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    {
     "cells": [
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "# Chapter 2: Classification"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
    
        "As we have learned in the previous chapter *classification* belongs to the field of *supervised learning*. In such problems the aim is to predict a category. Such categories can be \n",
    
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        "\n",
        "- ok/not ok\n",
        "- good / bad / dont't know\n",
        "- digit 0 ... / digit 9\n",
        "- etc \n",
        "\n",
    
        "In this chapter we introduce the core concepts of classification."
    
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       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "## How could we  build  a simple classifier  ?"
       ]
      },
      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "## Geometrical interpretation of feature vectors\n",
        "\n",
    
        "\n",
        "If you take the values of an input-feature vector you can imagine it as a point in a d-dimensional space.\n",
    
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        "\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",
    
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        "\n",
        ""
    
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       ]
      },
      {
       "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 the points in green or red to indicate the according classes:"
    
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       ]
      },
      {
       "cell_type": "code",
    
       "execution_count": 2,
    
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       "metadata": {},
       "outputs": [
        {
         "data": {
    
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\n",
 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          "text/plain": [
    
           "<matplotlib.figure.Figure at 0x7ffb463d2a90>"
    
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          ]
         },
         "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": [
    
        "This plot tells us that:\n",
        "1. The two features lack information for a 100% separation of the classes. \n",
    
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        "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": [
    
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        "Now we can see how additional features can support (improve?) classification. We add the `darkness` feature as the third dimension.\n",
        ""
    
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       ]
      },
      {
       "cell_type": "code",
    
       "execution_count": 3,
    
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       "metadata": {},
       "outputs": [
        {
         "data": {
    
          "image/png": 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\n",
 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          "text/plain": [
    
           "<matplotlib.figure.Figure at 0x7ffb051510b8>"
    
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          ]
         },
         "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 and we don't see the effects of the third feature.\n",
    
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        "\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": [
    
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        "If we look at the beer example, we can assume that the person who rated tbe beers has preferences like, \"I don't like high alcohol content\", \"I like fruity beer\", etc."
    
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       ]
      },
      {
       "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",
    
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       "execution_count": 15,
    
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       "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"
          ]
         },
    
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         "execution_count": 15,
    
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         "metadata": {},
         "output_type": "execute_result"
        }
       ],
       "source": [
    
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        "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",
    
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        "beer_data.describe()"
       ]
      },
      {
       "cell_type": "code",
    
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       "execution_count": null,
    
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       "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",
    
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       "execution_count": null,
    
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       "metadata": {},
       "outputs": [
        {
         "data": {
    
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          "image/png": 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=\n",
    
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          "text/plain": [
    
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           "<Figure size 432x288 with 1 Axes>"
    
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          ]
         },
         "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",
    
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        "plt.hist(scores_good,  bins=25, color=\"blue\", alpha=.5) # alpha makes bars translucent\n",
    
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        "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."
       ]
      },
    
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      {
       "cell_type": "code",
       "execution_count": 19,
       "metadata": {},
       "outputs": [
        {
         "name": "stdout",
         "output_type": "stream",
         "text": [
          "not yummuy\n",
          "yummy\n"
         ]
        }
       ],
       "source": [
        "def classify(beer_feature):\n",
        "    scores =( -0.1 * beer_feature[\"alcohol_content\"] + 3 * beer_feature[\"bitterness\"] \n",
        "             + 0.8 * beer_feature[\"darkness\"] + 1.8 * beer_feature[\"fruitiness\"])\n",
        "    if scores > 3.5:\n",
        "        return \"yummy\"\n",
        "    else:\n",
        "        return \"not yummuy\"\n",
        "    \n",
        "print(classify(beer_data.iloc[0]))\n",
        "print(classify(beer_data.iloc[1]))"
       ]
      },
    
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      {
       "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."
       ]
      },
    
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      {
       "cell_type": "markdown",
       "metadata": {},
       "source": [
        "## Exercise section 1\n",
        "\n",
        "Modify the weights in the beer classifiers and check if you can improve separation in the histogram.\n",
        "\n",
        "Try weights  `[-0.05837955,  3.69479038,  0.6666397 ,  1.62751838]` in the beer classifier. These are the weights the `LogisticRegression` classifier in the previous script computed.\n"
       ]
      },
    
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      {
       "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",
    
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       "execution_count": null,
    
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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": [
    
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           "<Figure size 432x288 with 1 Axes>"
    
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          ]
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ],
       "source": [
        "xv = beer_data[\"alcohol_content\"]\n",
        "yv = beer_data[\"bitterness\"]\n",
        "\n",
    
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        "colors = [\"rb\"[i] for i in beer_data[\"is_yummy\"]]\n",
    
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        "\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",
    
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       "execution_count": null,
    
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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": [
    
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           "<Figure size 1440x504 with 2 Axes>"
    
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          ]
         },
         "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",
    
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        "colors = [\"rb\"[i] for i in beer_data[\"is_yummy\"]]\n",
    
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        "\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": [
    
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        "###### Decision surfaces\n",
        "\n",
        "The concept of decision surfaces is crucial in classification. \n",
    
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        "\n",
    
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        "Lets start with an easy to visualize example 2D:\n",
        "\n",
        "For a weighted sum for two features `x` and `y` the equation\n",
    
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        "\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 opposite sides of this line. Such a classifier thus determines a line which separates the feature space in two parts according to the two classes."
    
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       ]
      },
      {
       "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",
    
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       "execution_count": null,
    
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       "metadata": {},
       "outputs": [
        {
         "data": {
    
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          "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",
    
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          "text/plain": [
    
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           "<Figure size 432x288 with 1 Axes>"
    
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          ]
         },
         "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",
    
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        "plt.scatter(above_points[:, 0], above_points[:, 1], c=\"b\", marker=\".\", label=\"above\")\n",
    
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        "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",
    
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        ""
    
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       ]
      },
      {
       "cell_type": "code",
    
       "execution_count": 10,
    
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       "metadata": {},
       "outputs": [
        {
         "data": {
    
          "image/png": 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\n",
 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          "text/plain": [
    
           "<matplotlib.figure.Figure at 0x7ffb04e6ab38>"
    
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          ]
         },
         "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": [
        "### 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 of generality.\n",
    
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        "\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",
    
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       "execution_count": 23,
    
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       "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"
          ]
         },
    
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         "execution_count": 23,
    
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         "metadata": {},
         "output_type": "execute_result"
        }
       ],
       "source": [
        "df = pd.read_csv(\"2d_points.csv\")\n",
        "df.head(3)"
       ]
      },
      {
       "cell_type": "code",
    
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       "execution_count": 24,
    
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       "metadata": {},
       "outputs": [
        {
         "data": {
    
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          "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 = df[\"a\"]\n",
        "yv = df[\"b\"]\n",
        "\n",
    
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        "colors = [\"rb\"[i] for i in df[\"label\"]]\n",
    
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        "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",
    
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       "execution_count": 25,
    
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       "metadata": {},
       "outputs": [
        {
         "data": {
    
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          "image/png": 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\n",
    
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          "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": [
    
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        "### Another example for feature engineering"
    
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       ]
      },
      {
       "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",
    
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       "execution_count": 26,
    
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       "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"
          ]
         },
    
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         "execution_count": 26,
    
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         "metadata": {},
         "output_type": "execute_result"
        }
       ],
       "source": [
        "xor = pd.read_csv(\"xor.csv\")\n",
        "xor.head()"
       ]
      },
      {
       "cell_type": "code",