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ML_U3_1_Perceptron.ipynb
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ML_U3_1_Perceptron.ipynb
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{
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"cells": [
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{
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"attachments": {},
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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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"## 3.1 Das einfache Perzeptron als linearer Klassifikator\n",
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"\n",
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"In dieser Übung wird ein einfaches Perzeptron (engl. perceptron) programmiert, trainiert und als linearer Klassifikator eingesetzt.\n",
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"\n",
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"\n",
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"\n",
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"Weitere Informationen zur Wirkweise des einfachen Perzeptrons sind im PDF-Handout für diese Übung zu finden."
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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:** In dieser Übung sollen Sie ein Perzeptron objektorientiert erstellen. Dazu ist bereits eine vorstrukturierte Klasse *Perceptron* mit den Methoden *_init_* zur Initialisierung des Perzeptrons (z.B. Gewichte, Lernrate), *predict* zur Klassifizierung eines Datenpunktes und *fit* zum Trainieren des Perzeptrons vorbereitet.\t\tVervollständigen Sie diese Methoden."
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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": null,
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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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"# numpy: Mathematikbibliothek\n",
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"import numpy as np \n",
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"import pandas as pd"
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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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"#### Hilfen für die Klasse Perzeptron\n",
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"\n",
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"##### Allgemein\n",
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"Verwendete Variblenbezeichnungen:\n",
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"- inputs $\\hat{=} \\textrm{ } \\lbrace x_1, \\ldots x_n \\rbrace$; Sollte als Numpy Array definiert werden.\n",
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"- eta $\\hat{=} \\textrm{ } \\eta$\n",
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"\n",
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"##### Methode _init_(self, number_of_inputs, epochs, learning_rate):\n",
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"In Python entspricht \\_\\_init\\_\\_ dem Konstruktor. Die \\_\\_init\\_\\_() Methode initialisiert die Klasse Perceptron. Definiere und initialisiere hier die folgenden Variablen: \n",
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"- die zu lernenden Gewichte $\\textbf{w}$,\n",
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"- die maximale Anzahl der Epochen (Lernzyklen), die der Lernalgorithmus durchlaufen darf und\n",
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"- die Lernrate, die den Grad der Veränderung der Gewichte bei jedem Schritt durch die Trainingsdaten bestimmt.\n",
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"\n",
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"##### Methode predict(self, inputs):\n",
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"Die predict(...) Methode enthält die Aktivierungsfunktion h(z) (hier: die Signum-Funktion):\n",
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"\n",
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"\\begin{equation}\n",
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" h(z) =\n",
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" \\begin{cases}\n",
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"\t\t\t-1 \\textrm{ falls } z < 0 \\textrm{,} \\\\\t\n",
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"\t\t\t0 \\textrm{ falls } z = 0 \\textrm{,} \\\\\t\n",
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"\t\t\t1 \\textrm{ falls } z > 0 \\textrm{.} \\\\\n",
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"\t\t\\end{cases}\n",
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"\\end{equation} \n",
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"Die Eingabe der Methode (inputs) sollte als NumPy Array/Vektor definiert werden.\n",
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"\n",
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"##### Methode fit(self, training_inputs, labels):\n",
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"Die Methode fit(...) benötigt zwei Argumente:\n",
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"- training_inputs ist eine Liste von numpy-Vektoren und\n",
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"- labels ist ein Array von erwarteten Ausgabewerten.\n",
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" \n",
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"Beim Trainieren des Perzeptrons soll folgende Funktionalität implementiert werden: \n",
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"Ein einzelner Trainingsdatenpunkt wird betrachtet und eine Vorhersage (Methode predict) getroffen. Auf Basis der Vorhersage $\\hat{y}$ werden die Gewichte nach folgender Regel aktualisiert (siehe auch Handout):\n",
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"\\begin{equation}\n",
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"\\textbf{w} \\leftarrow \\textbf{w} + \\eta \\cdot \\left( y - \\hat{y} \\right) \\cdot \\textbf{x} \\textrm{.} \n",
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"\\end{equation}\n",
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"\n",
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"Der Block aus predict und update der Gewichte wird solange iterativ ausgeführt bis die maximale Anzahl der Epochen erreicht ist (oder optional bis die Fehlerfunktion konvergiert ist). \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": null,
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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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" \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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" \n",
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" # Dein Code kommt hierhin: \n",
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" \n",
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" ##########################\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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" \n",
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" # Dein Code kommt hierhin:\n",
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"\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": "markdown",
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"metadata": {},
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"source": [
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"**Aufgabe 2:** Wenden Sie das implementierte Perzeptron auf das `AND`, `OR` und `XOR` Problem im zweidimensionalen Raum an. Berechnen Sie anhand der gelernten Gewichte $\\mathbf{w}$ des Perzeptrons die Geradengleichung der Diskriminanzgeraden und plotten Sie diese zusammen mit den Datenpunkten des jeweiligen Problems."
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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": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Beispiel mit AND\n",
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"train_input_AND = 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([-1, -1, -1, 1])\n",
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"\n",
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"# Dein Code kommt hier hin:\n",
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"# Perceptron anlegen und trainieren\n",
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"\n",
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"\n",
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"# Geradengleichung berechnen und plotten\n",
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"\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": null,
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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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"train_input_OR = 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_OR = np.array([-1, 1, 1, 1])\n",
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"\n",
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"# Dein Code kommt hier hin:\n",
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"# Perceptron anlegen und trainieren\n",
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"\n",
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"\n",
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"# Geradengleichung berechnen und plotten\n",
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"\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": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Beispiel mit XOR\n",
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"train_input_XOR = 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_XOR = np.array([-1, 1, 1, -1])\n",
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"\n",
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"# Dein Code kommt hier hin:\n",
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"# Perceptron anlegen und trainieren\n",
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"\n",
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"\n",
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"# Geradengleichung berechnen und plotten"
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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:** Warum wird im Perzeptron der Bias $x_0$ benötigt beziehungsweise wieso werden bei $n$ Merkmalen ($x_1, \\ldots, x_n$), $n+1$ Gewichte ($w_0, \\ldots, w_n$) benötigt? "
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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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"Antwort:"
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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 4:** Wenden Sie das Perzeptron auf das Problem der Banknotenklassifizierung der letzten Übung an. Wählen und berechnen Sie dafür wieder zwei geeignete Merkmale der Trainingsbanknoten (Momentenberechnung auf den Farbkanälen mit `banknotes[i].compute_feature(moment, color)`). Mit welcher Genauigkeit (engl. *accuracy*) werden die Testbanknoten klassifiziert? Wie sind die erreichten Ergebnisse des Perzeptrons im Vergleich zum linearen Klassifikator der letzten Übung zu bewerten?"
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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": null,
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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 letzte Übung)\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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"\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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"# Pandas-Datenformat in reine Liste umwandeln\n",
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"y = y.values\n",
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"# Die Signum-Funktion unseres Perzeptrons benötigt die Label -1, 1\n",
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"y[y==0] = -1\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)))\n",
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"\n",
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"# Scatterplot der ausgewählten Merkmale und Klassen\n",
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"fig, ax = plt.subplots()\n",
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"ax.scatter(X[(y==-1),0] , X[(y==-1),1])\n",
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"ax.scatter(X[(y==1),0] , X[(y==1),1])\n",
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"ax.set(xlabel = iris_features[0], ylabel = iris_features[1])\n",
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"plt.show()"
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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": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Perzeptron auf Iris-Datensatz trainieren und anwenden\n",
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"# Dein Code kommt hierhin:"
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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 5:** Welchen Einfluss haben die Hyperparameter *Epoche* und *Lernrate* auf die Klassifizierung der Banknoten? Lassen sich die vorherigen Ergebnisse noch verbessern?"
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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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"Antwort:"
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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": "3.7.4"
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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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}
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151
iris.csv
Normal file
151
iris.csv
Normal file
@ -0,0 +1,151 @@
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5.1,3.5,1.4,0.2,Iris-setosa
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4.9,3.0,1.4,0.2,Iris-setosa
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4.7,3.2,1.3,0.2,Iris-setosa
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4.6,3.1,1.5,0.2,Iris-setosa
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5.0,3.6,1.4,0.2,Iris-setosa
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5.4,3.9,1.7,0.4,Iris-setosa
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|
4.6,3.4,1.4,0.3,Iris-setosa
|
||||||
|
5.0,3.4,1.5,0.2,Iris-setosa
|
||||||
|
4.4,2.9,1.4,0.2,Iris-setosa
|
||||||
|
4.9,3.1,1.5,0.1,Iris-setosa
|
||||||
|
5.4,3.7,1.5,0.2,Iris-setosa
|
||||||
|
4.8,3.4,1.6,0.2,Iris-setosa
|
||||||
|
4.8,3.0,1.4,0.1,Iris-setosa
|
||||||
|
4.3,3.0,1.1,0.1,Iris-setosa
|
||||||
|
5.8,4.0,1.2,0.2,Iris-setosa
|
||||||
|
5.7,4.4,1.5,0.4,Iris-setosa
|
||||||
|
5.4,3.9,1.3,0.4,Iris-setosa
|
||||||
|
5.1,3.5,1.4,0.3,Iris-setosa
|
||||||
|
5.7,3.8,1.7,0.3,Iris-setosa
|
||||||
|
5.1,3.8,1.5,0.3,Iris-setosa
|
||||||
|
5.4,3.4,1.7,0.2,Iris-setosa
|
||||||
|
5.1,3.7,1.5,0.4,Iris-setosa
|
||||||
|
4.6,3.6,1.0,0.2,Iris-setosa
|
||||||
|
5.1,3.3,1.7,0.5,Iris-setosa
|
||||||
|
4.8,3.4,1.9,0.2,Iris-setosa
|
||||||
|
5.0,3.0,1.6,0.2,Iris-setosa
|
||||||
|
5.0,3.4,1.6,0.4,Iris-setosa
|
||||||
|
5.2,3.5,1.5,0.2,Iris-setosa
|
||||||
|
5.2,3.4,1.4,0.2,Iris-setosa
|
||||||
|
4.7,3.2,1.6,0.2,Iris-setosa
|
||||||
|
4.8,3.1,1.6,0.2,Iris-setosa
|
||||||
|
5.4,3.4,1.5,0.4,Iris-setosa
|
||||||
|
5.2,4.1,1.5,0.1,Iris-setosa
|
||||||
|
5.5,4.2,1.4,0.2,Iris-setosa
|
||||||
|
4.9,3.1,1.5,0.1,Iris-setosa
|
||||||
|
5.0,3.2,1.2,0.2,Iris-setosa
|
||||||
|
5.5,3.5,1.3,0.2,Iris-setosa
|
||||||
|
4.9,3.1,1.5,0.1,Iris-setosa
|
||||||
|
4.4,3.0,1.3,0.2,Iris-setosa
|
||||||
|
5.1,3.4,1.5,0.2,Iris-setosa
|
||||||
|
5.0,3.5,1.3,0.3,Iris-setosa
|
||||||
|
4.5,2.3,1.3,0.3,Iris-setosa
|
||||||
|
4.4,3.2,1.3,0.2,Iris-setosa
|
||||||
|
5.0,3.5,1.6,0.6,Iris-setosa
|
||||||
|
5.1,3.8,1.9,0.4,Iris-setosa
|
||||||
|
4.8,3.0,1.4,0.3,Iris-setosa
|
||||||
|
5.1,3.8,1.6,0.2,Iris-setosa
|
||||||
|
4.6,3.2,1.4,0.2,Iris-setosa
|
||||||
|
5.3,3.7,1.5,0.2,Iris-setosa
|
||||||
|
5.0,3.3,1.4,0.2,Iris-setosa
|
||||||
|
7.0,3.2,4.7,1.4,Iris-versicolor
|
||||||
|
6.4,3.2,4.5,1.5,Iris-versicolor
|
||||||
|
6.9,3.1,4.9,1.5,Iris-versicolor
|
||||||
|
5.5,2.3,4.0,1.3,Iris-versicolor
|
||||||
|
6.5,2.8,4.6,1.5,Iris-versicolor
|
||||||
|
5.7,2.8,4.5,1.3,Iris-versicolor
|
||||||
|
6.3,3.3,4.7,1.6,Iris-versicolor
|
||||||
|
4.9,2.4,3.3,1.0,Iris-versicolor
|
||||||
|
6.6,2.9,4.6,1.3,Iris-versicolor
|
||||||
|
5.2,2.7,3.9,1.4,Iris-versicolor
|
||||||
|
5.0,2.0,3.5,1.0,Iris-versicolor
|
||||||
|
5.9,3.0,4.2,1.5,Iris-versicolor
|
||||||
|
6.0,2.2,4.0,1.0,Iris-versicolor
|
||||||
|
6.1,2.9,4.7,1.4,Iris-versicolor
|
||||||
|
5.6,2.9,3.6,1.3,Iris-versicolor
|
||||||
|
6.7,3.1,4.4,1.4,Iris-versicolor
|
||||||
|
5.6,3.0,4.5,1.5,Iris-versicolor
|
||||||
|
5.8,2.7,4.1,1.0,Iris-versicolor
|
||||||
|
6.2,2.2,4.5,1.5,Iris-versicolor
|
||||||
|
5.6,2.5,3.9,1.1,Iris-versicolor
|
||||||
|
5.9,3.2,4.8,1.8,Iris-versicolor
|
||||||
|
6.1,2.8,4.0,1.3,Iris-versicolor
|
||||||
|
6.3,2.5,4.9,1.5,Iris-versicolor
|
||||||
|
6.1,2.8,4.7,1.2,Iris-versicolor
|
||||||
|
6.4,2.9,4.3,1.3,Iris-versicolor
|
||||||
|
6.6,3.0,4.4,1.4,Iris-versicolor
|
||||||
|
6.8,2.8,4.8,1.4,Iris-versicolor
|
||||||
|
6.7,3.0,5.0,1.7,Iris-versicolor
|
||||||
|
6.0,2.9,4.5,1.5,Iris-versicolor
|
||||||
|
5.7,2.6,3.5,1.0,Iris-versicolor
|
||||||
|
5.5,2.4,3.8,1.1,Iris-versicolor
|
||||||
|
5.5,2.4,3.7,1.0,Iris-versicolor
|
||||||
|
5.8,2.7,3.9,1.2,Iris-versicolor
|
||||||
|
6.0,2.7,5.1,1.6,Iris-versicolor
|
||||||
|
5.4,3.0,4.5,1.5,Iris-versicolor
|
||||||
|
6.0,3.4,4.5,1.6,Iris-versicolor
|
||||||
|
6.7,3.1,4.7,1.5,Iris-versicolor
|
||||||
|
6.3,2.3,4.4,1.3,Iris-versicolor
|
||||||
|
5.6,3.0,4.1,1.3,Iris-versicolor
|
||||||
|
5.5,2.5,4.0,1.3,Iris-versicolor
|
||||||
|
5.5,2.6,4.4,1.2,Iris-versicolor
|
||||||
|
6.1,3.0,4.6,1.4,Iris-versicolor
|
||||||
|
5.8,2.6,4.0,1.2,Iris-versicolor
|
||||||
|
5.0,2.3,3.3,1.0,Iris-versicolor
|
||||||
|
5.6,2.7,4.2,1.3,Iris-versicolor
|
||||||
|
5.7,3.0,4.2,1.2,Iris-versicolor
|
||||||
|
5.7,2.9,4.2,1.3,Iris-versicolor
|
||||||
|
6.2,2.9,4.3,1.3,Iris-versicolor
|
||||||
|
5.1,2.5,3.0,1.1,Iris-versicolor
|
||||||
|
5.7,2.8,4.1,1.3,Iris-versicolor
|
||||||
|
6.3,3.3,6.0,2.5,Iris-virginica
|
||||||
|
5.8,2.7,5.1,1.9,Iris-virginica
|
||||||
|
7.1,3.0,5.9,2.1,Iris-virginica
|
||||||
|
6.3,2.9,5.6,1.8,Iris-virginica
|
||||||
|
6.5,3.0,5.8,2.2,Iris-virginica
|
||||||
|
7.6,3.0,6.6,2.1,Iris-virginica
|
||||||
|
4.9,2.5,4.5,1.7,Iris-virginica
|
||||||
|
7.3,2.9,6.3,1.8,Iris-virginica
|
||||||
|
6.7,2.5,5.8,1.8,Iris-virginica
|
||||||
|
7.2,3.6,6.1,2.5,Iris-virginica
|
||||||
|
6.5,3.2,5.1,2.0,Iris-virginica
|
||||||
|
6.4,2.7,5.3,1.9,Iris-virginica
|
||||||
|
6.8,3.0,5.5,2.1,Iris-virginica
|
||||||
|
5.7,2.5,5.0,2.0,Iris-virginica
|
||||||
|
5.8,2.8,5.1,2.4,Iris-virginica
|
||||||
|
6.4,3.2,5.3,2.3,Iris-virginica
|
||||||
|
6.5,3.0,5.5,1.8,Iris-virginica
|
||||||
|
7.7,3.8,6.7,2.2,Iris-virginica
|
||||||
|
7.7,2.6,6.9,2.3,Iris-virginica
|
||||||
|
6.0,2.2,5.0,1.5,Iris-virginica
|
||||||
|
6.9,3.2,5.7,2.3,Iris-virginica
|
||||||
|
5.6,2.8,4.9,2.0,Iris-virginica
|
||||||
|
7.7,2.8,6.7,2.0,Iris-virginica
|
||||||
|
6.3,2.7,4.9,1.8,Iris-virginica
|
||||||
|
6.7,3.3,5.7,2.1,Iris-virginica
|
||||||
|
7.2,3.2,6.0,1.8,Iris-virginica
|
||||||
|
6.2,2.8,4.8,1.8,Iris-virginica
|
||||||
|
6.1,3.0,4.9,1.8,Iris-virginica
|
||||||
|
6.4,2.8,5.6,2.1,Iris-virginica
|
||||||
|
7.2,3.0,5.8,1.6,Iris-virginica
|
||||||
|
7.4,2.8,6.1,1.9,Iris-virginica
|
||||||
|
7.9,3.8,6.4,2.0,Iris-virginica
|
||||||
|
6.4,2.8,5.6,2.2,Iris-virginica
|
||||||
|
6.3,2.8,5.1,1.5,Iris-virginica
|
||||||
|
6.1,2.6,5.6,1.4,Iris-virginica
|
||||||
|
7.7,3.0,6.1,2.3,Iris-virginica
|
||||||
|
6.3,3.4,5.6,2.4,Iris-virginica
|
||||||
|
6.4,3.1,5.5,1.8,Iris-virginica
|
||||||
|
6.0,3.0,4.8,1.8,Iris-virginica
|
||||||
|
6.9,3.1,5.4,2.1,Iris-virginica
|
||||||
|
6.7,3.1,5.6,2.4,Iris-virginica
|
||||||
|
6.9,3.1,5.1,2.3,Iris-virginica
|
||||||
|
5.8,2.7,5.1,1.9,Iris-virginica
|
||||||
|
6.8,3.2,5.9,2.3,Iris-virginica
|
||||||
|
6.7,3.3,5.7,2.5,Iris-virginica
|
||||||
|
6.7,3.0,5.2,2.3,Iris-virginica
|
||||||
|
6.3,2.5,5.0,1.9,Iris-virginica
|
||||||
|
6.5,3.0,5.2,2.0,Iris-virginica
|
||||||
|
6.2,3.4,5.4,2.3,Iris-virginica
|
||||||
|
5.9,3.0,5.1,1.8,Iris-virginica
|
||||||
|
|
||||||
|
Loading…
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Reference in New Issue
Block a user