252 lines
10 KiB
Plaintext
252 lines
10 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Maschinelles Lernen (ML) - Übung 3\n",
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"# Perzeptronen und mehrschichtige Perzeptronen\n",
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"# 3.2 Loss Function, Backpropagation und Gradient Descent\n",
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"\n",
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"In dieser Aufgabe wird die Aktualisierungsfunktion (Lernalgorithmus) aus der Vorlesung durch das Verfahren der Fehlerrückführung (engl. backpropagation) und des Gradientenverfahrens (engl. gradient descent) ersetzt.\n",
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"\n",
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"In dieser Übung sollen Sie das bereits ausgearbeitete Perzeptron anpassen."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 49,
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"metadata": {},
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"outputs": [],
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"source": [
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"# matplotlib: Modul zum Plotten von Daten\n",
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"from matplotlib import pyplot as plt \n",
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"\n",
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"# numpy: Mathematikbibliothek\n",
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"import numpy as np \n",
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"import pandas as pd\n",
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"import time"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Aufgabe 1:** Ersetzen Sie die bisherige Aktivierung in der Methode *predict* durch die Sigmoidfunktion.\n",
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" "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Aufgabe 2:** Implementieren Sie das beschriebene Gradientenlernverfahren mit Backpropagation in die Methode *fit*."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Aufgabe 3:** Schauen Sie sich die Ausgabe des Perzeptrons (perceptron.predict(.)) auf einem der bisher verwendeten Datensätze (z.B. *AND*, Iris) an. Was fällt gegenüber einem Perzeptron mit der Signum-Funktion als Aktivierung auf? Was bedeutet das für den Einsatz als binärer Klassifikator?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 50,
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"metadata": {},
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"outputs": [],
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"source": [
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"class Perceptron(object):\n",
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" def __init__(self, number_of_inputs, epochs, eta):\n",
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" \"\"\"\n",
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" Beispielaufruf des Konstruktors:\n",
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" >>> Perceptron(2, 100, 0.1)\n",
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" \"\"\"\n",
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" ### Dein Code kommt hierhin:\n",
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" self.weights = np.zeros(number_of_inputs+1)\n",
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" self.epochs = epochs\n",
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" self.eta = eta\n",
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" self.bias = 0\n",
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" ##########################\n",
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" pass\n",
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" \n",
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" def predict(self, inputs):\n",
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" \"\"\"\n",
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" Beispiel des Funktionsaufrufes:\n",
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" >>> inputs = np.array([0, 1])\n",
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" >>> h = perceptron.predict(inputs) \n",
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" \"\"\"\n",
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" # Dein Code kommt hierhin: \n",
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" z = self.bias * self.weights[0]\n",
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" z += np.dot(inputs, self.weights[1:])\n",
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" return 1/(1 + np.exp(-z))\n",
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" ##########################\n",
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" pass\n",
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"\n",
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" def fit(self, training_inputs, labels):\n",
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" \"\"\"\n",
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" Beispiel des Funktionsaufrufs:\n",
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" >>> perceptron.fit(train_input, labels)\n",
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" \"\"\"\n",
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" # Dein Code kommt hierhin:\n",
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" for e in range(self.epochs):\n",
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" L_old=0\n",
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" h_old=0\n",
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" z_old=-1\n",
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" weights_old=-np.ones(len(self.weights))\n",
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" for xi, target in zip(training_inputs, labels):\n",
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" h = self.predict(xi)\n",
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" h_diff = h - h_old\n",
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" L = (target - h) ** 2\n",
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" L_diff = L - L_old\n",
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" z = self.bias * self.weights[0] + np.dot(xi, self.weights[1:])\n",
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" z_diff = z - z_old\n",
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" weights_diff = self.weights - weights_old\n",
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" #Ableitung\n",
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" deriv_z = np.where(weights_diff!=0, z_diff/weights_diff, 0)\n",
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" deriv_h = h_diff/z_diff if z_diff!=0 else 0\n",
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" deriv_L = L_diff/h_diff if h_diff!=0 else 0\n",
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" deriv = deriv_L * deriv_h * deriv_z\n",
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" delta_weights = self.eta * deriv\n",
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" weights_old = self.weights\n",
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" L_old = L\n",
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" h_old = h\n",
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" z_old = z\n",
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" self.weights -= delta_weights\n",
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" ##########################\n",
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" pass\n",
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" \n",
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" def status(self):\n",
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" \"\"\"\n",
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" Die Methode status(...) gibt die aktuellen Gewichte aus.\n",
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"\n",
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" Beispiel des Funktionsaufrufes und der Ausgabe:\n",
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" >>> perceptron.status()\n",
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" Perceptron weights: [0. 1. 1.]\n",
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" \"\"\"\n",
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" print(\"Perceptron weights: \", self.weights)\n",
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" \n",
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" def getWeights(self):\n",
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" return self.weights"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 51,
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": [
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"[3.0643397 3.0643397 3.0643397]\n"
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]
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},
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{
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"output_type": "error",
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"ename": "NameError",
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"evalue": "name 'train_input_AND' is not defined",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-51-fc9213e067f7>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 22\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 23\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0max\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 24\u001b[0;31m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrain_input_AND\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlabels_AND\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m,\u001b[0m \u001b[0mtrain_input_AND\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlabels_AND\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 25\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrain_input_AND\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlabels_AND\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m,\u001b[0m \u001b[0mtrain_input_AND\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlabels_AND\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 26\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_AND\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my_AND\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;31mNameError\u001b[0m: name 'train_input_AND' is not defined"
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]
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}
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],
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"source": [
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"# AND-Datensatz\n",
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"train_input = np.array([\n",
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" [0, 0],\n",
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" [0, 1],\n",
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" [1, 0],\n",
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" [1, 1]\n",
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" ])\n",
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"\n",
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"labels_AND = np.array([0, 0, 0, 1])\n",
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"\n",
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"perceptron_AND = Perceptron(2,100,0.1)\n",
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"perceptron_AND.fit(train_input,labels_AND)\n",
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"\n",
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"# Geradengleichung berechnen und plotten\n",
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"weights = perceptron_AND.getWeights()\n",
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"print(weights)\n",
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"\n",
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"slope = -weights[1]/weights[2]\n",
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"offset = -weights[0]/weights[2]\n",
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"x_AND = np.linspace(0,1)\n",
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"y_AND = slope * x_AND + offset\n",
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"\n",
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"fig, ax = plt.subplots()\n",
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"ax.scatter(train_input_AND[(labels_AND==-1),0] , train_input_AND[(labels_AND==-1),1])\n",
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"ax.scatter(train_input_AND[(labels_AND==1),0] , train_input_AND[(labels_AND==1),1])\n",
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"plt.plot(x_AND,y_AND)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Beispiel mit OR\n",
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"labels_OR = np.array([0, 1, 1, 1])\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Hier wird der Iris-Datensatz geladen und vorbereitet (siehe Übung 2)\n",
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"\n",
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"# Datensatz laden\n",
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"names = [\"sepal-length\", \"sepal-width\", \"petal-length\", \"petal-width\", \"class\"]\n",
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"iris_data = pd.read_csv(\"iris.csv\", names = names)\n",
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"\n",
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"# Klassen auswählen (Bei Bedarf ändern)\n",
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"iris_data = iris_data.loc[lambda x: x['class'] != 'Iris-setosa']\n",
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"\n",
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"# Merkmale auswählen (Bei Bedarf ändern)\n",
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"iris_features = ['petal-length', 'petal-width']\n",
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"X = iris_data[iris_features]\n",
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"# Pandas-Datenformat in reine Liste umwandeln\n",
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"X = X.values\n",
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"\n",
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"# Label vorbereiten\n",
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"from sklearn.preprocessing import LabelEncoder\n",
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"lb_make = LabelEncoder()\n",
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"iris_data[\"class_code\"] = lb_make.fit_transform(iris_data[\"class\"])\n",
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"y = iris_data.class_code\n",
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"y = y.values\n",
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" \n",
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"# Trainings- und Testdatensplit\n",
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"from sklearn.model_selection import train_test_split\n",
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"X_train, X_test, y_train, y_test = (\n",
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" train_test_split(X, y, test_size=.2, random_state=np.random.seed(42)))"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.6-final"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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} |