 0].max() \n",
      "y_min = X_test[:, 1].min() \n",
      "y_max = X_test[:, 1].max() \n",
      "\n",
      "step = 0.01\n",
      "X, Y = np.meshgrid(np.arange(x_min, x_max, step), np.arange(y_min, y_max, step))\n",
      "\n",
      "Z = sgd_clf2.predict(np.c_[X.ravel(), Y.ravel()])\n",
      "Z = Z.reshape(X.shape)\n",
      "\n",
      "# Plots decision regions\n",
      "plt.contourf(X, Y, Z)\n",
      "\n",
      "\n",
      "# Plots samples from training data set\n",
      "plt.scatter(X_train[:, 0], X_train[:, 1], c=y_train)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Saving the processed datasets"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Pickle"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The in-built [`pickle`](https://docs.python.org/3.4/library/pickle.html) module is a convenient tool in Python's standard library to save Python objects in byte format. This allows us, for example, to save our NumPy arrays and classifiers so that we can load them in a later or different Python session to continue working with our data, e.g., to train a classifier."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# export objects via pickle\n",
      "\n",
      "import pickle\n",
      "\n",
      "pickle_out = open('standardized_data.pkl', 'wb')\n",
      "pickle.dump([X_train, X_test, y_train, y_test], pickle_out)\n",
      "pickle_out.close()\n",
      "\n",
      "pickle_out = open('classifiers.pkl', 'wb')\n",
      "pickle.dump([lda_clf, sgd_clf], pickle_out)\n",
      "pickle_out.close()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# import objects via pickle\n",
      "\n",
      "my_object_file = open('standardized_data.pkl', 'rb')\n",
      "X_train, X_test, y_train, y_test = pickle.load(my_object_file)\n",
      "my_object_file.close()\n",
      "\n",
      "my_object_file = open('classifiers.pkl', 'rb')\n",
      "lda_clf, sgd_clf = pickle.load(my_object_file)\n",
      "my_object_file.close()\n",
      "\n",
      "print('Confusion Matrix of the SGD-classifier')\n",
      "print(metrics.confusion_matrix(y_test, sgd_clf.predict(X_test)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Confusion Matrix of the SGD-classifier\n",
        "[[14  0  0]\n",
        " [ 0 18  0]\n",
        " [ 0  0 22]]\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Comma-Separated-Values"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And it is also always a good idea to save your data in common text formats, such as the CSV format that we started with. But first, let us add back the class labels to the front column of the test and training data sets."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "training_data = np.hstack((y_train.reshape(y_train.shape[0], 1), X_train))\n",
      "test_data = np.hstack((y_test.reshape(y_test.shape[0], 1), X_test))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, we can save our test and training datasets as 2 separate CSV files using the [`numpy.savetxt`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.savetxt.html) function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.savetxt('./training_set.csv', training_data, delimiter=',')\n",
      "np.savetxt('./test_set.csv', test_data, delimiter=',')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    }
   ],
   "metadata": {}
  }
 ]
}