{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.svm import LinearSVC, SVC\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Daten einlesen "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "iris = pd.read_csv('data/iris.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir beschränken uns in diesem Beispiel auf die beiden Klassen `setosa` und `versicolor`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = iris[iris['species'] != 'virginica']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ausserdem verwenden wir nur die Attribute `sepal_length` und `sepal_width`, d.h. wir bewegen uns im 2-dimensionalen Raum. Alles darüber würde schwieriger mit der Darstellung werden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[['sepal_length','sepal_width']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = df['species']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Erstellen des SVM Modells\n",
    "\n",
    "Wir benutzen hier den SVC Classifier. Standardmäßig benutzt der eine nicht-lineare Ebene.\n",
    "\n",
    "Da wir uns aber in diesem Beispiel auf _lineare Modelle_ konzentrieren, erzeugen wir mit dem Parameter `kernel='linear'` eine lineare SVM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = SVC(kernel='linear')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir trainieren das Modell auf unserem Datensatz:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "m.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das Modell bietet die Möglichkeit an die Koeffizienten und den `intercept` zu gelangen.\n",
    "\n",
    "Daraus kann man die eigentliche Ebene wieder berechnen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(f\"Intercept: {m.intercept_}\")\n",
    "print(f\"Gewichte: {m.coef_}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir rekonstruieren die Ebene und erzeugen in xs, ys (x,y)-Werte zum Plotten der Ebene:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = m.coef_[0]\n",
    "a = -w[0] / w[1]\n",
    "xs = np.linspace(4, 7)\n",
    "ys = a * xs - (m.intercept_[0]) / w[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zum Abschluss plotten wir die Daten und die Ebenen-Werte (x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "colors = y.map({'setosa': 'r', 'versicolor': 'b'})\n",
    "plt.plot(xs, ys)\n",
    "plt.scatter(X['sepal_length'], X['sepal_width'], c = colors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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