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    {
     "cells": [
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "# Chapter 2: Classification"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "As we learnd *classification* belongs to the field of *supervised learning* where we want to predict a category. Such categories can be \n",
        "\n",
        "- ok/not ok\n",
        "- good / bad / dont't know\n",
        "- digit 0 ... / digit 9\n",
        "- etc \n",
        "\n",
        "This chapter now introduces core concepts of classification."
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "## Examples below only discuss the two classes case !?\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",
        "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"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": []
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "## How could we  build  a simple classifier  ?"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "## Geometrical interpretation of feature vectors\n",
        "\n",
        "If you take the values of a input-feature vector you can imagine this as a point in a d-dimensional space.\n",
        "\n",
        "\n",
        "E.g. if a data set consists of  feature vectors of length 2, you can interpret the first feature value as a x-coordinate and the second value as a y-coordinate.\n",
        "\n",
        "Labeled features then group such points to different point clouds.\n",
        "\n"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "### Example\n",
        "\n",
        "For sake of simplicity we restrict our beer data set to two features: `alcohol_content` and `bitterness`.\n",
        "\n",
        "The following plot shows how these reduced feature vectors can be interpreted as point clouds. For every feature vector we color points in green or red to indicate the according classes:"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 156,
       "metadata": {},
       "outputs": [
        {
         "data": {
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\n",
          "text/plain": [
           "<Figure size 432x288 with 1 Axes>"
          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "# read some data\n",
        "beer_data = pd.read_csv(\"beers.csv\")\n",
        "\n",
        "xv = beer_data[\"alcohol_content\"]\n",
        "yv = beer_data[\"bitterness\"]\n",
        "\n",
        "colors = [\"rg\"[i] for i in beer_data[\"is_yummy\"]]\n",
        "\n",
        "plt.scatter(xv, yv, color=colors, marker='.');\n",
        "plt.xlabel(\"alcohol_content\")\n",
        "plt.ylabel(\"bitterness\");"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "is tells us that the two features lack information for a 100% separation of classes. \n",
        "2. We could draw a line to separate most points of both clouds.\n",
        "3. Later we could use this line to make a guess for classifying a new feature vector.\n",
        "\n",
        "Eventually **classification is about finding a procedure to separate two or more point clouds.**"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "Now we can see why more features can support classification. We add the `darkness` feature as third dimension.\n"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 319,
       "metadata": {},
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": [
           "<Figure size 1440x504 with 2 Axes>"
          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "\n",
        "fig = plt.figure(figsize=(20, 7))\n",
        "\n",
        "xv = beer_data[\"alcohol_content\"]\n",
        "yv = beer_data[\"darkness\"]\n",
        "zv = beer_data[\"bitterness\"]\n",
        "\n",
        "colors = [\"rg\"[i] for i in beer_data[\"is_yummy\"]]\n",
        "\n",
        "def plot(ax):\n",
        "    ax.scatter(xv, yv, zv, c=colors, marker='.') \n",
        "\n",
        "    ax.set_xlabel('alcohol_content')\n",
        "    ax.set_ylabel('darkness')\n",
        "    ax.set_zlabel('bitterness');\n",
        "\n",
        "ax = fig.add_subplot(121, projection='3d')\n",
        "\n",
        "plot(ax)\n",
        "ax.view_init(5, 275)\n",
        "\n",
        "ax = fig.add_subplot(122, projection='3d')\n",
        "plot(ax)\n",
        "ax.view_init(5, 5);"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "The first view is very similar to the scatter plot before as we don't see the effects of the third feature.\n",
        "\n",
        "The second view shows the same cube rotated by 90˚ to the left. We see that the new dimenission adds extra information which could improve separation."
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "If we look at the beer example, we can assume that the person who rated beers has preferences like, \"I don't like high alcohol content\", \"I like fruity beer\", etc."
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "This means we could construct a score where high numbers relate to \"favorable beer\". One simple way to implement such a score is to use a weighted sum like\n",
        "\n",
        "\n",
        "     score = -0.1 * alcohol_content + 4 * bitterness + 0.8 * darkness + 1.8 * fruitiness \n",
        "\n",
        "Positive weights contribute to a heigher score and negative weights to a lower.\n",
        "\n",
        "The actual weights here are guessed and serve as an example.\n",
        "\n",
        "The size of the numbers also reflects the numerical ranges of the features: alcohol content is in the range 3 to 5.9, where as bitterness is between 0 and 1.08:"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 359,
       "metadata": {},
       "outputs": [
        {
         "data": {
          "text/html": [
           "<div>\n",
           "<style scoped>\n",
           "    .dataframe tbody tr th:only-of-type {\n",
           "        vertical-align: middle;\n",
           "    }\n",
           "\n",
           "    .dataframe tbody tr th {\n",
           "        vertical-align: top;\n",
           "    }\n",
           "\n",
           "    .dataframe thead th {\n",
           "        text-align: right;\n",
           "    }\n",
           "</style>\n",
           "<table border=\"1\" class=\"dataframe\">\n",
           "  <thead>\n",
           "    <tr style=\"text-align: right;\">\n",
           "      <th></th>\n",
           "      <th>alcohol_content</th>\n",
           "      <th>bitterness</th>\n",
           "      <th>darkness</th>\n",
           "      <th>fruitiness</th>\n",
           "      <th>is_yummy</th>\n",
           "    </tr>\n",
           "  </thead>\n",
           "  <tbody>\n",
           "    <tr>\n",
           "      <th>count</th>\n",
           "      <td>225.000000</td>\n",
           "      <td>225.000000</td>\n",
           "      <td>225.000000</td>\n",
           "      <td>225.000000</td>\n",
           "      <td>225.000000</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>mean</th>\n",
           "      <td>4.711873</td>\n",
           "      <td>0.463945</td>\n",
           "      <td>2.574963</td>\n",
           "      <td>0.223111</td>\n",
           "      <td>0.528889</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>std</th>\n",
           "      <td>0.437040</td>\n",
           "      <td>0.227366</td>\n",
           "      <td>1.725916</td>\n",
           "      <td>0.117272</td>\n",
           "      <td>0.500278</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>min</th>\n",
           "      <td>3.073993</td>\n",
           "      <td>0.000000</td>\n",
           "      <td>0.000000</td>\n",
           "      <td>0.000000</td>\n",
           "      <td>0.000000</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>25%</th>\n",
           "      <td>4.429183</td>\n",
           "      <td>0.281291</td>\n",
           "      <td>1.197640</td>\n",
           "      <td>0.135783</td>\n",
           "      <td>0.000000</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>50%</th>\n",
           "      <td>4.740846</td>\n",
           "      <td>0.488249</td>\n",
           "      <td>2.026548</td>\n",
           "      <td>0.242396</td>\n",
           "      <td>1.000000</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>75%</th>\n",
           "      <td>5.005170</td>\n",
           "      <td>0.631056</td>\n",
           "      <td>4.043995</td>\n",
           "      <td>0.311874</td>\n",
           "      <td>1.000000</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>max</th>\n",
           "      <td>5.955272</td>\n",
           "      <td>1.080170</td>\n",
           "      <td>7.221285</td>\n",
           "      <td>0.535315</td>\n",
           "      <td>1.000000</td>\n",
           "    </tr>\n",
           "  </tbody>\n",
           "</table>\n",
           "</div>"
          ],
          "text/plain": [
           "       alcohol_content  bitterness    darkness  fruitiness    is_yummy\n",
           "count       225.000000  225.000000  225.000000  225.000000  225.000000\n",
           "mean          4.711873    0.463945    2.574963    0.223111    0.528889\n",
           "std           0.437040    0.227366    1.725916    0.117272    0.500278\n",
           "min           3.073993    0.000000    0.000000    0.000000    0.000000\n",
           "25%           4.429183    0.281291    1.197640    0.135783    0.000000\n",
           "50%           4.740846    0.488249    2.026548    0.242396    1.000000\n",
           "75%           5.005170    0.631056    4.043995    0.311874    1.000000\n",
           "max           5.955272    1.080170    7.221285    0.535315    1.000000"
          ]
         },
         "execution_count": 359,
         "metadata": {},
         "output_type": "execute_result"
        }
       ],
       "source": [
        "beer_data.describe()"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 362,
       "metadata": {},
       "outputs": [],
       "source": [
        "scores =( -0.1 * beer_data[\"alcohol_content\"] + 3 * beer_data[\"bitterness\"] \n",
        "          + 0.8 * beer_data[\"darkness\"] + 1.8 * beer_data[\"fruitiness\"])"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "Now we can plot the histogram of the scores by classes:"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 363,
       "metadata": {},
       "outputs": [
        {
         "data": {
          "image/png": 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=\n",
          "text/plain": [
           "<Figure size 432x288 with 1 Axes>"
          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "scores_good = scores[beer_data[\"is_yummy\"] == 1]\n",
        "scores_bad = scores[beer_data[\"is_yummy\"] == 0]\n",
        "\n",
        "plt.hist(scores_good,  bins=25, color=\"green\", alpha=.5) \n",
        "plt.hist(scores_bad, bins=25, color=\"red\", alpha=.5);"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "Consequence: A simple classifier could use these scores and use a threshold around 3.5 to assign a class label."
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "**This is how so called linear classifiers work. The magic is in computing the weights and the final threshold to guarantee good results.**\n",
        "\n",
        "*Comment*: although this seems to be a simple concept, linear classifiers can work very well, especially for higher resp. very high dimensions."
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "## Geometrical interpretation of feature vectors\n",
        "\n",
        "If you take the values of a input-feature vector you can imagine this as a point in a d-dimensional space.\n",
        "\n",
        "\n",
        "E.g. if a data set consists of  feature vectors of length 2, you can interpret the first feature value as a x-coordinate and the second value as a y-coordinate.\n",
        "\n",
        "Labeled features then group such points to different point clouds.\n",
        "\n"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "### Example\n",
        "\n",
        "For sake of simplicity we restrict our beer data set to two features: `alcohol_content` and `bitterness`.\n",
        "\n",
        "The following plot shows how these reduced feature vectors can be interpreted as point clouds. For every feature vector we color points in green or red to indicate the according classes:"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 364,
       "metadata": {},
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": [
           "<Figure size 432x288 with 1 Axes>"
          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "# read some data\n",
        "beer_data = pd.read_csv(\"beers.csv\")\n",
        "\n",
        "xv = beer_data[\"alcohol_content\"]\n",
        "yv = beer_data[\"bitterness\"]\n",
        "\n",
        "colors = [\"rg\"[i] for i in beer_data[\"is_yummy\"]]\n",
        "\n",
        "plt.scatter(xv, yv, color=colors, marker='.');\n",
        "plt.xlabel(\"alcohol_content\")\n",
        "plt.ylabel(\"bitterness\");"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "\n",
        "What do we see here ?\n",
        "\n",
        "1. Both point clouds overlap, this tells us that the two features lack information for a 100% separation of classes. \n",
        "2. We could draw a line to separate most points of both clouds.\n",
        "3. Later we could use this line to make a guess for classifying a new feature vector.\n",
        "\n",
        "Eventually **classification is about finding a procedure to separate point clouds in an n-dimesional space.**"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "Next we illustrate how more features can support classification. We add the `darkness` feature as third dimension.\n"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 322,
       "metadata": {},
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": [
           "<Figure size 1440x504 with 2 Axes>"
          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "\n",
        "fig = plt.figure(figsize=(20, 7))\n",
        "\n",
        "xv = beer_data[\"alcohol_content\"]\n",
        "yv = beer_data[\"darkness\"]\n",
        "zv = beer_data[\"bitterness\"]\n",
        "\n",
        "colors = [\"rg\"[i] for i in beer_data[\"is_yummy\"]]\n",
        "\n",
        "def plot(ax):\n",
        "    ax.scatter(xv, yv, zv, c=colors, marker='.') \n",
        "\n",
        "    ax.set_xlabel('alcohol_content')\n",
        "    ax.set_ylabel('darkness')\n",
        "    ax.set_zlabel('bitterness');\n",
        "\n",
        "ax = fig.add_subplot(121, projection='3d')\n",
        "\n",
        "plot(ax)\n",
        "ax.view_init(3, 273)\n",
        "\n",
        "ax = fig.add_subplot(122, projection='3d')\n",
        "plot(ax)\n",
        "ax.view_init(3, 3);"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "The first view is very similar to the scatter plot before as we don't see the effects of the third feature. \n",
        "\n",
        "The second view shows the same cube rotated by 90˚ to the left. We see that the new dimenission adds extra information which could improve separation. So tiling the plane which separates in the first view could improve separation.\n"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "## Decision surfaces\n",
        "\n",
        "For a weighted sum for two features `x` and `y` the equation\n",
        "\n",
        "\n",
        "     weight_x * x + weight_y * y = threshold\n",
        "     \n",
        "\n",
        "defines a line in 2d space. Points fulfilling\n",
        "\n",
        "     weight_x * x + weight_y * y < threshold\n",
        "      \n",
        "      \n",
        "vs\n",
        "\n",
        "     weight_x * x + weight_y * y > threshold\n",
        "      \n",
        "\n",
        "are located on different sides of this line. Such a classifier thus determines a line which separates the feature space into two parts according to the two classes."
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "Lets visualize this! \n",
        "\n",
        "We \n",
        "\n",
        "- create random points in 2D,\n",
        "- compute scores for given weights\n",
        "- split points according to their score compared to the threshold \n",
        "- plot them in different colors.\n",
        "\n",
        "Additionally we did some math and computed the decision line:"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 283,
       "metadata": {},
       "outputs": [
        {
         "data": {
          "image/png": 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qiC4VvHYdY90HqRbYM1EjfCPudg0TnRh+2tnrW+1hWXFTWyF2JnpK6YaXOq1Y90Eq7drUUKNvxN2uYaLdw0+7e307PCy3b2pTPSXBXOK5D5Jt16aGqHwj7nYNE+0efjrR67stxlZjqqckmI1d94GpISrfiDvYe/HsumCm9vom09I5k1CNYDcttTETHSjlVmXegoICvXHjRlf2bTeJioyIUuI0PWcSqhHsxpQ2ppTapLUuiLWdrzx3E0imAZjY65tO03MmoRrBbrzWxgJuG+A3mmsAQuKU7SljwboFlO0pi2v7xlBNUAUlvCXYgtfamHjuFiMx9NRJdvRj4qSW4B+81sZE3C3Gaw3ARJId/kp4S7AbL7UxEXcbsLoBpNuEq4x+BCF1RNwNx5QZeieR0Y8gpI6Iu+F4bYbeKrw0/E2WdBuRCc4i4m44EqLwJ+k4IhOcRcTdAFrz4EwJUYiXaS3pOiITnMMX4u5l4YnHg3M7RJEOXqbTbUhGZILdeF7cvS48yXpwToqR371MN9qQHSMyLzs5puCnc+h5cXdDeJqra5Jsg0h2rUcnxcjvXqZbnVciI7JYbczrTo4J+O0cel7cnRaepg1g4ZiFzHllTtINIhkPzo1FwK3yMk30jEzvvOIRHb+PrpzAb+fQ8+Lu9IRj0wawZvualBtEojF1N8TIqtWTTPSMTJm0bol4RMf0DspOrHIY/HYOPS/u4OyEY9MGcM0517Bu9zrHhdZkMWoJkz0jtyetWyMe0fFqm0gVKx0Gv51DX4i7kzTXAAacMsDxBmGyGLWE3zyjZEjGy4xXdLzYJlLFaofBT+dQFusQHMXEmLtTmBqWMp3W2kw6nlNLF+tQSo0BHgGCwGNa6wea2WYicC+ggQ+01j9KyOI0Jd3Ezk+eUaKYHJYylVji7bdQipXEFHelVBBYDFwCVAAblFIlWuvtUdv0AeYCF2mtv1RKnWKXwX4iHb2OdEbCUokTT4eYzg5Da8TjuRcCH2utPwVQSv0ZuBLYHrXNdGCx1vpLAK31AasN9SPiyaUX4mUmjnSIyROPuJ8B7Il6XQEMbrJNXwCl1DuEQzf3aq1fscRCHyMNN/2Ix8tMt1Bda0iHmDxWZcu0AfoAxUA34G2l1ACt9VfRGymlZgAzALp3727Rrr2LNFyhKRKq+y4SdkmOeBbI/hzIi3rdreF/0VQAJVrrWq31Z8BOwmJ/AlrrpVrrAq11QdeuXZO12VcU5RUxd+hcTzXeRBev9vp+ndx3awusu3n8gjV88803OJWhGI/nvgHoo5TKJyzqk4GmmTDPAdcCjyuluhAO03xqpaGCGbjlWdq9X7vT7eINtbQUqhOP3mxaur5aa0KhEMFgkOeff56JEyeydetW+vbta7tNMcVda12nlLoFeJVwPH2Z1nqbUmoesFFrXdLw3qVKqe1APXCb1rrSTsMFd3BrEtjO/cYSzlT3nYgwtxSqk8l3c2l6fV//8etc2P1CysvLGTlyJEuWLOHyyy/n/PPP52c/+xlZWVmO2BVXzF1r/RLwUpP/3RP1twZubfgRfIxbk8B27jeWcKa670SFubkYs0y+m0vk+tbU8+2T3/KvX/wrL/7uRfLz8ykuLiY3NxeAHj168PDDDztml5QfEBLCrUlgO/cbSzhT3bcVwiyT72YyY8YMvgl8Q2ZeJjWZNZALg3oPAiArK4v/+q//cs02KT8gCNiffijpjf7g97//Pe+//z5/+tOfAJg1axYdO3bkipuvcOz6Wlp+QBD8jt3pdpLO503+8pe/8OSTT7JixQoCgQCVlZXs3buXUChEIBBg8eLFkW1Nu77xpEJ6HqdTyCRlTRC8QdN7tby8nJtvvpnKynA+yBdffMGGDRvYv38/AL/+9a95+eWXCQTMl07fh2USTSFLdfgsKWvpgYRZvE/ZnjJ+sOQHVL9XTWa/TN687U0CewOMGjWKl156iaFDh0Y8dJOQsEwDiWQqWCHMfkhZE+FqHbs6cDnv9lNXV8eqVavo3r076/Q6aupq0Gs1NVnhe/WOi+6gsrKSzMxMAOOEPRF8L+6JZCpYIcxeT1mTkUds7OjA5bzbR1lZGd988w2jRo0iEAjw85//nMsvv5ybfn0TWR2zqL69mqycLIp7FhMIBCLC7nV8L+6JpJBJypo/Rh52Y0cHLufdOvbs2UN5eTmXXHIJALfffjvV1dURcV+/fj3du3cnGAx6+l6Nhe9j7omS7kPjdPIgU7nWVrcTE8/70k1LWbN9Ddeccw0zBs1w1ZbW+Pbbb9mwYQPDhg0D4Cc/+QmrV6/m0KFDtGnThh07dnDqqafSuXNnly21hnhj7iLuwndIhw7ORDE16bwv3bSUf/5//xx5/ejYR40ReK015eXl9O7dm8zMTB5++GFuv/12KioqOOOMM9i5cyd1dXX069cPpVTyOyorg9JSKC6GInPuA5lQFZImHXKyTQyDmHTe12xf853Xbor7kSNHCAQC5OTk8Morr3DZZZfxxhtvMGLECCZPnsyAAQPo0qULgDVFucrKYORIqKmBzExYu9YogY8H704FC0IKNMbNgyroyYlvuzn/9PNbfW03oVCIY8eOAbB7925yc3Mjj/JffPHFPProo/Tv3x+AvLw8xowZY21BrtLSsLDX14d/l5Za990OIZ67kJZ4feLbbjpndUah0GgUis5Z9sera2trycjIoL6+nvz8fK655hr+4z/+g7y8PObPn89FF10EQE5ODjNm2DyKKC4Oe+yNnntxsb37swERdyFtMSkMYhq57XIJBoKEQiGy2mTZMrLRWkdi4uPHj+fbb7/lxRdfJBgMcsstt0Q8c6UUc+fOtXz/rVJUFA7FGBhzjxcRd8E2TJogFOKnbE8Zc16ZQ0iHCAaCLByz0PLrt2DBAlatWsX7778PQHFxMbW1tZH3b7/9dkv3lxRFRZ4U9UZE3H2OWwJrYjZKOmDF9W6cbA7pEApF5fHU1915/vnnueuuu1i/fj3t27enZ8+eDB48mKqqKrKzs7nllltS3odwIiLuPsZNgTUxG8WvNAp6brtc5rwyJ6Hr3VxnYMVDWlu3buXWW2/lkUce4ZxzzqFz587k5eVx6NAh2rdvz7XXXsu1116bzOE6g6FpkIkg4u5DGm/Y3Ud2uyawJpZh8HKYqCXboztwpRQhHSKkQ3Fd75Y6/2Qmmw8fPsxtt93GpEmTuPTSS+ncuTN79+7l4MGDAAwfPpzhw4enfiKcwAdpkCDi7juib9hgIEibQBsI4bjAmpaN4uViX63ZHj1CCugAwUAQhYrrerc2uoo12ay15v7776dXr15cd9115GzbxtpnnqGwSxe49FLy8vLYtm2bZefgBOz2qptLgxRx9x9e8/aib1hCMH3gdLp36u6K/SZlo6QSJorHa7Yz7NWa7U1HSAvHLKTyeGVc1zvR0dXTTz9NZWUlM2fORCnFc889R2FhIdf16kXG6NF8Vl2N+t3v4Kqr7BNDJ7xqH6RBgoh7q3hxUrDpDTvln6ZQlFcUWZTAK52U1SQbJorXa7Yz7NWa7amMkGJ9duPGjZSVlTF79mwA1qxZw86dO5k5cyYQrraYmZkJCxZATQ0qFLLf03XCq/ZBGiSIuLeKFycFm7thvdhJWU2yIpiI12xX2CuW7amMkKI/+/nnn/PCCy8wffp0gsEgL7zwAg899BA33ngjHTp04NFHH6Vjx46Rz0ZK4zrp6Tq1L4+nQYKIe6uYOCkYD01vdi92UnaQjAgm6zVbHc6zI8R1/Phx1q5dy4UXXkhubi5vvfUWP/3pTyksLGTgwIH8y7/8C7fddhsdOnQAoFOnTi0Y56Cn6xOv2gmkKmQMvBZzbw7x3FMj0TZg6vnWWvPBBx9w8skn0717dzZt2kRBQQHLly/nxz/+MUePHmX//v2ceeaZbpsqtIJUhbQIkyYFk8W0zBWvkWgbMGmkdOjQIb7++mt69erFkSNHKCgoYO7cucyfP58LLriAN954gwsvvBAI12zJyclxxU7BekTc0wQ/dFJewc1wXl1dHfv27SMvLw+tNQMHDmTIkCGsWrWKzp0789xzzzFo0CAgvD7oiBEjHLNNcBYRd0GwGKdHSl9++SUnnXQSAFdffTW7d+/mgw8+QCnF73//e84444zItmPHjrXVlhPwwVOeXkbEXRBswM6RUvVbb5H1179CcTH3vvoqv/3tb6msrCQzM5NZs2Zx9OjRSMXFK664whYbYuKTpzy9jIi7IBhOY9KDUopnFizg+v/7f/koEKBHVhaXLlxIh1//mpqaGjIzMxkzZozL1jbgk6c8vYysxCQIBrNt2zby8/N57bXXABhw6BA/UQoaHhi6sLKSX/7yl5F0RWNozEcPBj39lKeXEXEXBIM4duwYw4cPZ8mSJQDk5+czaNCgiHj3GT+eRdnZ9DBdNBvz0efPl5CMS8QVllFKjQEeAYLAY1rrB1rY7hpgNfB9rbX5SeyCYAAzZ87k1FNP5b777qNDhw6cfPLJtG/fHoB27dqxZk3UYtWmPcTT2qSpW095ykQuEIe4K6WCwGLgEqAC2KCUKtFab2+yXQ7wL8C7dhgqCH5h8eLFlJeX87vf/Q6AqqoqqqqqIu8/++yzrX+BKY/GmzhpaqJNLhFPWKYQ+Fhr/anWugb4M3BlM9vNBx4Eqpp5T/A5jYXJyvaUuW2Kcbz22mv85Cc/iUyM7t69m/Ly8sjrJ554ggcffNA5g8rKwsW+ylK8Vs1NmrqNiTa5RDxhmTOAPVGvK4DB0RsopQYCeVrrF5VSt1lon+ABTH3c3i3Ky8tZsmQJ8+bNo2PHjnz66ae89tprHDx4kFNOOYUHHnggsjB0SiQTfojl2SbynfEW8XIyTOKTcr1WkHIqpFIqAPw7MDWObWcAMwC6d++e6q5Twg81Y0zBpMft3eDw4cM88cQTjB07lr59+/LFF1/w6KOPMmHCBC666CJuuukmZsyYERF0y4Q9mfBDtGdbVQXLl//jc4l+Zzzxf6fDJKbNSbhIPOL+OZAX9bpbw/8ayQHOBUobGu1pQIlS6oqmk6pa66XAUggXDkvB7pRI1tOMXqsy3gUR0gGvVs9MltraWkpKSsjLy6OwsJDq6mp+8Ytf0K5dO/r27cvFF1/M4cOHadu2LQBt2tjwOEmyeeTFxeH0xPp60BoefxymTAl/NpnvjBX/dyPf3ZQ5CZeJp9VtAPoopfIJi/pk4EeNb2qtjwBdGl8rpUqBX5qcLZOMp9nYIVTXVRMiREAFyApmpX0IAtKjMNmGDRv49ttvGTZsGEoppk+fzsSJEyksLOT0009n7969nH766UBYzG0R9GiSDT8UFcG0afDoo2Fxr6v7h+DaEdKQMIlrxGyBWus6pdQtwKuEUyGXaa23KaXmARu11iV2G2k1yXiajR1CiBBA3IsQpwt+K0y2b98+/v73vzNs2DAAZs2aRUZGBu+88w5t2rShrKyM3r17R7ZvFHbHSCX8MGUKPPnkdwXXjpCGSWGSNEuRTNt67snW6PaC5y7zCYlTU1PD5s2bKSwsBODHP/4xr7zyCvv37ycQCLB161ZOO+00unbt6rKlFpFmQuenFMl467mnrbgngxdi7pK5Ej+ffPIJPXr0oE2bNvzmN7/hrrvuYv/+/XTt2pUPP/yQ2tpazj//fGsmQAV3WbAA7r47HPsPBsNPzs6dm/j3GNApymIdNuCF0EO6Z660xjfffINSinbt2vHCCy9wxRVX8M4773DhhRcyefJk+vfvH1ms4txzz3XZWsESGsU4Nzf12L/HvH8Rd5+RbpkrraG1pqqqirZt2/Lpp5/Sr18/lixZwo033sjFF1/MokWL6NWrFwC9evWK/C34hKZivHAhVFYm73V7rNKliLvPSIfMldYIhUIEAgHq6uro06cPkyZN4oEHHiA/P5877riDgQMHAnDSSScxe/Zsl60VbKWpGFdWJheKacRjmT8i7j7EC+EjO5g4cSKhUIjVq1fTpk0bbrjhhoiYK6WYN2+eyxYKjmK1GJuU+RMHIu6CZ1mwYAEvvvgi//M//wMQyXRp5N5773XBKsEY7ErtNFzUGxFxNwxJY2yZ559/nvvvv59169aRnZ3NqaeeSt++famtrSUjI4Nf/vKXbpsomIaHxNhqZLFWHiD4AAASHElEQVQOg2hMY7z7zbsZuXxk2ldY3LJlCz/84Q/55JNPAMjOzqZTp04cOHAAgGnTprFs2TIyMjLcNFMQTiS66qZVFTiTQDx3g0j3NMZDhw5xzz33MGnSJIYPH067du3YuXMnn3/+Ob1792b06NGMHj3abTOdwYB8aiEJojN02rQJl3ior3cldTJtPXcT6483pjEGVZA2gTbsPrLbCPvsOlehUIgHHniA1atXA9ChQwfWrFlDeXk5AGeeeeYJJQDShkaBuPvu8G8XvD4hSZpm6NTWulZbPi09d1Of4mxMY1z+wXKWbV7GH//2R5784ElX7bP6XD3zzDN8/fXXTJ06lUAgwIoVKxg2bBjjx48nOzubvXv3EgwGLTwCD+KxfGrPYsfoKDpDp6nn7nDqZFqKuxPhj2QnRovyiijdVUp9qN6I8Eyq5+pvf/sbmzZtYvr06QCsWLGC3bt3M3XqVAA2btwYKY0LiLCD5/KpPYldT5s2zdAB18JraSnudj/Fmaq3G21fdHjGDYFP9Fzt27ePV199lRtuuAGlFKtWreKRRx7h+uuvp23btjz22GN07tw5sn20sAsNeCyf2pPYOTpqmqHjVg2adC0cZmfK4YJ1C7j7zbup1/UEVZD5I+Yzd2hiT8aV7SmLhGfqQ/UphURSPdbWPv/tt9/y9ttvM2TIEDp16sTjjz/OtGnT2LJlCwMGDODAgQNkZmaeIOiC4DoeqxMTjRQOi4GdT3EmOzJoKqJWhGesiJlHnyutNeXl5XTq1Invfe97vP/++4wZM4ZVq1YxYcIErr76agYPHky/fv0AOOWUUxLalyA4QhqMjtJW3O0kmfouzYmwFeEjK+YXjhw5wtGjR+nWrRuHDh2if//+zJs3j7vuuovCwkJefvnlSEZL586dk/fSJf1PcBKfP+Ak4m4TiY4MmhPhuUPnplwELJkOIhQKceDAAU477TS01vTr149Ro0axfPlyunbtysqVKxkyZAgQXlJuzJgxCdv1HTw8TBYEExFxN4SWRDjV8FG8o4hjx47RoUMHAC6//HIOHTrEu+++i1KKhQsX0qNHj8i2EyZMSNqeFvFS+p+MMAQPIOJuCHaW6m2ug6irq4ss4nzPPffwn//5n+zfv59gMMj06dM5fvx4ZNuJEydaZkuLeCX9r6URhgi+YBgi7i3QUoaInVk2dpfq1VqjlGLNmjVMmzaN8vJyTj/9dEaMGEHbtm2prq6mXbt2XHXVVbbZ0CJWT3DZJbbNjTBAQkqCcYi4N0NLGSamPtkai61btzJ+/Hj++Mc/MmzYMM4++2yuvfZaamtrARgxYgQjRoxw2Uqsm+CyM37f3AjDrpCSjAaEFEjb2jKt0dzkZmv/N40jR45wySWX8MQTTwDQo0cPzjzzzEgYpn///ixZsoTu3bu7aKWNtORdW0HjCGP+/H90Go2CHwxaF1JKtb6Mi9UIBTMQz70ZWprctCI10a6wzqxZs8jLy+POO++kY8eOAAQC4b67Y8eOvPjii5bty3jsjt839wSi1TnTqYwGJPNIQMS9WVqa3Ex10tPKsM6SJUv47LPPePDBBwE4cOAA7du3B8JLyr322mtJfa8vcOMBFatzplPpoLyUeSTYhoh7C7Q0uZnKpGcqDxS9/vrrlJSUsGjRIgC2b9/Otm3bIpOkTz/9dFI2+RavP6CSSgfllcwjwVYk5u4g0fXaY4V1duzYwR133BFJSdy+fTtPP/00hw8fBuCRRx5h7dq1KKWcMP0fmBbLNc0eKykqgrlzE++kmpsXENKOtC0c5hYtxdwPHz7MU089xQ9/+EPy8/N59dVXufzyyyNFuWpqasjIyHBezE8w3rBYrmn2CIIDxFs4TDx3hynKK2Lu0LkUnFZASUkJmzdvBuDrr79m9uzZvP766wD84Ac/4PDhw5HH/DMzM90VdrA3C8UP9giCQYi4O8gHH3zAu+++C4QfKLruuut47LHHAOjZsyefffZZZFGLjIyMSDkAY7Aj5c8KewKB8E9urrv2CIJBSFjGRiorK/nkk08oLCwE4LzzzqNLly688cYbAGzZsoWzzjqLrKwsN81MDNMerFm6FGbNglAIsrLcCc2YcE5MsEFwBKnn7gJ1dXVs376d8847D4CZM2fy17/+lYqKCpRSLFu2jO9973uR7Ru3s4SWbm6rb3rTslAqK8PrVIZC7qT9mRD3N8EGwTjiCssopcYopXYopT5WSt3ZzPu3KqW2K6W2KKXWKqV6NPc9fqSiooJQKATA/fffz8CBA/nqq68AmDt3Ls8880xk24KCghPE3TJaepox1accvYDboSIT4v4m2OAHmmZeeTwTK6bnrpQKAouBS4AKYINSqkRrvT1qs/eBAq31caXUT4GHgEl2GOw2VVVVAGRnZ/Pss88ybtw4Nm7cyKBBg5g8eTL9+/ePhFkGDhzojFEtPbSSDg+zuL2ijgk55SbY4HWajn4WLoQ5czw9GoonLFMIfKy1/hRAKfVn4EogIu5a6zejtl8PXG+lkW6itaa2tpbMzEx27tzJ+eefz2OPPcaPfvQjLrroIv7t3/4t4o2fffbZnH322c4b2dLNnS43vZuhIrc7F1Ns8DpNHaE1azzvGMUj7mcAe6JeVwCDW9n+JuDlVIxym8anPqurq+nfvz/XX3899957L71792bWrFmcc845QHh90F/84hcuW0vLN7fc9M5gwjyECTZ4maaO0DXXwLp1nnaMLJ1QVUpdDxQAw1t4fwYwA7C1ImEqxbkmTZpEVlYWy5cvJysri3HjxnH++ecDEAwGefjhh+0wOXVaurnlpheE2DTnCA0Y4GnHKB5x/xzIi3rdreF/J6CUGgX8Chiuta5u7ou01kuBpRBOhUzY2jhItDjXggULeOutt3jllVcAToiZAzz00EN2mCkIgmk0V+3Tg6LeSDzZMhuAPkqpfKVUJjAZKIneQCl1AfAocIXW+oD1ZsZPrJrrzz//PMOHD48sVNGpUye6du1KXV0dEF5y7o477nDabOdJNBPA45kDgpBuxBR3rXUdcAvwKvARsEprvU0pNU8pdUXDZg8DHYCnlVKblVIlLXyd7TQtztXt226MGzeOPXv+MW0QCoXYv38/ADfffDMrVqyILGSRFiSaIpkOKZWC4DPiUjSt9UvAS03+d0/U36Mstitpzsw+k8s/vZyTC05mytgpdPy6I3dtuotdu3aRl5fHlVdeyZVXXum2me6SaIpkOqRUWo08MSq4jOfd1bq6OhYtWkTfvn0ZO3Ysbdu25dU1r/LQ4IcoyitCa82uXbvcL7plEommSKZLSqVVyBOjggF4UtxLSko4fvw4kydPJhgMsnjxYkaPHs3YsWPp0KEDBw8eJCMjA0BEvTkSTZGUlMrEkJGO0BQXRnKeLBx22WWXceDAARo///XXX0fWDRUE1xHPXYjG4vbg68Jhy5YtIzeqvKtnhF3isM3jt/MiIx0hGpdGcp4U99NOO81tExJHvLnm8et58XiOtGAhLs1ZeVLcPYkbvXe0R9xog2meZCrnxasev1ftFpLDpZGciLtTON17R3vEwSAoBXV15nnHyZ4Xr3r8XrXbbbzeIbowkhNxdwqne+9oj7ih3jxam5e9kex5cSsjJVWRkUya5mntvEqHmBQi7k7iZO8d7RE39dxNy1NP5ry4Ece0QmT8/MxAsh1frPPqhQ7RwJGFiLtfaeoRg3GNLyXciGNaITJ+zaRJpeOLdV5N6RBbW8rSwJGFiLufaa7KnZ9wOo5plcj4MZMmlY4v1nk1oUNsTcANHVmIuDdi4LBKMAwTRMZUUun44jmvbneIrQm4KSOLJnjyCdW4iVewTRpWSScjWImT7cnPbTeWRjh47L5+QjUuWrsYTS+EKcMqkzoZu/CzAJiG0+3Jbe/aTmKNLgw8dv+Ke0uC3VyDN2VYZUonYxfp0HmZhJ/akwlOgYEC3hr+FfeWBLu5Bj93rrOx1JYaqgmdjJ03kUliY4JY2I0J7ckKxClICv+Ke0vDqJYavFO9cmsN1e0JO7tvIlPEximxcLsDcbs9WYVJToGH8K+4Q/OCbXeDj3VDx2qobg797L6JTBEbJ8TCFG/TY6GEZjHFKfAY/hb3lrCrwcdzQ5vcUJ2wzQSxceI4xdu0DlOcAo+RnuJuF/Hc0CY3VJNtsxInjtPkTtyLmOAUeAx/57k7jSlDccEM3I65C75E8tzdIF08XyE+xNsUXETE3Wrkhm4d8WYFwRFE3AXnkLCVIDhGwG0DhDSiuQlnQRBsQcRdcI7GDJJgUDJIBMFmJCzjBfwSp5YJZ/9cS8F4RNxNx29x6nSecPbbtfQTPux0JSxjOhKnTp6yMliwIPzbBORamkljp3v33eHfprSXFBHP3XTkScfkMNFLlmtpJqWlUF0NoVD4t09KRYi4m47EqZPDxNouci3NJDc3LOwQ/p2b6649FhGXuCulxgCPAEHgMa31A03ezwKWA4OASmCS1nqXtaamMekcp04WU71kuZbmUVkJgUBY2AOB8GsfEFPclVJBYDFwCVABbFBKlWitt0dtdhPwpdb6TKXUZOBBYJIdBgtCXIiXLMRLcTFkZZnnCKRIPJ57IfCx1vpTAKXUn4ErgWhxvxK4t+Hv1cDvlVJKu1WVTBBAvGQhPnzqCMQj7mcAe6JeVwCDW9pGa12nlDoC5AKHrDBSEATBVnzoCDiaCqmUmqGU2qiU2njw4EEndy0IgpBWxCPunwN5Ua+7Nfyv2W2UUm2AToQnVk9Aa71Ua12gtS7o2rVrchYLgiAIMYlH3DcAfZRS+UqpTGAyUNJkmxLghoa/xwNvSLxdEATBPWLG3Bti6LcArxJOhVymtd6mlJoHbNRalwB/AlYopT4GDhPuAARBEASXiCvPXWv9EvBSk//dE/V3FTDBWtMEQRCEZJHaMoIgCD5ExF0QBMGHKLfmPZVSB4H/teCrupBe+fRyvP4lnY4V5HiTpYfWOma6oWvibhVKqY1a6wK37XAKOV7/kk7HCnK8diNhGUEQBB8i4i4IguBD/CDuS902wGHkeP1LOh0ryPHaiudj7oIgCMJ38YPnLgiCIDTBM+KulBqjlNqhlPpYKXVnM+9nKaVWNrz/rlKqp/NWWkccx3urUmq7UmqLUmqtUqqHG3ZaQaxjjdruGqWUVkp5OsMinuNVSk1suL7blFJPOW2jlcTRlrsrpd5USr3f0J4vc8NOK1BKLVNKHVBKfdjC+0optajhXGxRSg20zRittfE/hGvafAL0AjKBD4BzmmxzM7Ck4e/JwEq37bb5eEcA7Rr+/qlXjzeeY23YLgd4G1gPFLhtt83Xtg/wPnBSw+tT3Lbb5uNdCvy04e9zgF1u253C8Q4DBgIftvD+ZcDLgAKGAO/aZYtXPPfIalBa6xqgcTWoaK4Enmz4ezUwUimlHLTRSmIer9b6Ta318YaX6wmXYvYi8VxbgPmEl2+sctI4G4jneKcDi7XWXwJorQ84bKOVxHO8GujY8HcnYK+D9lmK1vptwsUTW+JKYLkOsx7orJQ63Q5bvCLuza0GdUZL22it64DG1aC8SDzHG81NhL0BLxLzWBuGrnla6xedNMwm4rm2fYG+Sql3lFLrGxao9yrxHO+9wPVKqQrCBQpnO2OaKyR6bydNXFUhBXNRSl0PFADD3bbFDpRSAeDfgakum+IkbQiHZooJj8jeVkoN0Fp/5apV9nEt8ITW+rdKqSLC5cPP1VqH3DbMy3jFc7dsNSiPEM/xopQaBfwKuEJrXe2QbVYT61hzgHOBUqXULsJxyhIPT6rGc20rgBKtda3W+jNgJ2Gx9yLxHO9NwCoArXUZkE24DosfievetgKviHu6rQYV83iVUhcAjxIWdi/HZFs9Vq31Ea11F611T611T8LzC1dorTe6Y27KxNOWnyPstaOU6kI4TPOpk0ZaSDzHuxsYCaCU6kdY3P26yHIJMKUha2YIcERrvc+WPbk9u5zALPRlhD2YT4BfNfxvHuEbHcIN4mngY+A9oJfbNtt8vK8D+4HNDT8lbtts17E22bYUD2fLxHltFeFQ1HZgKzDZbZttPt5zgHcIZ9JsBi512+YUjvW/gX1ALeER2E3ATGBm1LVd3HAuttrZluUJVUEQBB/ilbCMIAiCkAAi7oIgCD5ExF0QBMGHiLgLgiD4EBF3QRAEHyLiLgiC4ENE3AVBEHyIiLsgCIIP+f96QUe4oAZLJAAAAABJRU5ErkJggg==\n",
          "text/plain": [
           "<Figure size 432x288 with 1 Axes>"
          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "import numpy as np\n",
        "\n",
        "wx = -.5\n",
        "wy = 1.2\n",
        "threshold = 0.2\n",
        "\n",
        "weights = np.array((wx, wy))\n",
        "points_2d = np.random.random((200, 2))\n",
        "scores = points_2d @ weights   # matrix - vector product\n",
        "\n",
        "above_points = points_2d[scores > threshold]\n",
        "below_points = points_2d[scores < threshold]\n",
        "\n",
        "plt.scatter(above_points[:, 0], above_points[:, 1], c=\"g\", marker=\".\", label=\"above\")\n",
        "plt.scatter(below_points[:, 0], below_points[:, 1], c=\"r\", marker=\".\", label=\"below\")\n",
        "\n",
        "# plot decision line\n",
        "x = np.linspace(-.01, 1.01, 2)\n",
        "y = threshold / weights[1] - weights[0] / weights[1] * x\n",
        "plt.plot(x, y, 'k:')\n",
        "plt.legend();"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "**Higher dimensions**: For 3D features a linear classifiers separates classes by a plane, and for higher dimensions `n` we get `n-1` dimensional planes."
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "### Example\n",
        "\n",
        "In the beer example, features fulfilling\n",
        "\n",
        "    -0.1 * alcohol_content + 4 * bitterness + 0.8 * darkness + 1.9 * fruitiness == threshold\n",
        "    \n",
        "are located on a 3D-plane in 4D. \n",
        "\n",
        "Points in the \"not yummy\" class fulfilling\n",
        "\n",
        "    -0.1 * alcohol_content + 4 * bitterness + 0.8 * darkness + 1.9 * fruitiness < threshold\n",
        "    \n",
        "and points in the \"yummy class\"\n",
        "\n",
        "    -0.1 * alcohol_content + 4 * bitterness + 0.8 * darkness + 1.9 * fruitiness > threshold\n",
        "    \n",
        "are located on different sides of this plane.\n",
        "\n",
        "Again: **Here the classifier separates the 4d space into two parts, the separation boundary is a plane in this space.**"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "To illustrate this, we use ignore `fruitiness` such that we have 3 features:\n"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 319,
       "metadata": {},
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": [
           "<Figure size 1440x504 with 2 Axes>"
          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "\n",
        "fig = plt.figure(figsize=(20, 7))\n",
        "\n",
        "xv = beer_data[\"alcohol_content\"]\n",
        "yv = beer_data[\"darkness\"]\n",
        "zv = beer_data[\"bitterness\"]\n",
        "\n",
        "colors = [\"rg\"[i] for i in beer_data[\"is_yummy\"]]\n",
        "\n",
        "def plot(ax):\n",
        "    ax.scatter(xv, yv, zv, c=colors, marker='.') \n",
        "\n",
        "    ax.set_xlabel('alcohol_content')\n",
        "    ax.set_ylabel('darkness')\n",
        "    ax.set_zlabel('bitterness');\n",
        "\n",
        "ax = fig.add_subplot(121, projection='3d')\n",
        "\n",
        "plot(ax)\n",
        "ax.view_init(5, 275)\n",
        "\n",
        "ax = fig.add_subplot(122, projection='3d')\n",
        "plot(ax)\n",
        "ax.view_init(5, 5);"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "The first view is very similar to the scatter plot we have already seen before as we barely can see the effects of the third feature.\n",
        "\n",
        "The second view shows the same cube rotated by 90˚ to the left. We see that the new dimenission adds extra information which could improve separation."
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "### About 2D examples\n",
        "\n",
        "For the sake of simplicity and visualisation we continue with 2 dimensional examples.\n",
        "\n",
        "It is clear that such examples only represent very small subset of realistic ML scenarios. But most concepts can be illustrated in 2- or 3D without loss or generality.\n",
        "\n",
        "The examples also might look artificial, but general classifiers should work on all kind of problems."
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "## More complex decision surfaces"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "The next example data set can not bew classified by a line, the decision line is curved:\n"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 165,
       "metadata": {},
       "outputs": [
        {
         "data": {
          "text/html": [
           "<div>\n",
           "<style scoped>\n",
           "    .dataframe tbody tr th:only-of-type {\n",
           "        vertical-align: middle;\n",
           "    }\n",
           "\n",
           "    .dataframe tbody tr th {\n",
           "        vertical-align: top;\n",
           "    }\n",
           "\n",
           "    .dataframe thead th {\n",
           "        text-align: right;\n",
           "    }\n",
           "</style>\n",
           "<table border=\"1\" class=\"dataframe\">\n",
           "  <thead>\n",
           "    <tr style=\"text-align: right;\">\n",
           "      <th></th>\n",
           "      <th>a</th>\n",
           "      <th>b</th>\n",
           "      <th>label</th>\n",
           "    </tr>\n",
           "  </thead>\n",
           "  <tbody>\n",
           "    <tr>\n",
           "      <th>0</th>\n",
           "      <td>-3.591782</td>\n",
           "      <td>3.612599</td>\n",
           "      <td>1</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>1</th>\n",
           "      <td>6.580586</td>\n",
           "      <td>-2.105557</td>\n",
           "      <td>1</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>2</th>\n",
           "      <td>-0.670938</td>\n",
           "      <td>-5.905074</td>\n",
           "      <td>1</td>\n",
           "    </tr>\n",
           "  </tbody>\n",
           "</table>\n",
           "</div>"
          ],
          "text/plain": [
           "          a         b  label\n",
           "0 -3.591782  3.612599      1\n",
           "1  6.580586 -2.105557      1\n",
           "2 -0.670938 -5.905074      1"
          ]
         },
         "execution_count": 165,
         "metadata": {},
         "output_type": "execute_result"
        }
       ],
       "source": [
        "df = pd.read_csv(\"2d_points.csv\")\n",
        "df.head(3)"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 285,
       "metadata": {},
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": [
           "<Figure size 360x360 with 1 Axes>"
          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "xv = df[\"a\"]\n",
        "yv = df[\"b\"]\n",
        "\n",
        "colors = [\"rg\"[i] for i in df[\"label\"]]\n",
        "plt.figure(figsize=(5, 5))\n",
        "plt.xlim([-8, 8])\n",
        "plt.ylim([-8, 8])\n",
        "plt.scatter(xv, yv, color=colors, marker=\".\");"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "In this case the decision line is curved and is looks like a circle. A hand-crafted classifier could classify new points based on their distance to the center.\n",
        "\n",
        "\n",
        "It should be clear that a linear classifier is not suitable for this problem !\n",
        "\n",
        "### Example for feature engineering\n",
        "\n",
        "To improve ML performance we can try to enhance / transform a given feature-set by transformations. This process is called **feature engineering**.\n",
        "\n",
        "In the previous example we see that the distance of the origin of a point could be used to implement a classifier.\n",
        "\n",
        "Computing the distance of a point to the origin (0, 0) using the euclidian formula includes terms $x^2$ and $y^2$. \n",
        "\n",
        "Let us create a scatter plot for this transformation:"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 286,
       "metadata": {},
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": [
           "<Figure size 432x288 with 1 Axes>"
          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "plt.scatter(xv ** 2, yv ** 2, color=colors, marker='.');"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "As you can see both sets can be separated by a line now !"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "### Another example for feature engineering\n",
        "\n",
        "**COMMENT UWE: is this section too much ?**"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "The so called \"xor-problem\" is a typical benchmark problem for machine learning. The following example illustrates this problem:"
       ]
      },
      {
       "cell_type": "code",
       "execution_count": 370,
       "metadata": {},
       "outputs": [
        {
         "data": {
          "text/html": [
           "<div>\n",
           "<style scoped>\n",
           "    .dataframe tbody tr th:only-of-type {\n",
           "        vertical-align: middle;\n",
           "    }\n",
           "\n",
           "    .dataframe tbody tr th {\n",
           "        vertical-align: top;\n",
           "    }\n",
           "\n",
           "    .dataframe thead th {\n",
           "        text-align: right;\n",
           "    }\n",
           "</style>\n",
           "<table border=\"1\" class=\"dataframe\">\n",
           "  <thead>\n",
           "    <tr style=\"text-align: right;\">\n",
           "      <th></th>\n",
           "      <th>x</th>\n",
           "      <th>y</th>\n",
           "      <th>label</th>\n",
           "    </tr>\n",
           "  </thead>\n",
           "  <tbody>\n",
           "    <tr>\n",
           "      <th>0</th>\n",
           "      <td>-1.539782</td>\n",
           "      <td>0.950822</td>\n",
           "      <td>False</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>1</th>\n",
           "      <td>0.436266</td>\n",
           "      <td>-1.768324</td>\n",
           "      <td>False</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>2</th>\n",
           "      <td>-1.466436</td>\n",
           "      <td>1.391890</td>\n",
           "      <td>False</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>3</th>\n",
           "      <td>-1.037642</td>\n",
           "      <td>-0.953587</td>\n",
           "      <td>True</td>\n",
           "    </tr>\n",
           "    <tr>\n",
           "      <th>4</th>\n",
           "      <td>-0.691444</td>\n",
           "      <td>-0.219826</td>\n",
           "      <td>True</td>\n",
           "    </tr>\n",
           "  </tbody>\n",
           "</table>\n",
           "</div>"
          ],
          "text/plain": [
           "          x         y  label\n",
           "0 -1.539782  0.950822  False\n",
           "1  0.436266 -1.768324  False\n",
           "2 -1.466436  1.391890  False\n",
           "3 -1.037642 -0.953587   True\n",
           "4 -0.691444 -0.219826   True"
          ]
         },
         "execution_count": 370,
         "metadata": {},
         "output_type": "execute_result"
        }
       ],
       "source": [
        "xor = pd.read_csv(\"xor.csv\")\n",
        "xor.head()"
       ]