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       "execution_count": 27,
    
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       "metadata": {},
       "outputs": [
        {
         "data": {
    
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    schmittu committed
          "image/png": 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\n",
    
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          "text/plain": [
           "<Figure size 360x360 with 1 Axes>"
          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "xv = xor[\"x\"]\n",
        "yv = xor[\"y\"]\n",
        "\n",
    
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        "colors = [\"rb\"[i] for i in xor[\"label\"]]\n",
    
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        "plt.figure(figsize=(5, 5))\n",
        "plt.xlim([-2, 2])\n",
        "plt.ylim([-2, 2])\n",
        "plt.title(\"green points have label True\")\n",
        "plt.scatter(xv, yv, color=colors, marker=\".\");"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "Again, this example data set can not be separated by a line. But we see that points where the sign of x and y are the same appear to form one class, and point with different signs for x and y belong to the other class.\n",
        "\n",
    
        "How can we engineer a more descriptive feature which describes \"x and y have the same sign\" ? Here we can use the fact that the product of two numbers is postive if and only if both numbers have the same sign.\n",
    
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        "\n",
        "So lets plot a histogram over `x * y`:"
       ]
      },
      {
       "cell_type": "code",
    
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       "execution_count": 28,
    
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       "metadata": {},
       "outputs": [
        {
         "data": {
          "image/png": 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eXgU8Oqssq0mym6V/pr21qv5n1nlOM16qYkJJAtwCHK2qT8w6z2qSDF5Y/ZXkpcCVzNmf46p6f1VtrartLP0+/HIfZQ4W+kof7XYdHAbexNJR6HnyN8ArgP3d0sq/m3WglZK8LcljwOuBf0ly76wzwdKlKljahXYvSwfz7pi3S1Uk+TTwVeDiJI8luX7WmVa4HLgWuKL7/Xeom2XOky3Age7P8NdZ2ofe27LAeeeZopLUCGfoktQIC12SGmGhS1IjLHRJaoSFLkmNsNAlqREWuiQ1wkKXpEb8H34J5hL8mzEZAAAAAElFTkSuQmCC\n",
          "text/plain": [
           "<Figure size 432x288 with 1 Axes>"
          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "products = xor[\"x\"] * xor[\"y\"]\n",
        "\n",
        "features_class_true = products[xor[\"label\"]]\n",
        "features_class_false = products[~xor[\"label\"]]\n",
        "\n",
        "plt.hist(features_class_true,  bins=30, color=\"g\", alpha=.5, histtype=\"stepfilled\")\n",
        "plt.hist(features_class_false,  bins=30, color=\"r\", alpha=.5, histtype=\"stepfilled\");"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "In this case a simple classifier would just introduce a threshold of 0 to distinguish both classes."
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
    
        "### Other examples of feature engineering\n",
        "\n",
    
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        "\n",
    
        "Feature engineering requires understanding your data to extract meaningful and discriminative (?) information.\n",
    
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        "\n",
        "Proper feature engineering can boost the performance of a classifier significantly.\n",
        "\n",
        "Examples:\n",
        "\n",
    
        "- ~~nudity classifier~~: color histograms of full image and image patches\n",
    
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        "\n",
        "\n",
        "- spam classifier: choice of dictionary, extra feature which counts words only in capital cases or words with unusual characters (like \"pill$\")\n",
        "\n",
        "\n",
        "- to distinguish background noise from speach audio samples, the frequency distribution might help. Also std deviation  or a histogram of loudness / energy of a sample might help.\n",
        "\n",
        "\n",
    
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        "- to classify DNA sequences, n-gram histograms (n>=1) can be benefitial.\n",
    
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        "\n",
        "\n",
    
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        "- for geopolitical data a feature \"state\"  can be enhanced by \"political system\" and / or \"gross national product (GNP)\".\n",
    
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        "\n",
        "\n",
        "- for sales data add a feature \"is week day\".\n",
        "\n",
        "\n",
    
        "Most cases are beyond the 2- or 3D case and visual inspection can be difficult. Thus engineering features as we did in the 2D examples becomes tricky. But here are some general recommendations:\n",
    
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        "\n",
        "- use statistics (mean, std deviations, higher order features) as well as histograms if applicable.\n",
        "\n",
    
        "- polynomial features (e.g. extend `x, y` to `x, y, x * y, x ** 2, y ** 2`) (see examples section).\n",
    
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        "\n",
        "- image classification: dig into *computer vision* to learn about image descriptors.\n",
        "\n",
        "- audio classification: learn about FFT, wavelets, filter banks, power spectrum, ...\n",
        "\n",
        "- try to incorporate external data.\n",
        "\n",
        "*Comment*: \n",
        "\n",
    
        "We will see later that adding too many features can introduce other problems (-> *overfitting*) but there are also methods for feature selection in this case (see https://scikit-learn.org/stable/modules/feature_selection.html)"
    
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "## Examples below only discuss the two classes case !?\n",
        "\n",
        "\n",
        "The following examples in this script will only consider two class problems. \n",
        "Before we dig deeper into classification, we want to say a few words on how can we handle more than two classes. \n",
        "\n",
        "\n",
        "The general idea for `n > 2` classes is to build multiple 2-class classifiers and determine a winner:\n",
        "\n",
        "- the **one-vs-all** approach builds `n` classifiers for \"label n vs. the rest\". \n",
        "\n",
        "\n",
        "- the **one-vs-one** approach builds  classifiers for `label i vs label j` (in total `n x (n - 1) / 2` classifiers).\n",
        "\n",
        "For new incoming data then the `n` resp. `n x n` classifiers are applied and the overall winner class is the final result.\n",
        "\n",
        "For the digit classificaton example:\n",
        "\n",
        "- we could build 10 classifiers `is it 0 or one of the others`, `is it 1 one or one of the others`, etc.\n",
        "  \n",
        "  A new image then would hopefully yield `True` for exactly one of the classifier, in other situations the result is unclear.\n",
        "   \n",
        "   \n",
        "- we could build 45 classifiers `is it 0 or 1`, `is it 0 or 2`, etc.\n",
        "\n",
        "  For a new image we could choose the final outcome based on which of the classifiers \"wins\" most often.\n",
        "\n",
        "\n",
        "#### Note:\n",
        "In `scikit-learn` many classifiers support such multi-class problems out of the box and also offers functionalities to implement `one-vs-all` or `one-vs-one` for specific cases. See https://scikit-learn.org/stable/modules/multiclass.html"
       ]
      },
    
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      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
    
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        "## Exercise section 2"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "To prepare the next bigger exercise, we quickly introduce how to add so called polynomial features to our data:"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 54,
       "metadata": {},
       "outputs": [
        {
         "name": "stdout",
         "output_type": "stream",
         "text": [
          "          0         1         2         3         4\n",
          "0 -1.539782  0.950822  2.370928 -1.464059  0.904063\n",
          "1  0.436266 -1.768324  0.190328 -0.771460  3.126968\n",
          "2 -1.466436  1.391890  2.150435 -2.041118  1.937358\n",
          "3 -1.037642 -0.953587  1.076700  0.989482  0.909329\n",
          "4 -0.691444 -0.219826  0.478094  0.151997  0.048323\n",
          "5  1.436550 -0.046027  2.063676 -0.066121  0.002119\n",
          "6  0.664361 -1.234410  0.441375 -0.820094  1.523768\n",
          "7  0.164649 -1.848453  0.027109 -0.304346  3.416779\n",
          "8 -1.883945 -0.222088  3.549248  0.418402  0.049323\n",
          "9  0.934993 -1.081893  0.874212 -1.011563  1.170493\n"
         ]
        }
       ],
       "source": [
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "\n",
        "df = pd.read_csv(\"xor.csv\")\n",
        "features = df.iloc[:10, :-1]\n",
        "preproc = PolynomialFeatures(2, include_bias=False)\n",
        "data = preproc.fit_transform(features)\n",
        "print(pd.DataFrame(data))"
    
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       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
    
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        "In this case \n",
        "- columns 0 and 1 are $x$ and $y$ from the original data set.\n",
        "- column 2 is $x^2$\n",
        "- column 3 is $x y$\n",
        "- column 4 is $y^2$.\n",
    
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        "\n",
    
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        "A complete description can be found here: https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html"
    
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       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
    
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        "The following script now learns classifiers on different data sets and plots decision surfaces."
    
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       ]
      },
      {
       "cell_type": "code",
    
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       "execution_count": null,
    
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       "metadata": {},
       "outputs": [
        {
         "name": "stdout",
         "output_type": "stream",
         "text": [
    
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          "113 out of 200 predicted correctly\n"
    
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         ]
        },
        {
         "data": {
    
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          "image/png": 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          "text/plain": [
    
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           "<Figure size 432x432 with 1 Axes>"
    
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          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "from sklearn.linear_model import LogisticRegression\n",
        "from sklearn.svm import LinearSVC, SVC\n",
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "\n",
        "\n",
        "def train_and_plot_decision_surface(clf, preproc, features, labels, marker=\".\", N=400):\n",
        "    \n",
        "    features = np.array(features)\n",
        "    xmin, ymin = features.min(axis=0)\n",
        "    xmax, ymax = features.max(axis=0)\n",
        "    \n",
        "    x = np.linspace(xmin, xmax, N)\n",
        "    y = np.linspace(ymin, ymax, N) \n",
        "    points = np.array(np.meshgrid(x, y)).T.reshape(-1, 2)\n",
        "  \n",
        "    if preproc is not None:\n",
        "        points_for_clf = preproc.fit_transform(points)\n",
        "        features = preproc.fit_transform(features)\n",
        "    else:\n",
        "        points_for_clf = points\n",
        "    \n",
        "    clf.fit(features, labels)\n",
        "    predicted = clf.predict(features)\n",
        "    print(sum(predicted == labels), \"out of\", len(labels), \"predicted correctly\")\n",
        "    classes = np.array(clf.predict(points_for_clf), dtype=bool) \n",
    
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        "    plt.plot(points[classes][:, 0], points[classes][:, 1], \"b\" + marker, markersize=1, alpha=.05);\n",
    
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        "    plt.plot(points[~classes][:, 0], points[~classes][:, 1], \"r\" + marker, markersize=1, alpha=.05);\n",
        "\n",
        "\n",
        "df = pd.read_csv(\"2d_points.csv\")\n",
    
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        "# df = pd.read_csv(\"xor.csv\")\n",
    
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        "\n",
        "features = df.iloc[:, :-1]\n",
        "labels = df.iloc[:, -1]\n",
        "\n",
        "plt.figure(figsize=(6, 6));\n",
        "\n",
        "clf = LinearSVC()\n",
        "# clf = LogisticRegression()\n",
        "# clf = SVC(gamma=.1)\n",
        "# clf = DecisionTreeClassifier(max_depth=6)\n",
        "# clf = KNeighborsClassifier(10)\n",
        "\n",
    
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        "#preproc = PolynomialFeatures(2, include_bias=False)\n",
        "preproc = None\n",
    
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        "\n",
        "train_and_plot_decision_surface(clf, preproc, features, labels)\n",
        "\n",
    
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        "colors = [\"rb\"[i] for i in labels]\n",
    
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        "plt.scatter(features.iloc[:, 0], features.iloc[:, 1], color=colors, marker='.');"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "- modify the script to use the `xor.csv` data set.\n",
        "\n",
    
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        "- play with the other classifiers which are outcommented in the script.\n",
        "- play with their parameters.\n",
        "- activate the feature engineering step and experiment with classifiers and their parameters.\n",
        ""
    
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       ]
      },
      {
       "cell_type": "code",
       "execution_count": 369,
       "metadata": {},
       "outputs": [
        {
         "name": "stderr",
         "output_type": "stream",
         "text": [
          "/Users/uweschmitt/Projects/machinelearning-introduction-workshop/venv3.6/lib/python3.6/site-packages/ipykernel_launcher.py:9: UserWarning: get_ipython_dir has moved to the IPython.paths module since IPython 4.0.\n",
          "  if __name__ == '__main__':\n"
         ]
        },
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           "    \n",
           "    .rendered_html strong code\n",
           "    {\n",
           "        background: #f5f5f5;\n",
           "    }\n",
           "    \n",
           "    .CodeMirror pre {\n",
           "    font-family: 'Source Code Pro', monocco, Consolas, monocco, monospace;\n",
           "    }\n",
           "    \n",
           "    .cm-s-ipython span.cm-keyword {\n",
           "        font-weight: normal;\n",
           "     }\n",
           "     \n",
           "     strong {\n",
           "         background: #f5f5f5;\n",
           "         margin-top: 4pt;\n",
           "         margin-bottom: 4pt;\n",
           "         padding: 2pt;\n",
           "         border: 0.5px solid #a0a0a0;\n",
           "         font-weight: bold;\n",
           "         color: darkred;\n",
           "     }\n",
           "     \n",
           "    \n",
           "    div #notebook {\n",
           "        # font-size: 10pt; \n",
           "        line-height: 145%;\n",
           "        }\n",
           "        \n",
           "    li {\n",
           "        line-height: 145%;\n",
           "    }\n",
           "\n",
           "    div.output_area pre {\n",
           "        background: #fff9d8 !important;\n",
           "        padding: 5pt;\n",
           "       \n",
           "       -webkit-print-color-adjust: exact; \n",
           "        \n",
           "    }\n",
           " \n",
           "    \n",
           " \n",
           "    h1, h2, h3, h4 {\n",
           "        font-family: Kameron, arial;\n",
           "    }\n",
           "    \n",
           "    div#maintoolbar {display: none !important;}\n",
           "    </style>"
          ],
          "text/plain": [
           "<IPython.core.display.HTML object>"
          ]
         },
         "execution_count": 369,
         "metadata": {},
         "output_type": "execute_result"
        }
       ],
       "source": [
        "#REMOVEBEGIN\n",
        "# THE LINES BELOW ARE JUST FOR STYLING THE CONTENT ABOVE !\n",
        "\n",
        "from IPython import utils\n",
        "from IPython.core.display import HTML\n",
        "import os\n",
        "def css_styling():\n",
        "    \"\"\"Load default custom.css file from ipython profile\"\"\"\n",
        "    base = utils.path.get_ipython_dir()\n",
        "    styles = \"\"\"<style>\n",
        "    \n",
        "    @import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
        "    \n",
        "    @import url('http://fonts.googleapis.com/css?family=Kameron');\n",
        "    @import url('http://fonts.googleapis.com/css?family=Crimson+Text');\n",
        "    \n",
        "    @import url('http://fonts.googleapis.com/css?family=Lato');\n",
        "    @import url('http://fonts.googleapis.com/css?family=Source+Sans+Pro');\n",
        "    \n",
        "    @import url('http://fonts.googleapis.com/css?family=Lora'); \n",
        "\n",
        "    \n",
        "    body {\n",
        "        font-family: 'Lora', Consolas, sans-serif;\n",
        "       \n",
        "        -webkit-print-color-adjust: exact important !;\n",
        "        \n",
        "      \n",
        "       \n",
        "    }\n",
        "    .rendered_html code\n",
        "    {\n",
        "        color: black;\n",
        "        background: #eaf0ff;\n",
        "        background: #f5f5f5; \n",
        "        padding: 1pt;\n",
        "        font-family:  'Source Code Pro', Consolas, monocco, monospace;\n",
        "    }\n",
        "    \n",
        "    p {\n",
        "      line-height: 140%;\n",
        "    }\n",
        "    \n",
        "    strong code {\n",
        "        background: red;\n",
        "    }\n",
        "    \n",
        "    em  {\n",
        "        color: green;\n",
        "    }\n",
        "    \n",
        "    .rendered_html strong code\n",
        "    {\n",
        "        background: #f5f5f5;\n",
        "    }\n",
        "    \n",
        "    .CodeMirror pre {\n",
        "    font-family: 'Source Code Pro', monocco, Consolas, monocco, monospace;\n",
        "    }\n",
        "    \n",
        "    .cm-s-ipython span.cm-keyword {\n",
        "        font-weight: normal;\n",
        "     }\n",
        "     \n",
        "     strong {\n",
        "         background: #f5f5f5;\n",
        "         margin-top: 4pt;\n",
        "         margin-bottom: 4pt;\n",
        "         padding: 2pt;\n",
        "         border: 0.5px solid #a0a0a0;\n",
        "         font-weight: bold;\n",
        "         color: darkred;\n",
        "     }\n",
        "     \n",
        "    \n",
        "    div #notebook {\n",
        "        # font-size: 10pt; \n",
        "        line-height: 145%;\n",
        "        }\n",
        "        \n",
        "    li {\n",
        "        line-height: 145%;\n",
        "    }\n",
        "\n",
        "    div.output_area pre {\n",
        "        background: #fff9d8 !important;\n",
        "        padding: 5pt;\n",
        "       \n",
        "       -webkit-print-color-adjust: exact; \n",
        "        \n",
        "    }\n",
        " \n",
        "    \n",
        " \n",
        "    h1, h2, h3, h4 {\n",
        "        font-family: Kameron, arial;\n",
        "    }\n",
        "    \n",
        "    div#maintoolbar {display: none !important;}\n",
        "    </style>\"\"\"\n",
        "    return HTML(styles)\n",
        "css_styling()\n",
        "#REMOVEEND"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": null,
       "metadata": {},
       "outputs": [],
       "source": []
      }
     ],
     "metadata": {
      "kernelspec": {
       "display_name": "Python 3",
       "language": "python",
       "name": "python3"
      },
      "language_info": {
       "codemirror_mode": {
        "name": "ipython",
        "version": 3
       },
       "file_extension": ".py",
       "mimetype": "text/x-python",
       "name": "python",
       "nbconvert_exporter": "python",
       "pygments_lexer": "ipython3",
    
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      }
     },
     "nbformat": 4,
     "nbformat_minor": 2
    }